mm MODERN BUSINESS ARlTHMtliC COMPLETE COURSE FINNEY AND BROWN GIFT OF p.^ MODERN BUSINESS ARITHMETIC COMPLETE COURSE BY HARRY ANSON FINNEY LECTURER IN ACCOUNTING, WALTON SCHOOL OF COMMERCE CHICAGO, ILLINOIS AND JOSEPH CLIFTON BROWN PRESIDENT, STATE NORMAL SCHOOL, ST. CLOUD, MINN. LMMJV. •'':> di^^-j^^ NEW YORK HC )LT AND COMPANY BY HENRY HOLT AND COMPANY PREFACE This book provides a year's work in the arithmetic of modern business. All topics which have no reason for inclusion except tradition have been omitted. Topics which have recently acquired importance because of changes that have been brought about in the organization and conduct of business are included. Among the topics so included are Contract Purchases and Installment Payments, Depreciation, Advertising, Insolvency and Bankruptcy, Comparative Statistics to Promote Buying and Selling Efficiency, Profit and Loss by Departments, Finding the Profit and Loss on Each Sale, Factory Costs, Tabulations for the Sales Manager, and the Income Tax. The illustrations and model forms were chosen with a view to acquainting the student with actual business conditions. The problems were selected from those which actually arise in impor- tant business activities, and the methods of solution are those which are used in business practice. Many of the drill exercises are put into ruled forms such as will be met in the business world; and the student is given practice in the art of presenting business statistics and other material in a neat, concise, and attractive manner. The traditional sequence of topics has been abandoned in some cases in favor of a grouping of topics in which there is a relation of business experience. The necessity for a high degree of accuracy and facility in arithmetical computation has been fully recognized. Abundant material for practice and drill in the fundamental processes is pro- vided. The student is required to check his results at every point in order to secure accuracy; and numerous exercises to be finished within a time limit are included to improve speed in IV PREFACE computation. Since business expediency demands that many- problems shall be solved orally, a large amount of oral work has been included. From the point of view of both material and method this book is based not on theory but on actual business conditions and practices. The material has been successfully subjected to the test of preparing hundreds of students to meet the exacting demands of the business world. The ruled forms and the tabu- lated business statistics so extensively used in the book have demonstrated their effectiveness in developing rapidity, accuracy, and neatness. Many men who are specialists in various business and industrial activities were consulted, and the statements of business customs as well as the tabulation of materials and the arrangement of problems are based on their advice. The authors wish to acknowledge their indebtedness to the numerous teachers, business men, and professional men who have so kindly aided them by offering valuable suggestions and dis- criminating criticisms, and by furnishing materials. They acknowledge especial indebtedness to : Mr. Seymour Walton, Certified Public Accountant, Dean of the Walton School of Com- merce, Chicago, who read several of the chapters, the subject matter of which borders on accountancy; Professor Norris A. Brisco, head of the School of Commerce and of the Departments of Political Economy and Sociology in the University of Iowa and Editor of the Efficiency Society Journal ; Mr. Stanley C. Crafts, Auditor of Customs, Port of Chicago ; Mr. T. H. Fuller, Auditor for Carson, Pirie, Scott & Co., Chicago ; Mr. H. A. Brinkman, Cashier of the Harris Trust and Savings Bank, Chicago ; and Mr. H. V. Church, Principal of the Cicero Township High School, Berwyn, 111. HARRY ANSON FINNEY. JOSEPH CLIFTON BROWN. CONTENTS FUNDAMENTAL PBOC ESSES mAPTEB PAGE I. Addition 2 II. Subtraction 16 III. Multiplication . . .24 IV. Division 39 V. Average 48 VI. Factors and Multiples „ 55 VII. Common Fractions 59 VIII. Decimal Fractions 73 IX. Short Methods Involving Aliquot Parts 85 UNITS OF MEASURE AND THE IB APPLICATIONS X. Denominate Numbers . . .94 XI. The Metric System 103 XII. Practical Business Measurements 112 XIII. Drawings and Graphs 137 PERCENTAGE XIV. Percentage 152 TRADING ACTIVITIES: PROFIT AND LOSS XV. Buying and Selling Merchandise ...... 176 XVI. Commercial Discounts . . 183 XVII. Recording Purchases and Sales ....,, 196 XVIII. Paying for Goods 206 XIX. Collecting Bills 225 XX. Foreign Money and Exchange . 233 XXI. Accounts . 245 XXII. Taking Inventory 249 XXIII. Gross Trading Profit 255 V VI CONTENTS BORROWING AND LOANING CHAPTER TAQK XXIV. Interest 257 XXV. Partial Payments 274 XXVI. Compound Interest 279 XXVII. Savings Banks 282 XXVIII. Contract Purchases and Installment Payments . . . 288 XXIX. Discounting Notes and Other Commercial Paper . . 291 BUSINESS EXPENSES XXX. Wages and Payrolls . 303 XXXI. Postage, Freight, and Express Rates 311 XXXII. Depreciation 323 XXXIII. Advertising 327 XXXIV. Property Insurance 333 XXXV. Taxation 345 XXXVI. The Income Tax 351 XXXVII. Customs Duties 351 BUSINESS ORGANIZATION XXXVIII. Individual Proprietorship .362 XXXIX. Partnership 368 XL. Insolvency and Bankruptcy 378 XLI. Corporations, Stocks, and Bonds 381 TABULATIONS TO PROMOTE EFFICIENT MANAGEMENT XLII. Buying Expenses ; Selling Expenses ; Net Profit . . 398 XLIII. Finding the Profitable Departments 411 XLIV. Finding the Profit or Loss on Each Sale .... 416 XLV. Factory Costs 421 XL VI. Tabulations for the Sales Manager 438 MISCELLANEOUS XL VII. Consignments and Commissions 452 XL VIII. Life Insurance 458 XLIX. Farm Records . 464 APPENDIX .477 INDEX 483 INTRODUCTION To the Student If you expect to succeed in the business world, you should cultivate accuracy, neatness, and speed in all computations. A high degree of accuracy is indispensable. Be very careful about all of your work, and use adequate means of checking your results. Take pride in the appearance of your work. Your papers from day to day should be prepared with ink, because that is the way business records are kept. When ruling is to be done, make the lines fine. Make your figures small and similar to those in the following model : / ^ 3 ¥ S 6 J S f O Work as rapidly as you can without detriment to your accuracy. The material in this book has been prepared with the special purpose of making students accurate, careful, and rapid business workers. FUNDAMENTAL PROCESSES CHAPTER I ADDITION 1. Drill Tables. The following table contains the forty -five combinations of two numbers, each of which is less than ten. Practice until you can state these forty-five sums, without error, in less than twenty-five seconds. Do not repeat the numbers to be added. State results only. 264617472233121 98492769 5 456185 7 1 8 5 4 8 2 3 4 5 2 1 5 9 4 8 4 8 9 5 9 3 4 9 5 7 3 6 9 7 1 6 3 6 1 3 1 5 2 3 5 1 2 4 3 9 7 3 6 7 8 8 7 2 9 8 6 6 8 7 The following group of thirty-six combinations contains all the inversions possible, omitting the pairs of equal numbers. Prac- tice until you can state the sums in any order without hesitation. 4 7 9 2 6 3 6 8 7 4 7 8 3 5 5 1 5 1 1 5 4 1 6 3 7 4 7 8 9 8 9 9 5 6 9 8 1 2 2 4 3 6 7 2 2 4 4 7 9 8 9 3 9 8 6 5 7 5 5 6 8 1 6 2 1 2 3 4 3 1 3 2 ADDITION 3 Following are the eighty-one combinations, including inversions, of two numbers, each of which is less than ten. Practice on this exercise until you can state the sums in less than a minute. 1 3 2 4 6 4 7 3 2 9 1 8 3 2 6 8 8 2 1 1 8 1 9 8 6 4 5 8 5 6 7 4 7 8 9 9 8 5 6 3 9 7 7 8 8 4 8 9 4 3 7 7 6 2 9 9 1 1 2 3 4 9 5 8 7 9 3 1 7 6 5 9 2 2 6 4 9 5 7 8 2 6 8 6 9 42762887321291775 6842569517373 3425149345521 The following exercise contains the nine digits in groups of three. Practice on these combinations until you can state the sums in less than two and a half minutes. 887584589675446854 683532567553343243 223222332332333222 3 5 3664576978679866 223364474827232765 222222.4 23222222134 789898779968798957 786548454353694854 332321223223212344 4 ADDITION 889997599897889676 469364368867575476 667899987899579989 467777556878468859 446457355765336828 798999778898999878 566959654698574767 £5^^^!5i51f?1^4344 899896997899 79867 5 697887 56764563 5 543 Oral Work Add the following. In this, and in all other work in addition, name the sums only. For example, in adding 3, 4, 7, 9, say 7, 14, 23. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 3 5 7 2 9 1 6 8 5 4 9 3 5 5 7 9 7 3 9 1 5 3 7 5 6 9 8 9 3 9 3 8 2 8 3 5 7 1 4 9 6 4 6 7 9 4 9 3 6 3 8 1 4 2 7 8 9 6 7 8 7 8 2 7 6 3 7 5 2 9 5 1 7 4 8 4 1 9 8 5 7 8 5 3 9 1 4 7 6 4 3 9 8 7 9 9 8 4 9 5 7 3 5 8 5 9 9 6 9 8 9 8 9 2 5 3 7 4 8 5 9 6 6 1 6 3 5 6 Name the sums in each of the following. The first two num- bers in each example should be thought of as one number. Thus, in the first example, think 10, 17. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12 13. 14. 7 5 9 1 2 5 8 2 4 6 3 7 5 9 2 4 1 6 7 4 1 7 3 2 8 4 3 9 8 4 6 9 2 9 5 7 3 8 5 3 7 5 ADDITION 15. 8 6 4 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 8 4 8 5 3 6 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 77495746836579 673695 83674573 74853738542694 2. Adding numbers by grouping will increase your speed. Most rapid computers use group addition. For example, 4 _2 17 6 Use this method to find the sums in the following exercise. This work should be done orally. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14 6 5 8 4 7 4 8 5 2 6 3 5 4 6 3 2 2 3 4 3 6 7 3 7 7 8 9 6 5 7 3 4 8 5 3 7 5 4 9 4 7 3 4 3 6 2 3 5 7 6 4 8 4 1 3 o 15„ 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28 3 7 4 2 5 3 6 2 4 6 8 •9 7 5 3 6 4 8 5 3 7 6 4 8 5 7 3 6 7 5 3 6 5 8 4 5 6 4 7 3 8 2 7 6 3 4 1 7 4 7 4 8 9 5 3 7 29. 30. 31. 32. 33. 34. 35. 36 37. 38. 39. 40. 41. 42 3 2 6 8 6 4 2 4 6 4 8 5 2 3 3 6 2 5 8 9 5 3 7 5 3 5 7 9 9 5 3 6 8 9 5 2 6 2 8 5 3 9 5 2 7 4 2 7 3 7 9 4 2 7 4 6 6 ADDITION 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53 48953268436 36842674368 7463. 7 853679 47528648379 26479642675 74839593675 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 7 3 2 8 5 3 7 3 7 5 5 3 6 8 7 4 2 6 8 3 4 5 6 4 7 3 8 4 2 8 5 2 3 5 7 8 5 3 6 7 4 7 6 4 8 9 2 6 3 7 2 3 6 7 8 4 2 5 6 3 Find the sums in examples 1-14 by the following method : 43 24 Think 43, 63, 67. 67 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 24 46 37 53 58 67 48 39 68 73 33 52 4463475973584286 ___ _ __ 3. Recording Addition by Columns. For convenience in check- ing, the total of each column may be recorded separately. This will enable you to resume the work where it was discontinued if you are interrupted after having added one or more columns. Three slightly different methods are in use. 11. 12. 13. 14 66 81 93 65 59 78 38 75 a. h. c. 369 369 369 487 487 487 352 352 352 896 896 896 294 294 294 28 20 28 37 37 39 20 28 23 2398 2398 ADDITION 7 Illustrations (a) and (5) show the method of adding each column without carrying the tens. The column totals must be added to obtain the final result. Illustration ((?) shows the method of adding to each column the amount carried from the column at the right. Written Work Make the figures plain and easily legible and place units of the same order in the same vertical column. Copy and find the sum of : 1. 2. 3. 4. 5. 5823 84239 887935 9328577 88421 4923 42937 512937 4912374 31238 9382 31629 491327 5823746 312 5128 49238 395825 4923748 273845 3258 83153 416239 7239482 39547 7362 42841 482423 1423849 815288 8127 52384 923857 8237421 4234 4239 94856 412831 9423748 21582 6. 7. 8. 9. 10. 11. 27 371 419 372 97 996 83 927 82 496 86 37 95 482 92 18 547 821 84 413 412 739 969 493 82 958 892 847 38 782 15 285 9216 96 487 946 81 , 381 594 882 692 531 48 294 5 75 99 28 79 148 592 989 881 327 Each student should prepare original examples for addition, fol- lowing the instruction of the teacher. Exchange papers, criticize the form, and find the sums. 8 ADDITION The ability to give and to take dictation of numbers should be developed. Numbers may be dictated by the teacher, or by members of the class. Written Work The following table shows the weekly sales report made by a number of salesmen during a certain week. Find the total sales made by each salesman during the weeki and enter these totals in the proper places at the bottom of the table. Find the total sales made each day, and enter these totals in the column at the right. Find the total sales made by all salesmen during the week. The grand total should be found in two ways: by adding the totals at the foot of the blank, and those at the right. If these two grand totals agree, you may assume that the additions are correct ; if they do not agree, you should find the error. DAY xI.COLSEK D.R.BACOK KG. BATES D.O.ESTEY TOTAL M ON- DAY &/6 'A5 ^s-^s Jf- 8/C 9^ ■3> /(^ ^7 TVESDA Y 3S-8 q3 Cfc7 8¥- yns ^8 CH^ ^7 -WEDNESDAY ^/Q. s-j ^c,3 ^7 <:,3<7 7/ TAS- 8^ THUJiSDAY 3 SsS- /3 ca^A 9^ yat/- // •s-cr¥^ 7^ FRIDAY ^ / 8 qs. '7 /S q(. (^3q 3J ^8¥- 38 SATURDAY 6.3(^ 4^7 ^3(7 C& 7^cr ^7 8^C <^'A TOTAL 4. Courtis Standards. S. A. Courtis has determined certain standards of achievement in addition, subtraction, multiplication, division, and the copying of figures. His test in addition includes twenty-four examples similar to the two which follow. ADDITION 9 127 996 375 320 Qrq 778 ^^ *^® thousands of students examined by means of the Courtis tests about 5% are able to obtain the correct result to twenty-four such examples in addition in eight minutes or less. 167 972 554 119 Note. Information in regard to the Courtis Standards and Tests may be ob- tained by addressing S. A. Courtis, Detroit, Michigan. 5. How to Rule a Blank Form. Ruling the forms for your written work will furnish you excellent practice in the use of pen, ink, and ruler. This practice will be valuable as a preparation for bookkeeping in school or in a business office. Follow the instructions given below: a. Make the columns just wide enough for the figures, — about seven figures to an inch. Remember that the total may have one or two more figures than any of the addends (numbers added). h. Make the horizontal lines parallel and about \ of an incn apart. c. Make the spaces for headings and totals f of an inch deep. d. Try to place the form as nearly as possible in the middle of the paper. 6. How to Enter Statistics. Much of the clerk's work in a business office consists of entering statistics on ruled forms. a. Always write figures on the line. 5. Point off figures in groups of three. c. Make small figures; they look better and are more easily read than large ones. d. Keep the figures close to the right side of the column. e. Keep the columns vertical: units above units, tens above tens, etc. /. Write the figures at equal distances from each other. 10 ADDITION Written Work 1. The following table shows the delivery records of a store running five wagons. A record of each day's deliveries is kept and the week's totals are found. If the summary shows that any one wagon is required to make an unreasonably large number of deliveries, a change in the routes may be necessary. By finding the total number of deliveries made each week, the average cost per delivery may be computed. X>AY- ■VfAGOK WAOOJV HO 2. JV0 3 ■iYAOOK J^OJ/- TOTAL MOKDAY :i^3 /Cf 3.7 S / /A5> S.Uf TUrSVAY Ji./C 3^^ 3cf/ /nfZ wrourSDAY £.sy ZS'T 2.^^ /Zf 33,2. TKUJZSDAY 30/ Z,Cf/ 3^/ /^^-r Cb^C> mi DAY Ht?^ 3x0 U 3nS> 3./E 3./^ SATVJiDAY 3/8 3^/ ^a.o ibii,3 ^o/ TOTAL G-X. Rule a blank form similar to this model; copy the statistics, and find; a. The total number of deliveries made during the week by each wagon. h. The total number of deliveries made each day. c. The total numbel* of deliveries for the week. 2. Rule a blank form similar to the first of the tables on the opposite page, copy the statistics, and find the totals indicated. 3. Referring to the second of the tables on the opposite page, what was the value of each crop in each of the geographical divi- sions, and in the entire United States ? Rule a blank in ink and indicate these values as totals. ADDITION 11 Weekly Sales Report by Departments Dept. No. Monday TXXESDAT "Wednesday Thursday Friday Saturday Total 1 $932.87 $823.75 $239.75 $724.16 $295.16 $840.19 2 829.47 584.92 395.58 645.97 396.74 492.10 3 723.85 486.47 523.78 419.52 296.15 492.58 4 836.47 594.38 723.91 391.16 749.15 581.07 6 486.74 432.95 312.85 492.43 723.85 239.57 6 728.74 483.96 472.58 439.17 396.14 211.64 7 385.75 539.59 542.87 734.67 723.96 447.92 8 648.57 823.85 514.29 439.76 824.57 238.11 9 923.37 239.73 629.85 329.54 385.47 294.10 10 473.48 865.94 518.59 172.39 749.80 663.19 Total Grand Total Value of the Wheat, Corn, and Oat Crops in the Various States (In Thousands of Dollars) State and Division Corn Wheat Oats State and Division Corn Wheat Oats Maine ... 480 72 2,347 Minnesota . . . 28,925 48,938 31,962 New Hampshire 794 225 Iowa . . . 151,207 10,023 58,811 Vermont .... 1,296 24 1,589 Missouri . , . 112,196 21,375 12,994 Massachusetts . . 1,629 128 North Dakota 3,766 99,236 20,948 Rhode Island . . 401 26 South Dakota 28,248 36,008 13,098 Connecticut . . . 2,310 166 Nebraska . . 67,568 37,985 .16,653 New York . . . 13,834 7,054 38,797 5,306 1,433 21,204 15,420 814 14,915 Kansas . . N. C. W. Miss Kentucky Tennessee Alabama . . R. 69,690 68.295 19,264 New Jersey . . . Pennsylvania . . 60,192 53,862 42,802 6.791 7,077 359 N. Atlantic . . 1,775 2,632 3,224 Mississippi . 40,356 93 1,180 Louisiana . . 22,093 361 Delaware . . . 3,381 1,864 55 Texas . . . 98,112 10.253 13,390 Maryland . . . 13,450 8,536 608 Oklahoma 41,770 15,072 7,988 Virginia .... West Virginia . . 33,739 15,928 8,682 3,412 2,020 1,461 Arkansas . . 33,828 884 1,741 S. Central Montana . . N Carolina 42,418 29,136 5,907 865 2,352 4,598 S. Carolina , . . 428 12.381 7.997 Georgia .... 45,864 1,498 4,921 Wyoming . . 236 1.745 3,171 Florida . . 6,727 518 Colorado . . New Mexico Arizona . . 4,368 1,562 528 8,006 1,109 778 4,717 S. Atlantic . . 828 188 Utah . . . 202 4,544 2,069 Nevada . . 29 1,137 208 Ohio 78,484 9,565 30,782 Idaho . . . 276 9,613 5,956 Indiana .... 83,733 9,374 23,940 Washington . 651 36,535 5,476 Illinois .... 174,791 8.641 54,818 Oregon . . 472 15,132 5,623 Michigan .... 31,492 29,714 6,720 2,958 17,103 27,119 California Far Western 1,635 5,850 4,290 Wisconsin . . . N. C. E. Miss. R. United Stat es . Note. Different classes, or different groups of students of the same class, should be held responsible for computing the desired sums for different geographical divisions. 12 ADDITION Checking Addition by Casting Out Nines 7. Excess of Nines. The remainder after dividing any number by nine is called the Excess of Nines. If the number 47 is divided by 9, the excess of nines is 2. The excess of nines in 30 is 3, because when 30 is divided by 9, there is a remainder of 3. When we " cast out nines " from a number, we divide the number by 9, and indicate the excess. What is the excess of nines in 17 ? 14 ? 39 ? 45 ? 117 ? 23 ? 8. Method of Checking. If two numbers, each exactly divis- ible by 9, are added, their sum also is divisible by 9. If one number with an excess of 3 is added to a number with an excess of 2, the sum will have an excess of 5. The excess of nines in a sum is equal to the excess in the sum of the excesses of the numbers added. Examples. Add 80 and 19; check the result by casting out nines. Solution : 30 + 19 = 49. The excess of nines in the sum, 49, is 4. 30 has an excess of 3 ; 19 has an excess of 1. The sum of the excesses of the numbers added is 4, therefore the addition checks. For convenience, the work may be arranged as follows : Numbers Added Excesses a. 30 3 19 Sura 49 1 4 Excess of sum 4 NuMBBBS Added Excesses NiTMBBBS Added EXOESBBS h. 23 5 c. 49 4 13 4 34 7 Sum 36 9 or Sum 83 11 or 2 Excess of sum Excess of sum 2 CASTING OUT NINES 13 9. Short Method of Finding the Excess. The excess of nines in any number may be found by the following method : Add the digits composing the number. If the sum is composed of two or more digits add them. Continue this procedure until a result of one digit is secured. Examples. 1. What is the excess of nines in 25 ? Solution : 2 + 5 = 7, the excess. 2. What is the excess of nines in 328 ? Solution: 3 + 2 + 8 = 13 1 + 3 = 4, the excess. The addition of digits to find the excess will be further sim- plified by observing the following suggestions : a. Ignore 9's, and combinations which add to 9 or multiples of 9. Example. What is the excess of nines in 9457 ? Solution : Ignore 9 and 5 + 4 ; the excess is 7. h. When the addition results in a number of two digits, add the digits and proceed as before. Example. What is the excess of nines in 7528 ? Solution : 7 + 5 = 12;l + 2 = 3; 3 + 2 + 8 = 13; 1 + 3 = 4, the excess. 10. Limitation of the Method. Casting out nines is not an abso- lute check for any process. It will not disclose an error of 9 or any multiple of nine, neither will it disclose an interchange of digits, such as 763 for 673. 14 ADDITION Add and check Written Work Numbers to bk Added EXCESSKS 213 412 617 362 145 215 829 657 923 ? 9 ? ? ? ? ? ? ? ? ? 2. Rule a suitable blank form for the following : At the right of each column of figures rule a narrow column in which to indi- cate the excesses. Find the totals as indicated ; check all additions by casting out nines. Value of Farm Lands, Buildings, and Implements in the United States Division Land Ex. Buildings Ex. Implements Ex. Total Ex. New England . Middle Atlantic E.N. Central . W.N. Central . South Atlantic . E. S. Central . W.S. Central . Mountain . . . Pacific. . . . 382,134,424 1,462,321,005 7,231,699,114 10,052,560,913 1,883,349,675 1,326,826,864 2,716,098,530 1,174,370,096 2,246,313,548 336,410,384 980,628,098 1,642,292,480 1,562,104,957 603,086,799 411,570,975 412,498,352 145.026,777 231,832,706 50,798,826 167,480,384 268,806,550 368,635,544 98,230,147 75,339,333 119,720,377 49,429,975 66,408,647 U.S. Totals . Grand Total 3. The following table shows a method used by department stores to determine the cost of the purchases made for various departments during the month. For example, Invoice No. 1, CASTING OUT NINES 15 purchased on January 2, included goods for the six departments of the store. Invoice No. 2 included goods for only three depart- ments. The total amount of the invoice may be found by horizontal addition. The total purchases for each department during the month may be found by vertical addition. Rule a blank suitable for this material, enter the data, and find: a. The total of each invoice. h. The total purchases for each department during the month. c. The total purchases for all departments during the month. Check all additions by casting out nines. Invoice No. Date Deft. 1 Dept.2 Dept. 3 Dept. 4 Dept. 5 Dept. 6 Total 1 Jan. 2 129 30 340 60 290 39 360 89 240 30 376 80 2 Jan. 3 276 90 347 80 174 44 3 Jan. 3 295 67 298 87 350 27 289 67 287 57 4 Jan. o 246 32 238 47 350 27 347 25 250 68 276 57 5 Jan. 6 231 53 350 21 378 89 190 23 6 Jan. 8 212 23 325 67 345 67 367 78 310 57 185 67 7 Jan. 8 227 85 346 78 357 89 298 67 8 Jan. 10 170 67 9 Jan. 11 160 87 325 67 287 67 367 57 287 00 189 00 10 Jan. 15 170 97 341 28 321 67 378 98 287 89 11 Jan. 15 180 89 333 33 278 90 2.34 86 12 Jan. 15 345 67 345 67 328 98 300 00 350 90 13 Jan. 16 203 25 356 78 378 68 14 Jan. 17 204 67 367 78 376 56 267 87 347 52 15 Jan. 19 290 87 356 87 278 65 378 67 16 Jan. 23 297 76 347 89 398 67 256 28 250 00 17 Jan. 24 234 56 388 88 18 Jan. 25 245 67 287 98 367 34 256 78 234 56 19 Jan. 28 229 39 323 23 376 29 234 56 167 89 20 Jan. 31 236 78 310 21 289 98 387 85 245 67 245 67 ■ Total CHAPTER II SUBTRACTION 11. Drill Tables. Daily practice on the following combinations will increase your speed and accuracy in the process of subtraction. Drill on these combinations until you can state all of the results in less than thirty seconds. 9879674736878458 2153124436438213 2 7 9 5 9 5 6 5 9 4 4 9 8 2 6 8 1 7 4 5 5 4 3 2 7 4 3 8 5 2 4 6 5 8 4 8 6 7 7 9 8 1 3 3 5 7 9 6 3 8 1 6 2 1 6 1 2 1 2 1 5 7 6 5 Drill on the following until you can state all of the results in less than thirty seconds. 16 14 15 18 13 17 12 11 16 11 12 17 11 8689495976684 13 12 15 16 11 12 12 12 11 13 15 11 12 5369 3 38779789 11 12 13 14 14 13 14 15 14 11 13 5 4 7 8 7 6 5 16 9 9 2 8 SUBTRACTION 17 When performing subtraction, one is frequently obliged to "borrow" as in the following. Copy these examples, and make the subtractions. 1. 479 284 2. 636 198 3. 4279 3682 4. 14973 8297 5. 3084 1596 6. 12379 3084 7. 42937 39048 8. 946320 298452 9. 37649 20863 10. 947302 842943 11. 794680 409694 12. Checking Subtraction. Subtraction may be checked by either of the following methods : (a) Difference + Subtrahend = Minuend. (6) Minuend — Difference = Subtrahend. Example. Solution. 78 Minuend 21_ Subtrahend 57 Diiference Subtract 21 from 78 Check. a. 57 Difference 21 Subtrahend 78 Minuend b, 78 Minuend 57 Difference 21 Subtrahend Written Work Perform the subtractions indicated ; check the first five by method (a), and the last five by method (5), 1. 2. 3. 4. 5. 489 7932 82578 63217 49216 392 494 58214 41283 21953 6. 7. 8. 9. 10. 68310 40513 53821 79608 184732 49168 39458 41927 20973 75806 11. The following data show the sales in the various depart- ments of a large store for the month of August, 1914, and the month of August, 1915. 18 SUBTRACTION Rule a blank similar to the following: Comparative Sales Record Depart- ment No. August, 1914 August, 1915 Increase o* Decrease 1 $ 5,483.85 $ 5,834.75 2 7,239.74 8,238.74 3 15,493.67 14,835.92 4 9,834.56 10,385.47 5 23,842.12 22,147.94 6 15,858.43 16,614.34 7 6,395.75 6,114.32 8 19,432.86 22,324.73 9 9,445.87 10,302.95 10 43,221.42 46,932.56 11 29,496.56 31,416.47 12 18,853.16 17,542.85 13 22,542.19 25,436.83 14 25,746.91 24,427.85 15 18,422.16 21,541.86 Total Enter the sales in the proper column of the blank. Find the increase or decrease in the amount of the sales in each department for August, 1915, over the sales in the same de- partment for August, 1914. Enter increases in black ink; decreases in red ink. Find the net increase for the entire store. 12. The following shows the total population of the United States for the years indicated. 1790 — 3,929,214; 1800— 5,308,483 1830—12,866,020 1860—31,443,321 1890 — 62,947,714 1810— 7,239,881 1840—17,069,453 1870—38,558,371 1900—75,994,575 1820—9,638,453; 1850—23,191,876; 1880—50,155,783; 1910 — 91,972,266. Rule a blank form to show the year the census was taken, the population each census year, and the increase in population for each interval of 10 years. See how simple you can make this blank. SUBTRACTION 19 13. Rule a form, enter the following statistics, find the gross profit of each department, and the gross profit of the entire store. Gross Profit of a Department Store Dept. No. Sales Cost of Goods Sold Gkoss Profit 1 $5,629.80 $4,984.37 2 7,358.92 6,295.16 3 4,916.09 4,192.86 4 7,329.16 6,593.54 5 10,609.15 9,835.17 6 6,123.18 5,902.52 7 7,212.47 6,275.43 8 9,475.37 8,594.48 9 4,238.16 3,725.91 10 5,824.78 5,014.78 Total 14. Rule a suitable form, enter the following statistics, and find : a. The gross profit by departments. h. The gross profit of the entire store (two ways). c. The net profit or net loss by departments; enter net profit in black, net loss in red. d. Net profit or net loss of the entire store (two ways). Dept. No. Sales Cost of Goods Sold Gross Profit Expenses Net Profit OR Loss 1 $7816.40 $6715.32 $423.85 2 9317.42 849^.17 530.08 3 6842.56 5914.72 731.96 4 7319.62 6593.57 671.42 5 8295.17 7942.17 456.72 6 5732.88 5101.59 322.75 7 9514.82 8899.55 693.15 8 2289.74 1856.80 216.77 9 5793.66 5135.60 788.51 10 9559.38 8625.50 523.80 13. Subtracting by Adding Complements. A series of additions and subtractions may be performed by the method of adding com- plements. 20 SUBTRACTION The difference between any number and the next higher power of 10 is called the complement of the number. Thus, the comple- ment of 7 is 3 ; the complement of 6 is 4 ; the complement of 83 is 17. If, instead of subtracting a number less than ten from a given number, its complement be added, the result will be 10 too large. Thus, 13 - 6 = 7 or 13 + 4 = 17 (a result 10 too large). If, instead of subtracting two numbers less than ten from a given number, their complements are added, the result will be 20 too large ; if the complements of three such numbers are added, the result will be 30 too large, etc. Examples. 1. 29-6-7 = ? Solution. 29 + 4 + 3 = 36. Since two complements were added, the re- sult is 20 too large. Therefore, subtract 20, leaving 16. 2. 38-4-7-8 = ? Solution. 38 + 6 + 3 + 2 = 49. Since three complements were added, sub- tract 30, leaving 19. 3. 46-8 + 4-7=? Solution. 46 + 2 + 4 + 3 = 55. Since two complements were added, 20 must be subtracted, leaving 35. The practical value of this method will be shown by solving the following examples. 1. 36-24 + 19-12+21-13-6=? Solution. By combining as indicated in the units' column, beginning 36 at the top (complements are marked with an *) we have — 24 6 + 6* +9 + 8* +1 + 7* + 4* = 41 ^^ Since four complements were added, the result is 40 too large. — 12 Therefore write 1 and drop the 4. 21 ^ o By combining as indicated in the tens' column we have _ g 3 + 8* + 1 + 9* +2 + 9* = 32 • 21 Since three complements were added, the result is 30 too large. Write 2 and drop the 3. Result, 21. SUBTRACTION 21 2. 985 + 234-126-34-125-174 + 386=? 985 234 Solution. Combining in the units' column, beginning at the top — 126 "^'^ have _ 3^ 5 + 4 + 4* + 6* + 5* + 6* + 6 = 36 1 oc tt^A Write the 6. Since four complements were added, the result is 40 " ooa ^^ large. Therefore we must drop the 3 in 36, and also subtract 1 from the 8 at the top of the tens' column. 1146 Combining in the tens' column we have 7 + 3 + 8* + 7* + 8* + 3* + 8 = 44 Since four complements were added, we must deduct 40, leaving 4 which is written in the tens' column of the result. Combining in the hundreds' column we have 9 + 2 + 9* + 9* + 9* + 3 = 41 Three complements were added, the result is therefore 30 too large. Sub- tract 30 and write 11. Result, 1146. Oral Work Find the results by the addition of complements : 1. 46 - 4 - 7 = 2. 72-8-6-3 = 3. 39_7 + 3-9 = . 4, 48-17-6 = 5. 81 _ 23 - 42 = 6. 49 - 22 + 15 - 11 7. 85-26-35 + 62- 16 = 8. 643 - 289 + 364 = 9. 781 _ 247 + 64 = 10. 1046-987+649 = 11. 943 - 876 + 629 = 12. 1349 - 268 + 421 = 13. 1264 - 34 + 1321 = 14. 1789 - 347 + 736 = 15. 16. 17. 2346 1932 923,578 + 1267 + 9845 - 5,284 ~ 321 - 932 + 28,956 + 6964 + 2122 - 123,749 -1235 -2375 + 83,219 + 367 - 23 - 259,734 -2960 + 692 + 125,982 - 985 -1243 - 429,764 22 SUBTRACTION Written Work 1. The following model shows the ruling of the ledger in which banks keep accounts with their depositors. Deposits are added to the balance of the previous day, and checks are subtracted, to find the new balance to the credit of the depositor's account. Find the daily balances: William Hatfield Date Deposits Checks Balance June 1 $328.57 $ 85.68 $ 14.25 ? 2 125.80 65.90 12.73 ? 3 245.85 127.89 114.56 35.87 ? 4 319.45 38.51 26.82 102.50 ? 5 95.90 141.66 95.68 ? 6 450.00 132.88 6.20 ? 8 139.75 216.45 39.46 19.99 213.55 66.82 ? 2. The following blank shows a convenient method of keeping a record of cash received and paid by a small business. Rule a blank similar to the model and enter the statistics. Date Cash Kboeived Cash Paid Daily Cash Cash Sales On Account Purchases On Account Expenses Balance Feb. 1 1 2 $215.78 294.80 $124.35 95.88 $ 80.75 157.47 $ 68.55 113.25 $ 8.75 3.73 $216.27 ? ? 3 188.47 148.23 95.48 316.57 27.49 ? 4 218.43 49.47 17.49 42.39 9.12 ? 5 388.92 112.67 221.81 76.29 75.84 ? 6 478.07 290.04 88.12 448.14 6.90 ? ? ? ? ? ? ? SUBTRACTION 23 a. Find the daily cash balances. To the balance of the preceding day add the receipts from cash sales and receipts on account, and subtract the various amounts listed under " Cash Paid." Thus, 1216.27 -f 215.78 + 124.35 - 80.75 - 68.55 - 8.75 = ? h. Find the totals for each column. 3. Add upward; subtract across: a. 7,463-2,847= 5. 174,638-94,273 = 5,928-3,804= 38,270-27,409 = 9,604-2,870= 70,563- 2,879 = 3,962 - 1,436 = 924,360 - 14,287 = 9,287-5,426= 7,503- 2,769 = CHAPTER III MULTIPLICATION Accuracy and speed in multiplication depend largely upon a thorough mastery of the multiplication tables. The student should thoroughly review the tables previously learned and should con- tinue with daily drills on combinations up to 25 times 25. 14. Drill Tables. Multiply across ; add upward : 1. 2. 3. 4. 74 X 436 = 83 X 423 = 25 X 624 = 35 X 624 = 74 X 523 = 83x157 = 25 X 726 = 35 X 706 = 74 X 287 = 83 x 284 = 25 X 37 = 35 X 753 = 74 X 492 = 83 X 307 = 83 X 596 = 25 X 869 = 25 X 493 = 35 X 496 = 74 X ? = 35 X 548 = 83 X ? = 25 X 468 = 35x784 = 25x ? = 35 X ? = Oral Work Use 2, 3, 4, 5, 6, 7, 8, and 9 as multipliers. Name the results V each column in less than 20 seconds. 1. 2. 3. 4. 5. 3 18 5 4 9 5 10 8 9 11 7 4 12 15 16 14 7 15 20 30 11 9 7 17 25 6 15 30 8 14 8 16 22 13 17 9 20 16 18 11 15 12 25 22 16 24 MULTIPLICATION 25 Written Work 1. A factory made an investigation of the number of articles of a certain kind manufactured by each of its employees. It found that ; 9 men produced 46 articles each. 9 men produced 48 articles eacli. 11 men produced 53 articles each. 15 men produced 55 articles each. 18 men produced 59 articles each. 23 men produced 61 articles each. 25 men produced 62 articles each. 25 men produced 63 articles each. 21 men produced 64 articles each. 17 men produced 63 articles each. 17 men produced 6Q articles each. 14 men produced 68 articles each. 12 men produced 69 articles each. 8 men produced 70 articles each. Rule a form with a heading similar to the following : Production Record NuMBlEE OF Men Number of Articles Made by Each Total Enter the statistics, find the number of articles produced by each group of employees, and the total number of articles produced by all of the employees. 2. Nine workmen were employed in the manufacture of differ- ent articles, and were paid a certain number of cents for each piece completed. Complete the following table, finding the wages earned by each workman. 26 MULTIPLICATION Daily Piecework Labor Cost Workman No. Number of Articles Made WAr.E Kate PER Piece Wages Earned 1 17 $0.27 2 19 .22 3 38 .16 4 79 .06 5 32 .15 6 28 .18 7 64 .07 8 81 .05 9 29 .21 15. Checking Multiplication. Multiplication may be checked by several methods. The following methods are commonly used. a. Repeating the multiplication and assuming that if the same product is obtained the work is correct. This is not a reliable check because an error may be repeated. h. Dividing the product by the multiplier to obtain the multi- plicand, or by the multiplicand to obtain the multiplier. c. Casting out nines. 16. Casting Out Nines. The method is as follows : Find the excess of 7iines in the multiplicand and in the multiplier. Find the product of these excesses. Find the excess of nines in this product. It should equal the excess of nines in the result. Example. Multiply 23 by 16 ; check by casting out nines. Solution. 23 5 = the excess of nines in 23. 16 7 = the excess of nines in 16. 368 35 = the product of these excesses. Check. 8 = the excess in this product. The excess of nines in 368 is also 8. The multiplication, therefore, checks. Without performing the multiplications determine the probable correctness of the following products, by means of casting out nines : 1. 25 38 950 2. 82 35 3. 36 87 4. 286 37 5. 4172 39 6. 344 281 7. 733 492 2870 3132 10,382 162,698 96,664 362,636 MULTIPLICATION 27 8. 398 241 9. 43,962 47,835 95,918 2,102,922,270 10. 34,276 21,578 738,627,528 Written Work Multiply and check by casting out nines : 11. 12. 13. 14. 15. 16. 347 279 627 132,879 63,154 78,293,567 861 439 123 642,378 9,837 20,417,839 17. The following table gives information regarding the corn crop in the United States in a recent year. Corn Production in the United States States North Atlantic Maine New Hampshire Vermont Massachusetts Rhode Island Connecticut New York New Jersey Pennsylvania South Atlantic Delaware Maryland ....... Virginia West Virginia North Carolina South Carolina Georgia Florida North Central, East of Miss. Ohio Indiana Illinois Michigan Wisconsin Number of Thousands of Acres 16 23 45 47 11 60 512 273 1,499 195 670 1,980 725 2,808 1,915 3,910 655 4,075 4,947 10,658 1,625 1,632 Average Yield PER Acre 40.0 46.0 40.0 45.0 41.5 50.0 38.6 38.0 42.5 34.0 36.5 24.0 33.8 18.2 17.9 13.8 13.0 42.8 40.3 40.0 34.0 35.7 Average Price PER Bushel. IN Cents 75 75 75 77 86 77 70 68 63 51 55 71 65 83 85 85 79 45 42 41 57 51 28 MULTIPLICATION Corn Production in the United States — Continued States Number of Thousands of Acres Average Yield PER Acre North Central, West of Miss. Minnesota Iowa Missouri North Dakota South Dakota Nebraska Kansas South Central Kentucky . . . .... . Tennessee Alabama Mississippi Louisiana Texas Oklahoma Arkansas Far Western Montana ........ Wyoming Colorado New Mexico Arizona Utah . Nevada Idaho Washington Oregon California 2,266 10,047 7,622 328 2,495 7,609 7,575 3,600 3,332 3,150 3,106 1,805 7,300 5,448 2,475 24 16 420 93 19 9 1 12 31 20 52 34.5 43.0 32.0 26.7 30.6 24.0 23.0 30.4 26.5 17.2 18.3 18.0 21.0 18.7 20.4 25.5 23.0 20.8 22.4 33.0 30.0 30.0 32.8 27.3 31.5 37.0 Prepare a blank similar to the modeL States Acres Average Yield per Acre Total Bushels Produced Average Price per Bushel Total Crop Value Ex. Ex. Ex. Ex. $ i Ex. SHORT METHODS 20 a. Find the total number of bushels of corn produced in each state. h. Find the total value of the corn crop of each state. Different classes or various groups of a class should make the required com- putations for assigned geographical divisions of the country. In checking the results, the "excesses" should be placed in the columns marked "Ex." Many interesting comparisons may be made from the data of the preceding table. For illustration : Name the five states which produced the most corn and compare the yields in these states. What geographical section of the country produced the largest corn crop? What relation, if any, is there between the size of the corn crop in the various states and the average price per bushel in the various states ? Short Methods op Multiplication These short methods will be found to be very practical. Master two or three of them thoroughly before taking up others. Use those that you have mastered whenever you have opportunity to do so. It is not necessary that all of these short methods be mastered before the succeeding chapters are studied. 17. To multiply by 10, 100, 1000, 10000, etc. a. When the multiplicand is an integer. Annex to the multi- plicand as many zeros as there are zeros in the multiplier. Thus, to multiply an integer by 10, annex one zero ; to multiply by 100, annex two zeros. Examples. 1. 37 x 10 = 370. 2. 29 x 100 = 2900. h. When the multiplicand is a decimal fraction. Move the decimal point as many places to the right as there are zeros in the multiplier. It may be necessary to annex zeros in order to move the decimal point the desired number of places. Examples. 1. Multiply .1357 by 100. Solution. Move the decimal point two places to the right, 13.57- 2. Multiply 32.46 by 1000. Solution. In order to move the decimal point three places to the rightr it is necessary to annex one zero, giving, as a result, 32,460. 30 MULTIPLICATION Oral Work Multiply as indicated : 1. 37,946x100. 2. 5293 X 10,000. 3. 639x100,000. 4. 120 X 1000. 5. .376x1000. 6? 1.349 X 1000. 7. 27.9637x100. 8. .000932 - 10. 9. .00873x1000. 10. .7032 X 1000. 11. 3.69 x 1000. 12. .0027 X 100,000. 13. 1427.834x10,000. 14. 625.086 X 1000. 18. To multiply numbers ending with zeros. a. When both numbers are integers. Multiply the numbers represented by the significant figures. To the product thus obtained^ annex as many zeros as there are final zeros in both the multiplicand and multiplier. Example. Multiply 3400 by 1200. Solution. 34 x 12 = 408. Annexing four zeros, we obtain the product 4,080,000. Perform the following multiplications. Whenever possible, do the work orally. 1. 169 X 300. 2. 210 X 300. 3. 4567 X 700. 4. 1390 x 1200. 5. 2300x1500. 7. 3194 X 23,000. .6. 19,000x16. 8. 420 X 3400. b. When one of the numbers is a decimal fraction. Multiply the numbers represented by the significant figures. Move the decimal point as many places to the right in the product as there are final zeros in the integer. (This may necessitate annexing zeros.) Eza^iples. 1. Multiply .486 by 300. Solution. 3 x .486 = 1.458. Move the decimal point two places to the right, the result is 145.8. SHORT METHODS 31 2. Multiply 8.2 by 400. Solution. 4 x 3.2 = 12.8. Move the decimal point two places to the right, the result is 1280. Written Work Perform the following multiplications: 1. .47 X 200. 2. 3.786 x 4000. 3. 17.682 X 500. 4. .0746 x 3000. 5. .072 X 6000. 6. .382 x 1200. 7. .0837x14000. 8. .042x170. 9. .0036 x 1500. 10. 4.26 x 7000. 19. To multiply by 9, 99, 999, etc. a. To multiply by 9. Annex one zero to the number to he multi- plied^ thus multiplying it hy 10; from this result subtract the num- ber to be multiplied. Example. Multiply 846 by 9. Solution. 3460 346 3114 b. To multiply by 99. Annex two zeros to the number to be mul- tiplied^ thus multiplying it by 100; from this result subtract the number to be multiplied. Example. Multiply 298 by 99. Solution. 29300 293 29007 Written Work Multiply each of the following numbers by 9, 99, and 999 : 1. 632. 2. 748. 3. 185. 4. 737. 5. 427. 6. 166. 20. To multiply by numbers slightly smaller than 10, 100, 1000, 10,000, etc. A modification of the short method explained in the preceding section may be used to multiply by numbers slightly smaller than 10, 100, 1000, 10,000, etc. 32 MULTIPLICATION To multiply by 98. Annex two zeros to the number to he multi- 'plied and from this result subtract twice the number to be multiplied. How can the short method be used if you are to multiply by 97, 96, 95, or Written Work Apply short methods to the following examples: 1. 675 X 96. 2. 350 x 95. 3. 535 x 91. 4. 687 X 97. 5. 94 x 3.4. 6. 995 x 82. 7. 634 X 994. 8. .48 x 997. 9. 23 x 99. 10. 48 X 997. 11. 12 x 988. 12. 47 x 998. 21. To multiply by 11. a. When the multiplicand contains two digits. Place between these two digits^ their sum. Example. 34 x 11 = 374. When the sum of the two digits is 10 or more, 1 must be carried to the digit at the left. Example. 68 x 11 = 748. Written Work Multiply each of the following numbers by 11: 1. 27. 2. 63. 3. 93. 4. 74. 5. 26. 6. 35. 7. 22. 8. 87. 9. 28. 10. 46. ii. 75. 12. 96. 13. 37. 14. 36. 15. 57. 16. 85. 17. 98. 18. 72. b. When the multiplicand contains three or more digits: The units' digit of the multiplicand is the units' digit of the prod • uct; the sum of the units' and tens' digits is the tens' digit of the product ; the sum of the tens' and hundreds' digits is the hundreds' digit of the product., etc. Whenever the sum of two digits is ten or more, 1 must be carried. SHORT METHODS 33 Examples. 1. Multiply 793 by 11. Solution. 3 (the units' digit of the multiplicand) becomes the units' digit of the product. 9 4- 3 = 12 (carry the 1) 1 + 7 + 9 = 17 (carry the 1) 1 + 7= 8 8723 2. Multiply 52,635 by 11. Solution. 52,635 x 11'= 578,985. Written Work Multiply each of the following by 11: 1. 363. 2. 271. 3. 823. 4. 456. 5. 3742. 6. 876,394. 7. 3,578,962. . 8. 34,579. 9. 263,789. 10. 123,496,287. 22. To multiply by 111. 362,941x111=? When the multiplication is performed in the customary manner, the multiplicand is repeated as follows: 362941 362941 362941 When the short method is applied, the units' digit of the multi- plicand i& the units' digit of the product ; the sum of the units' and tens' digits of the multiplicand is the tens' digit of the product ; the sum of the units'^ tens' ^ and hundreds' digits of the multiplicand is the hundreds' digit of the product; the sum of the tens\ hundreds'^ and thousands' digits of the multiplicand is the thousands' digit of the products etc. The excess above 10 is always to be carried to the next sum. 34 MULTIPLICATION Written Work Without recopying, write the products obtained by multiplying each of the following by 111: 1. 729,361. 2. 124,396. 3. 1,793,862. 4. 5,374.. 5. 235,692. 6. 8,354,927. 23. To multiply two numbers ending in 5. a. When the sum of the digits at the left of the 5's is an even number. Multiply the digits at the left of the o's ; to this product add one half the sum of these digits ; to this result annex 25. Examples. 1. Multiply Q5 by 25. Solution. 2 x 6 = 12, the product of the digits at the left of the 5's. i of (2 + 6)= J 16 1625, result obtained by annexing 25. 2. Multiply 625 by 445. . Solution. 62 x 44 = 2728 I of (62 + 44) = 53 2781 278125, result obtained by annexing 25. Written Work Multiply as indicated: 1. 35 X 75. 2. 95 X 75. 3. 35 X 55, 4. 25 X 45. 5. 325 X 45. 6. 725 x 65. 7. 835x175. 8. 145x165; 9. 195x115. 10. 225x185. h. When the sum of the digits at the left of the 5's is an odd number. Multiply the digits at the left of the 5'8 ; to this product add one half the sum of these digits^ dropping the I ; to this result annex 75. SHORT METHODS 35 Examples. 1. Multiply 75 by 45. Solution. 4x7 = 28, the product of the digits at the left of the 5*s. i of (4 + 7) = Jl 3375, the result obtained by dropping the fraction I, and annexing 75. 2. Multiply 325 by 475. Solution. 32 x 47 = 1504 ^ of (32 +47)= 391, 1543, adding and dropping the I. 154,375, result secured by annexing 75. Written Work Multiply as indicated: 1. 75x65. 2. 125x135. 3. 95 X 85. 4. 145 X 175. 5. 225 X 75. 6. 165 x 135. 7. 145 X 215. 8. 435 x 125. 24. To multiply two numbers, when certain digits of the multi- plier are contained an integral number of times in other digits of the multiplier. Multiply 224 by 279. Since 9 is contained 3 times in 27, first multiply 224 by 9, then multiply this product by 3. Thus, 224 279 2016 = 9x224 6048 =3x2016 62496 When using this method, be careful to place the product of the second multiplication in the proper position. Example. 1. Multiply 341 by 618. 341 Solution. Since 18 is a multiple of 6, multiply g;[g first by 6. Place the right-hand figure of the product, 904^ _ a qj.1 2046, directly under the 6 of the multiplier. The prod- "~ • net of 18 X 341 can now be obtained by multiplying __6138 = 3 X 2046 2046 by 3. The right-hand figure of this product, 210738 6138, is placed directly under the 8 of the multiplier. 36 MULTIPLICATION Written Work . Multiply the following, stating by Avhat numbers you multiplied in order to take advantage of the short method: 1. 468 X 243. 2. 1,235 x 981. 3. 719 x 427. 4. 687 X 654. 5. 739 x 848. 6. 7,362 x 1,248. 7. 1,247 X 1,864. 8. 146,387 x 315. 9. 1,235 x 819. 25. The supplement of a number is the difference between the number and the next lower power of 10. The supplement of 15 is 5 ; the supplement of 134 is 34 ; the supplement of 1042 is 42. 26. To multiply two numbers each of which is a little larger than 100. To either of the numbers add the supplement of the other; to this sum annex the product of the supplemerits. Example. Multiply 131 by 103. Solution. 131 + 3 = 134 (or 103 + 31 = 134). Annex 93 (31 x 3). The result is 13,493. The same rule may be applied to numbers a little larger than 1000. Example. Multiply 1,062 by 1,006. Solution. 1062 + 6 = 1068 62 X 6 = ^72 1068372 Note. When the supplements are based on 100 and the product of the supple- ments is a number of only one digit, a zero must be put in tens' place. For example : 102 x 103 = 10,506. Similarly, when the supplements are based on 1000 and the product of the supplements is a number of less than three digits, zeros must be put in the proper places. Written Work 1. 104 X 120. 2. 127 X 102. 3. 113 x 106. 4. 114 x 105. 5. 114 X 106. 6. 109 x 106. 7. 126 x 107. 8. 109 x 111. 9. 1,007 x 1,003. SHORT METHODS 37 10. 1,009 X 1,012. 11. 1,214 X 1,006. 12. 1,206 x 1,012. 13. 1,112x1,006. 14. 1,416x1,009. 15. 1,374x1,005. 16. 1,674x1,012. 27. The complement of a number is the difference between the next higher power of 10 and the number. The complement of 92 is 8 ; the complement of 89 is 11 ; the complement of 996 is 4. 28. To multiply two numbers both slightly less than 100. From either 'number subtract the complement of the other number. To this result annex the product of the complements. Example. Multiply 96 by 93. Solution. 96 - 7 = 89 (or 93 - 4 = 89). 4 X 7 = 28 (product of the complements). Annex 28 to 89 and the result is 8928. Note. When the complements are based on 100 and the product of the comple- ments is less than 10, a zero must be put in tens' place. For Illustration : 98 x 97 = 9506. Similarly, the tens' and hundreds' places must be filled when the complements are based on 1000. Written Work Multiply as indicated. Perform orally as much of this work as possible. 1. 98 X 95. 2. 97 X 84. 3. 87 x 91. 4. 95x80. 5. 93x85. 6. 87x97. 7. 88 X 87. 8. 91 X 92. 9. 86 x 94. The same method may be applied to numbers slightly less than 1000. Example. Multiply 996 by 987. Solution. 996-13 (the complement of 987) = 983. 4 X 13 = 52 (the product of the complements). Since the complements are based on 1000 and the product of the comple- ments is a number of only two digits, a zero must be put in hundreds* place. The result is 983,052. 38 MULTIPLICATION Multiply : Written Work 1. 994 2. 996 3. 983 4. 987 992 984 991 992 5. 991 6. 983 7. 978 . 8. 981 981 • 982 983 988 29. To multiply any two numbers in the teens. To either of the nmnbers add the units' digit of the other number and annex a zero. To this result add the product of the units' digits. Example. Multiply 15 by 17. Solution. 15 + 7 = : 22 ' ; annex a zero, 220 255 Oral Work Multiply 1. 17 12 2. 13 12 3. 16 18 4. 17 13 5. 14 13 6. 19 15 7. 13 16 8. 17 19 9. 18 12 10. 13 19 11. 17 16 12. 15 17 CHAPTER IV DIVISION Oral Work 30. Short Division. 1. Divide by 2 : 16, 28, 76, 248, 368, 926, 1,054. 2. Divide by 3 : 27, eS6, 57, 75, 417, 732, 873. 3. Divide by 4 : 32, 48, 64, 72, 96, 196, 384, 748. 4. Divide by 5 : 75, 95, 145, 545, 725, 965, 1,025, 1,370. 5. Divide by 6 : 72, 96, 126, 366, 528, 732, 1,044. 6. Divide by 7 : 36, 91, 147, 203, 476, 924, 1,575. 7. Divide by 8 : 72, 96, 144, 360, 424, 792, 1,240. 8. Divide by 9 : 54, 98, 171, 243, 378, 567, 981. State the remainder when each of the following numbers is divided by 3, 4, 5, 7, 8, and 9. 9. 10. 11. 473 9,846 2,638 692 3,723 7,284 876 9,264 3,047 479 3,749 2,636 14. How many pounds of meat can be bought for $1.26 at 18^ per pound ? 15. How many weeks in 91 days? 175 days ? 266 days ? 16. The dividend is 176 and the quotient is 8. What is the divisor ? 17. The divisor is 9, the quotient is 7, and the remainder is 3. What is the dividend ? 18. Six dozen oranges were bought for S 1.62. What was the price per dozen? 19. How many yards in 186 feet ? 924 feet ? 5280 feet ? 39 12. 13. 4,020 19,206 7,302 47,308 7,960 23,074 8,403 95,306 40 DIVISION 20. A grocer buys 9 dozen eggs for $2.07. What is the cost per dozen ? 21. If you are to discharge a debt of -> fe 1 < S >-» ^ < m o ;? ^ Massachus 3tts 37 38 36 35 33 34 31 33 34 34 32 35 Rhode Isla nd. 35 39 39 34 34 36 32 32 35 34 34 34 Connecticu t . 36 39 38 35 34 35 33 34 34 36 34 36 New York . . 34 35 32 31 31 30 27 29 29 30 32 35 New Jersej r . 37 40 35 34 34 34 32 32 33 32 34 36 Pennsylvar lia 33 35 33 31 31 29 26 27 28 30 32 34 Maryland . . 28 29 29 28 25 25 25 25 26 28 29 28 Virginia . . 25 26 26 26 25 23 21 22 22 24 26 26 West Virgi oia 26 26 26 26 26 22 21 21 22 24 25 27 Georgia . . 25 25 28 24 24 24 24 24 24 25 25 26 Ohio . . . 27 28 27 25 25 24 22 23 24 25 27 29 Indiana . . 25 26 25 24 24 22 21 22 22 24 25 27 Illinois . . . 27 28 26 25 25 24 24 23 24 26 26 28 Michigan . . 30 31 28 27 27 25 23 23 24 25 27 29 Wisconsin . 33 34 28 28 29 26 25 25 26 .27 28 31 Minnesota . 31 32 29 27 27 27 24 24 25 26 28 30 Iowa . 29 30 27 26 26 25 24 24 24 25 27 29 Missouri . 23 23 23 23 23 22 21 21 21 22 23 24 Nebraska . . 26 26 24 24 23 22 21 21 22 23 25 27 Kansas . 26 26 25 24 24 22 21 22 22 24 25 26 Kentucky . 21 22 21 21 21 21 19 19 18 20 20 23 Tennessee . 21 22 21 20 20 19 18 18 18 19 20 22 Louisiana . . 28 30 28 27 28 27 26 27 27 27 28 30 Texas . . . 22 25 23 22 21 21 21 20 21 23 23 24 Oklahoma . 27 25 23 22 22 22 20 20 19 23 24 25 Montana . 36 37 35 33 31 31 30 29 31 31 32 35 Colorado . 33 33 30 30 28 28 26 26 28 28 32 31 Utah . . 33 31 30 29 31 30 29 27 28 30 32 32 Idaho . . 35 33 32 32 31 28 28 27 29 31 32 34 Washingtoi 1 . 36 37 32 32 30 28 28 30 30 32 33 35 Oregon . . 34 35 33 32 31 26 28 28 30 30 35 36 Oalifornia . 34 36 34 32 30 29 20 31 31 33 34 36 4. The following table gives the acreage planted to certain crops in the United States, and the crops raised. Compute the average yield per acre. Carry your results to two decimal places. Show the statistics on a ruled form. 50 AVERAGE Acreage and Production of Crops Crop 1911 1912 1000 Acres 1000 Bushels Bushels per Acre 1000 Acres 1000 Bushels Bushels per Acre Corn . . Wheat . . Oats . . Rye . . . Potatoes . 105,825 49,543 37,763 2,127 3,619 2,531,488 621,338 922,298 33,119 292,737 107,083 45,814 37,917 2,117 3,711 3,124,746 730,267 1,418,337 35,664 420,647 5. The following table shows the number of cases of eggs shipped to seven leading markets iri the United States. Receipts of Eggs at Seven Leading Markets in the United States 1906-1912 Year Boston . Chicago Cincin- nati Mil- waukee New York St. Louis San Francisco Total 1906 ... . 1907 .... 1908 .... 1909 .... 1910 .... 1,709,531 1,594,576 1,436,786 1,417,397 1,431,686 3,583,878 4,780,356 4,569,014 4,557,906 4,844,045 484,208 588,636 441,072 519,652 511,519 187,561 176,826 207,558 160,418 169,448 3,981,013 4,262,153 3,703,990 3,903,867 4,380,777 1,023,125 1,288,977 1,439,868 1,395,987 1,375,638 137,074 379,429 347,436 340,185 469,698 Av. 1906-1910 1911 .... 1912 .... 1,441,748 1,580,106 4,707,335 4,556,643 605,131 668,942 175,270 136,621 5,021,757 4,723,558 1,736,915 1,391,611 587,115 6:i8,920 Av. 1911-1912 Find (1) the total receipts of eggs each year, (2) the average receipts at each city for the periods indicated. 6. A subscription was taken to secure funds to purchase a gift. 3 men gave $1.00 each 1 man gave .75 2 men gave 1.50 each 1 man gave .60 4 men gave .90 each Find the average amount given. AVERAGE 51 7. The following table shows the number of men employed and the total weekly wages in each of the four departments of a faccory. Find the average wage in each department and the average wage for the four departments. Department Number of Men Employed 47 18 62 26 Total Wage I 960 290 1054 318 Average Wage Oral Review 1. What is the difference in the meaning of the following state- ments ? a. Each of the 300 employees in our factory earns $2.50 per day. b. The average daily wages of employees in our factory is f 2.50 per day. 2. What would you have to know and how would you proceed to find : a. The average weight of twenty boxes? b. The average value of a herd of cattle ? c. The average number of miles a train traveled per hour, going from Chicago to St. Louis ? d. The average age of the students in your class ? e. The average daily sales of a clerk ? 3. What could you find if you were told: a. The average value of farm land per acre in your state, and the number of acres of farm land ? b. The average daily sales of a clerk during the twenty-five week days of June ? c. The average monthly grocery bill of your family ? 52 AVERAGE 4. If you were told : a. The daily circulation of the Evening Herald for the twenty- six week days of July, and the average daily circulation of the Evening Transcript for the same month, how could you compare their circulation ? h. The average daily wages of A, who worked 265 days last year and the average dail}^ wages of B, who worked 303 days, how could you find the yearly wages of each, and which one earned the larger amount ? c. The difference between the average daily outputs of two shoe factories, how could you find the difference in their production for a year of 300 working days ? 5. What would you have to know and what would you do to find the average daily speed of an ocean liner on a given voyage ? 6. Several boys worked for a farmer picking strawberries. One earned $5.00 more than the average of the other boys' earnings. What else must you know and what would you do to find the total earnings of all the boys ? What else would you have to know and how would you find the average wage cost of picking a quart of strawberries ? Written Work 1. A merchant kept a record of the deliveries of goods made to his customers for a week. The record follows; Day Dblivebies • Monday 213 Tuesday 187 Wednesday 208 Thursday 221 Friday 168 Saturday 251 a. What was the average number of deliveries per day ? ' h. The expense of running the delivery wagons for a week, in- cluding care of horses, interest on the money invested in horses and wagons, repairs and wages, was $64.75. What was the average cost per delivery ? AVERAGE 53 2. Five clerks in a store sold the following amounts of goods during a month: A. $1246.50 B. 1076.85 ' C. 944.90 D. 1388.20 E. 1109.75 a. What was the average amount of sales per clerk ? h. Which clerks sold more than the average ? Which clerks sold less than the average ? 3. The distance from Chicago to Aurora, Illinois, via the C. B. & Q. Railroad, is 37.4 miles. Train No. 55 makes no stops between these stations. It leaves Chicago at 6:10 p.m. and arrives at Aurora at 7 : 10 p.m. How many miles an hour does this train travel ? What fractional part of a mile does it run in one minute ? 4. The single fare between these two stations is 74 cents. Ten- trip tickets may be purchased for $6.25. What is the saving in fare per trip ? 5. A 25-trip ticket may be purchased for $13.00. What is the average cost per trip ? 6. The following table shows the number and value of pianos and organs manufactured in the United States in 1904 and 1909. Pianos 1909 1904 Number 261,197 374,154 Value $41,476,479 $59,501,225 Obgans Number 113,065 64,111 Value $4,162,053 $ 2,595,429 What was the average value of a piano manufactured in each of the years ? What was the average value of an organ manufactured in each of the years ? 54 AVERAGE 7. In 1900 the population of the United States was, in round numbers, 77 million. The combined daily circulation of all daily newspapers was about 15 million copies; an average of 1 copy of a daily paper to every persons. In 1910 the population had increased to 93 million, and the circulation of daily newpapers to 24 million, or an average of one copy for every persons. 8. During the year 1913 the United States Congress appro- priated $1,098,678,788 for the expenses of the government. The last preceding census showed a population of 93,402,151. What was the average governmental expenditure per person on this basis ? CHAPTER VI FACTORS AND MULTIPLES 35. Terms. An integer is a number of whole units. The factors of a number are the integers which, multiplied together, produce the given number. Thus, the factors of 15 are 3 and 5 ; the factors of 18 are 3 and 6, or 2 and 9. A factor of a number is a divisor of that number. A number which is not exactly divisible by any other number (except 1) is called a prime number. Thus, 1, 3, 5, 7, 11, and 13 are prime numbers. Numbers are said to be prime to each other when they have no common factor except 1. Thus, 10 and 27 are prime to each other, although neither is a prime number. 36. Test of Divisibility of Numbers. A number is divisible by : a. Two, if it ends with 0, 2, 4, 6, or 8. * b. Three, if the sum of its digits is divisible by 3. c. Four, if the number expressed by its last two digits is divisible by 4. d. Five, if it ends in or 5. e. Six, if it is divisible by both 2 and 3. /. Eight, if the number expressed by its last three digits is divisible by 8. g. Nine, if the sum of its digits is divisible by 9. h. Ten, if its right-hand digit is zero. i. Eleven, if the difference between the sums of the numbers represented by the odd and even orders of digits is divisible by 11. Thus, 16,280 is divisible by 11, since (8 + 6)-(0 -f- 2 + 1) is divisible by 11. (There is no simple method of testing divisibility by 7.) 55 56 FACTORS AND MULTIPLES 37. Factoring is the process of separating a number into its factors. . Oral Work 1. Learn the prime numbers from 1 to 100 so that you can recognize them at sight. 2. Apply the tests of divisibility to the following. Find the prime factors of : 28 160 728 478 76 720 42 320 640 96 84 37 72 48 386 84 90 145 36 360 31 92 360 390 98 280 100 81 760 625 3. What numbers between 161 and 200 are divisible by 9 ? 4. What numbers between 746 and 800 are divisible by 6 ? 5. Name the factors of 36 which are not prime to each other. 38. Cancellation is the process of shortening certain computa- tions involving division by removing or canceling equal factors from both dividend and divisor. Example. Divide the product of 4, 9, 8, 36, 24, and 7 by the product of 18, 2, 8, 3, 14, and 4. 2 18 ;t^ Solution. ^ x ^ x ^ x 3^ x ^^ x 7 ^ 3^^ ;^x;2x^x3x;^X)f In all Gomputations involving only multiplication and division, cancellation should be used when possible. Indicate the multi- plication and division as in the illustration above, then cancel the common factors. Written Work (Use cancellation when possible.) 24 X 36 X 15 . 4 X 37 X 16 X 5 X 60 1 16 X 5 X 9 * 48 X 32 X 74 48 X 32 X 100 X 360 27 x 64 x 96 x 38 16 X 50 X 72 * * 19 X 16 X 9 X 2 FACTORS AND MULTIPLES 57 130x14 X 18x121 xl5 ^ 144 x 32 x 63 x 7 7 X 27 X 13 X 11 ' ' 16 X 9 X 28 * 1728x360x100x32x3 ^ 21x72x160x340x27 7. 18 X 144 X 64 X 75 * 180 x 36 x 35 39. Greatest Common Divisor. An integer that is a factor of two or more numbers is called a common divisor, or a common factor of those numbers. The greatest common divisor of two or more numbers is the greatest factor common to the numbers. " Greatest common divisor" is usually expressed as g. c. d. Example. Find the greatest common divisor of 12, 20, and 36. Solution. 12 = 2 x 2 x 3 20 = 2 X 2 X 5 36 = 2x2x3x3. The factor 2 occurs twice in all the numbers and none of the other factors occurs in all the numbers, hence, 4 is the g. c, d. of 12, 20, and 36. To find the g. c. d. of two or more numbers, separate the numbers, into prime factors and find the product of the prime factors common to the numbers. Written Work Find the g. c. d. of : 1. 12, 18, 24. 2. 24, 60, 72. 3. 15, 20, 30. 4. 60, 90, 100. 5. 84, 32, 60. 6. 60, 96, 120. 7. 18, 32, 48. 8. 27, 36, 45. 9. 360, 120,* 40. 10. 121, 88, 242. 11. Find the g. c. d. of 8 ft. and 12 ft. 12. Find the g. c. d. of $ 48 and f 60. 40. Least Common Multiple. A multiple of a number is an integral number of times that number. Thus, 28 is a multiple of 7. 60 is a multiple of 12. 58 FACTORS AND MULTIPLES A common multiple of two or more numbers is a number that is a multiple of each of them. It is therefore divisible by each of them. The least common multiple of two or more numbers is the least number that is a multiple of each of them. Thus, 60 is the least common multiple of 12, 15, and 30. Example. Find the least common multiple (1. c. m.) of 18, 20, and 24. Solution. 18 = 2 x 3 x 3 20 = 2 X 2 X 5 24 = 2 X 2 X 2 X 3. 1. cm. = 2x2x2x3x3x5 = 360. To find the least common multiple of two or more numbers, separate each number into its prime factors. Find the product of these factors^ using each factor the greatest number of times it occurs in any one of the given numbers. Written Work P^ind the 1. c. m. of the following : 1. 12, 15. 2. 8, 12. 3. 6, 15. 4. 7, 8, 12. 5. 8, 9, 12, 15. 6. 24, 36, 60. 7. 8, 12, 16. 8. 36, 24, 75. 9. 360, 345. 10. 75, 130, 190. 11. 425, 345, 336. 12. 360, 240, 420. Find the g. c. d. and the 1. c. m. of the following : 13. 60, 80, 95. 14. 36, 75, 48. 15. 480, 360, 120. CHAPTER VII COMMON FRACTIONS 41. Terms. A fraction is one or more equal parts of a unit. A common fraction is usually expressed by writing one figure above and one below a short line; thus, |. The numerator of a fraction is the number which shows how many of the equal parts of the unit are taken. It is written above the line. The denominator of a fraction is the number which shows into how many equal parts the unit is divided. It is written below the line. The numerator and the denominator are called the terms of the fraction. Thus, 3 and 4 are the terms of the fraction |. A common fraction may be either proper or improper. A proper fraction is one whose numerator is less than its de- nominator, as |. An improper fraction is one whose numerator is equal to or greater than its denominator, as | or f . A mixed number consists of a whole number and a fraction, as 5|. Oral Work Which is greater, ^ or | ? ^ or ^^^ ? 2V ^^ t2 ^ How is the value of a fraction affected by increasing the numerator, the denominator remaining the same ? Reduction of Fractions 42. Reducing Fractions to Lower Terms. When the numerator and the denominator contain one or more common factors, the fraction may be reduced t9 a fraction of equivalent value ex- pressed in lower terms. 59 60 COMMON FRACTIONS Thus, \^ may be reduced to the equivalent fraction J, by divid ing both terms by 2. Similarly, J| = f ; g^ = J- State a rule for reducing fractions to lower terms. 43. Reducing Fractions to Higher Terms. Fractions may be raised to equivalent fractions in higher terms, hi/ multiplying both the numerator and the denominator hy the same number. Example. Express ^ as an equivalent fraction whose denomi- nator is 60. Solution. The given denominator, 5, must be multiplied by 12 to obtain the desired denominator, 60. Therefore, multiply both terms of the fraction by 12, and obtain the equivalent fraction f ^. Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction. 44. Reducing Improper Fractions to Mixed Numbers. An im- proper fraction may be reduced to a mixed number. The follow- ing example shows the method: Example. Reduce ^^- to a mixed number. Solution. 19 -=- 4 = 4|. State a rule for changing an improper fraction to a mixed number. 45. Reducing Mixed Numbers to Improper Fractions. A mixed number may be reduced to an improper fraction. The following example shows the method. Example. Reduce 13|^ to an improper fraction. Solution. 13 x 7 = 91. 91 + 3 = 94, the numerator of the improper frac- tion. The denominator of the fraction in the mixed number is retained as the denominator of the improper fraction. 13f = -"7^. Oral Work 1. Reduce to lowest terms: ^^, -f^, ^^ ^^, ^f, ||, Jf, ||. 2. Express each of the following frg-ctions with the denomina- tor 16: f,f,i, i|,|,f,i3. ADDITION AND SUBTRACTION 61 3. Express with the denominator 36: J, |, |, f^"* iV h h h 8 17 i' 9' 2' 4. Reduce to twenty-f ourths : |, -^^^ h h h iV' ^* 5. Reduce to lowest terras: -j^g' iV T*6' iV 1^2 ' ie* 6. Reduce to fiftieths: |, ^9_, JL., la, |, JL. 7. Reduce to improper fractions: 3 J, 5 J, 7|, 8|, 4f, 7|, 9^, 8|. 8. Reduce the following fractions to equivalent fractions in InwPQf tprm fraction. Add these products to form the nuynerator. Multiply the de- nominators to form the denominator. Reduce to lowest terms. Example. Add | and |. Solution. 2x4 = 8. 3x3 = 9. 9 + 8 = 17, the numerator. 3 X 4 = 12, the denominator. Hence, f + | = \h H = 1^- SHORT METHODS 71 Oral Work Add as indicated : 1- f+f 2. f + f 3. J + |. *• fff + T^- 5- l + f 6- l + f '• A + l- . 8. f +iV 9- f + tV- 57. To subtract fractions by " cross multiplication." Multiply the numerator of each fraction by the denominator of the othet fraction. Subtract these products to form the numerator. Multiply the denominators to form the denominator. Heduce to lowest terms. Example. Subtract J from |^. Solution. 5 x 3 = 15. 6 X 2 = 12. 15 — 12 = 3, the numerator. 6 X 3 = 18, the denominator. Hence, i - f = t\, t\ = i- Written Work Subtract as indicated : 1. 4 _ 1 2-8 -3. 3 4 3_ 4 7 I_ Y 3- '^- 11 6- **• 1^ TO- *• g 11 58. To find the approximate product of mixed numbers. Multiply the integers. Multiply each integer by the other fraction to the nearest unit. Add these three products. Example. Multiply 13| by 6|. Solution. 13| 6| 13 X 6 = 78 ^ of 6 = 3 f of 13 =_£ (to the nearest unit). 90 Written Work Find approximate products : 1. 431 2. 891 3. 761 4. 152 5. ggi ^^ ^ 82| 40f 47J 72 COMMON FRACTIONS 6.- 17f 46| 7. 13f 16i 8. 79| 63i 9. 38| 71i 10. 73| 96| 59. To find the product of any two numbers ending in J. (a) When the sum of the integers is an even number. To the product of the integers, add one half of their sum and annex \ t6 the result. Example. Multiply 391 by 3J. Solution. 39i n 39 X 3 = 117 i the sum of 39 and 3 = 21 138| Result, Written Work Multiply : 1. 44J 2. 181 3. 381 4. 751 641 121 141 351 5. 29J 331 6. 81| 75J (6) When the sum of the integers is an odd number. To the product of the integers, add the result obtained by taking half of one less than their sum. To this result annex 4. Example. Multiply 39 'i by 61 Solution. 39^ Ji 234 22 256f Written Work Multiply: 1. 73J 2. 571 3. 92J 4. 85J 5. 98J 42J 24J 47J 58J in 6. 29* 7. 83J 8. 76J 9. 4ej 10. 98^ 361 96J 19J 46J 231 11. 481 12. 951 13. 73J 14. 47J 15. 271 72^ 81i 71J 33| ^H CHAPTER VIII DECIMAL FRACTIONS 60. Comparison of Common and Decimal Fractions. The denominator of a common fraction may be any number, and it is always expressed. The denominator of a decimal fraction is always some power of 10, and the power is indicated by the number of figures to the right of the decimal point. 7 .7 = < 10* .07 = 7 100 007 = 7 Thus, .7 = ;^. .0007 .423 = .027 = 10000 423 1000* 27 1000 1000 61. Reading and Writing Decimals. The names of the various decimal orders are stated in the following table : CO 4^ M T3 T3 C 2 to (0 o ■o C 3 •6 x: (0 SI 0> ■a 2 3 O 1- <•< c 1 c c O c. C ^ c a> 3 f 0) 3 •~ a> h- I 1- 1- I s 1- 1 2 3 4 5 6 7 The names of the various orders should be learned. You should know that the name of the third decimal order is thou- sandths i that of the fifth is hundred-thousandths ; that of the second is hundredths, etc. 73 74 DECIMAL FRACTIONS To read a decimal fraction^ read the number as if it were an integer and then state the name of the last decimal order which a digit of the number occupies. Pronounce the word "and" at the decimal point and omit it elsewhere, except in reading complex decimals as noted below : .045 is read forty-five thousandths. .505 is read five hundred five thousandths. 500.005 is read five hundred and five thousandths. .4206 is read four thousand two hundred six ten-thousandths. .0| is read two thirds of a tenth. 2.0| is read two and two thirds of a tenth. .2| is read two and two thirds tenths (a complex decimal). Read : 2. .1764. 3. 2.04. 5. 400.004. 6. .00|. 8. .000562. 9. 64.3. 11. .003726. 12. 542.54. 14. .000241. 15. 7.00707. Write decimally : 1. Seven tenths ; forty-two thousandths ; five hundred four thousandths. 2. Four hundred and three thousandths; eight hundred two ten-thousandths. 3. Three fourths of a tenth ; two and one seventh tenths. 4. Twenty-four ten-thousandths ; five millionths ; seventeen hundred-thousandths ; two hundred and three hundredths. 5. Five hundred seventeen millionths ; sixteen ten-thousandths; eighteen hundred and fifteen ten-thousandths. 6. Five thousand four hundred-millionths ; eighteen and four thousandths. 62. Addition of Decimal Fractions. Place the decimals so that the decimal points fall vertically. Add as with integers. Place the decimal point of the sum directly below those in the numbers added. 1. .043. 4. 500.17. 7. 214.0014. 10. 14.003. 13. 3005.016. DECIMAL FRACTIONS 75 Example. Find the sum of 4.023, .507, 2.003, and 1.125. Solution. 4.023 .507 2.003 1.125 7.658 Written Work 1. Add 2569.327, 1462.978, 47.9634, 2693.072, and .019. 2. Add 27.9548, 91.0005, 37.427, and 27563.974. 3. Add 2752.9374, .0003, 23.247, and 259.6347. Change the following common fractions to decimal fractions, and add : 24 372 19 254 ' 100' 1000' 10' loo' 3 24 675 170 1000' 10000' 10 ' 10000 6. 100 1000' 10000' 1000 Copy, find the totals required. and check : $ 324.80 1 3764.20 $7436.08 ? 17.04 762.83 427.36 ? 9320.87 9402.03 92.18 ? 473.26 1.18 4724.63 ? 791.14 13420.03 • 924.56 ? ? ? ? ? 63. Subtraction of Decimal Fractions. Place the decimals so that the points fall vertically. Subtract as with integers, then place the decimal point in the remainder immediately below the decimal points above. Example. Subtract 23.213 from 34.047. Solution. * 34.047 23.213 10.834 76 DECIMAL FRACTIONS Subtract as indicated. Check the results. 1. 394.237-1.027. 2. .47 -.0003. 3. .394237 -.15. 4. 7763.421-28.796. 5. 87.5932 2.3579. Change to decimal fractions and subtract : 6 i^-^ 7 ^^^43 235 8732 236547 1000 100* * 100 1000* * 10 100000 ' 9. The sum of two numbers is 342.086. One of the numbers is 206.78. What is the other number ? 10. A man deposited $5764.80 in a bank. He later drew out 13780.92 and then he deposited 14814.60. How much had he then? 64. Multiplication of Decimal Fractions. Multiply as with integers. From the right of the product, point off as many places as the sum of the number of decimal places in the multipli- cand and the multiplier. Examples*. 1. Multiply 4.625 by .05. Solution. 4.625 ^ .23125 2. Multiply .00362 by .06. Solution. .00362 .0Q_ .0002172 Written Work Multiply as indicated. Check the results. 1. 25.763 X .1463. 2. 75.46 x .03. 3. .2462 X. 347. 4. .083 x .0462. 5. 78.23 X .000007. 6. 17.13 x .042. 7. 570.04 x .00326. 8. 1374.26 x .055. 9. $9037.28 X .035. 10. 1473.54 x .335. 11. Find the cost of 46 lots at an average cost of 1847.60. 12. Find the cost of 143 barrels of apples at an average price of 83.64 per barrel. DECIMAL FRACTIONS 77 65. Division of Decimal Fractions. a. When the divisor is an integer. Examples. 1. .12-5-4 = .03; just as 112^4 = |3. 2. .426 ^3 = .142; just as 1426 ^ 3 = 1142. In making the division the decimal point should be written in the quotient when it is reached in the dividend. 3. Divide 157.25 by 37. Solution. 4.25 37)157.25 148 9.2 7.4 1.85 1.85 h. When the divisor is not an integer. Multiple/ both dividend and divisor hy the least power of ten that will make the divisor an integer. Divide as in case a. Example. Divide .028 by .4. Solution. First multiply both dividend and divisor by 10, to make the divisor an integer. Then divide the resulting dividend, .28, by 4. The result is .07. Similarly, .0456 -- .03 = 4.56 -^ 3 = 1.52. Similarly, 5.64 - .0004 = 56400 ^ 4 = 14100. If there is a remainder after all of the decimal places in the dividend have been used, zeros may be annexed to the dividend and the division may be carried as far as is desired. Oral Work 1. .08 by .4. 2. .014 by .2. 3. .364 by .04. 4. 3300 by .11. 5. 8.48 by .008. 6. .220 by .0011. 7. 1 by .01. 8. .10 by .1. 9. .018 by 18. 10. .0001 by .00001. 11. .042 by 2.1. 12. 1.1 by .011. 78 DECIMAL FRACTIONS Written Work 1. 268632^36.9. 2. 26863.2^36.9. 3. 26863.2-^369. 4. 2686.32-^-36.?. 5. 26.8632^36.9. 6. 2686.32-- .369. 7. 26.8632- .369. 8. 26.8632 -- .0369. 9. 2.68632 -.369. 10. 2.68632^-3.69. 11. 2. 68632 -J- 36.9. 12. 2.68632-369. 13. .268632-^369. 14. 2.68632-^3690. 15. 293.45-^14.24. ' 16. 2.734-1.32. 17. .73469 -f- 127.9638. 18. 762.397^36947.28. 19. .1479376^-293.4798. 20. .0097^12.34692. 21. The multiplier is .045, the product is .01665. What is the multiplicand ? 22. At f .24 per dozen, how many eggs can be bought for 14.08? 23. If a man's annual income is $5420 and his annual expenses are $4262, what are his average weekly savings ? 24. What number is ^ as large as .0427 ? 25. What number divided by 4.28 gives a quotient of .07 and a remainder of .04 ? 26. In a certain factory 30 men are employed at f 2.15 per day, 10 men at 13.60 per day, 28 men at $2.90 a day, and 12 men at $1.80 a day. Find the average daily wage. 27. Using the current market price find the cost of the follow- ing : 1 pk. of apples, J bu. of sweet potatoes, | lb. of tea, 6 bars of laundry soap, IJ lb. porterhouse steak. 28. A train ran at the rate of .87 mile a minute. At this rate how many miles would it travel in 3 J minutes ? In 10 minutes ? In 1 hour ? 29. An automobile traveled 72.25 miles in 2 J hours. What was the average rate of speed per hour ? DECIMAL FRACTIONS 79 66. Changing Decimal Fractions to Equivalent Common Fractions. Omit the decimal point; write for the denominator 1 with as many zeros annexed as there are places in the decimal. Reduce to longest terms. Examples. 1. Change .75 to a common fraction. Solution. .75 = ^-^ = f. 2. Change .00864 to a common fraction. Solution. .00864 = Written Work Change the following decimals to equivalent common fractions and reduce to lowest terms : 1. .48. 2. .095. 3. .3705. 4. .0012. 5 8.6425. 6. .125. 7. .9825. 8. .625. 9. .1875. 10 .0015. 11. .06 J. 12. .0021. 13. .37f 14. .333. 15. .012f 16. .006|. 17. .00625. 18. .0086. 19. .008 J. 20. .0093-L 21. .OOIJ. 67. Changing Common Fractions to Equivalent Decimal Fractions. Since a common fraction may be regarded as an indicated di- vision, the reduction may be made by the methods of division previously explained. Example. Change ^ to a decimal fraction. Solution. | = ^ of 4. Place a decimal point to the right of the 4, annex .8 zeros, and divide. 5)4.0 .875 Similarly, | = 1 of 7. 8)7.000 .0053+ Similarly, ^^ = ^\^ of 2. 375)2.000 1.875 .1250 .1125 125 It is usually not necessary to carry the division more than three or four places. For example, | may be expressed decimally as .142|^ or as -.1429". 80 DECIMAL FRACTIONS Written Work Considering the figures in the top row as numerators, and those at the left as denominators, change the common fractions thus formed to decimals, entering the results in the proper places. Carry the results to three decimal places. Prepare the work on a carefully ruled form. 68. Approximate Results. For most practical purposes it is un- necessary to carry a result to more than three decimal places. Thus, $25.86347 is stated with sufficient accuracy as 125.86. In finding approximate decimal fractious, follow these direc- tions. Carry the division at least one more place than the number of digits desired in the result. If the digit at the right of the last place de- sired in the result is less than 5, drop it; if it is 5 or larger than 5, increase the preceding digit by 1. Denominators Ntjmbratobs 3 7 6 26 47 126 79 814 1216 18 27 94 38 . 172 9 66 213 793 2361 43 109 DECIMAL FRACTIONS 81 Written Work The following table gives the land area, in acres, of the differ- ent geographical sections of the United States, and the number of acres in each section devoted to farming. Prepare a ruled form similar to the model. Find what decimal part of the land area of each section, and of the United States, is improved farm land. (Approximate results to the nearest thousandth.) Also find the total land area of the United States, the total area of the improved land, and the fraction of the total area which is improved. Arrange the different sections on the blank in the order of their rank, placing the section with the largest fraction of improved farm land at the top of the blank. Total Land Area Improved Farm Land Acres Acres Decimal Fraction of Total New England Middle Atlantic East North Central .... West North Central .... South Atlantic East South Central .... West South Central .... Mountain Pacific 39,664,640 64,000,000 157,160,960 326,914,560 172,205,440 114,885,760 275,037,440 549,840,000 203,580,800 7,254,904 29,320,894 88,947,228 164,284,862 48,479,733 43,946,846 58,264,273 15,915,002 22,038,008 United States Oral Work The following table shows : The value of the butter sold in each section of the United States in a recent year. The fractions which these values were of the total production of butter in each section. 82 DECIMAL FRACTIONS Value of Butter Produced in United States Section Value of Fraction of Total Value of Total Butter Sold Product Sold Production New England .... $ 8,533,864 .725 a Middle Atlantic . 15,229,862 .655 East North Central 31,855,809 .585 West North Central 20,333,127 .438 South Atlantic . . 7,622,916 .275 East South Central 4,842,959 .167 West South Central 5,381,690 .19 2,166,918 4,410,978 .422 Pacific .572 1. By referring to the table we find that .725 of the butter produced in New England was sold. How many tenths of the butter made in New England was sold ? 2. If f 4,410,978 is about fifty-seven hundredths of the value of all the butter made in the Pacific States in a year, how would you find the total value of the butter production in this section ? Note. When in doubt whether the solution of a given problem requires multi- plication or division, replace the given numbers by smaller numbers. Reread the problem v\rith these small numbers, and decide upon the process. 3. Will the numbers to be recorded in the last column of the preceding blank be larger or smaller than those in the first column ? Written Work Rule a blank similar to the one above. Find the total value of the butter produced in each section. (Approximate results to the nearest dollar.) Enter the sections on the blank in the order of their rank as butter producers. DECIMAL FRACTIONS 83 Review of Decimal Fractions Written Work 1. In a recent year 1,591,311,371 dozen eggs were produced in the United States. The following decimals show the fractional part of this number produced in the different geographical sections. New England 035 Middle Atlantic 102 East North Central 247 West North Central 28 South Atlantic 086 East South Central 081 West South Central . • 104 Mountain 022 Pacific 043 Find the number of dozen eggs produced in each section, and tabulate this on a ruled form. How can you check the accuracy of your work ? 2. The value of the wool produced by the mountain states in 1909 was .608 more than the value of the wool produced by these states in 1899. The increase in dollars was $ 11,039,843. What was the value in 1899 ? In 1909 ? • 3. The mountain states include a large portion of the grazing land of the country and for this reason produce a large part of the wool of the countr3^ In 1909 they produced .4332 of the total value of the wool grown in the United States. By referring to your results in the preceding problem, find the total value of the wool grown in the United States in 1909. 4." In 1909 Wyoming produced the largest value of wool grown in any state of the Union. The value of its product was 18,912,608. This was what decimal part of the value of the wool product of the entire country for the year ? 5. Montana, the second largest producer of wool, raised wool valued at 18,223,754. Ohio, the third largest producer, raised 84 DECIMAL FRACTIONS wool valued at $6,749,005. Fill in the blanks in the following sentences with the proper decimal fractions: Wyoming produced times as much wool as Montana. Ohio produced as much wool as Wyoming. 6. If a boy's average gain in weight is 8.25 lb. per year, how much will he gain in weight in 2^ yr. ? 7. If one turn of a screw advances the point .14 in., how far will 7 turns advance it ? 8. A gallon of milk weighs 8.622 lb. and a gallon of water weighs 8.355 lb. How much more does J gal. of milk weigh than } gal. of water ? 9. A boy can run 100 yd. in 11.2 sec. At this rate, how long would it take him to run 80 yd. ? 10. In a certain city the rainfall during March was 2.46 in., during April 3.15 in., and during May 1.09 in. Find the average for these months. 11. A man sold 24 dozen eggs, which was .4 of all that he had. How many did he have ? 12. If .375 of an acre of land sells for |48, what should 2| acres sell for, at the same rate ? 13. An English pound contains 113.00001 grains of pure gold, and an American gold dollar contains 23.22 grains of pure gold. Find the value of an English pound in American money. CHAPTER IX SHORT METHODS INVOLVING ALIQUOT PARTS 69. Equivalent Common and Decimal Fractions in Frequent Use. .50 = f •12| = i. •06i = ,V •62i = |. .331 = J. •iH = i .05=,V .75 = 1. .25 = i. •10 = tV .40 = |. .80 =|. .20 = 1 •09i\=xV .37J = |. .83J = f. .16-1 = 1 ■m=iV .60 = f. •87HI- .14f = f •06| = iV Commit these common fractions and their equivalent decimals to memory, as they can be used to shorten many computations.^ 70. A Short Method of Multiplying by These Fractions. Which is easier, 1218 x .16| = 208 ; or i of 1248 = 208 ? State a short method of multiplying by each of the decimal fractions in the table above. Oral Work Multiply: 1. 642 X .50. 2. 936 x .33J. 3. 488 X .25. 4. 650 x .20. 5. 366 X .16f. 6. 840 x .14f . 7. 720 X .121. 8. 456 x .08f 9. 930 X .06|. 10. 320 x .06^ The results in the preceding exercise are integers. The same method may be used when the division results in a fraction. Example. Multiply 4634 by .25. Solution. .25 = I. 4634 -4- 4 = 1158.5. 85 86 ALIQUOT PARTS Oral Work Without copying, find the results of the following: 1. 8735 X .50. 2. 3940 x .33j. 3. 267 X .25. 4. 379.3 x .16f. 5. 842 X. 20. 6. 3824 x.Hf 7. 5316 X .121-. 8. 4026 x .08J. 9. 1848 X .06f. 10. 1940 x .06|. 11. 35.69 X.33J. 12. 649.3 X. 25, 13. .8347 X .50. 14. 723.68 x .20. 15. 36.92 x.l4f 16. 56.82 X. 121 17.. 7836 X Ml. 18. 1223 x .16f. 19. 3380 X. 062. 20. Find the value of each of the following: 48 lb. at 371^ per pound. 30 yd. at 62^^ per yard. 32 lb. at 12 J ^ per pound. 21 lb. at 14|^ per pound. 21 lb. at 871^ per pound. 48 yd. at 6f ^ per yard. 24 yd. at 12| ^ per yard. 96 lb. at 83^^ per pound. 71. A Short Method of Dividing by These Fractions. Which is easier, 6 ^ .25 = 24 ; or 6 x 4 = 24 ? State a short method of dividing by each of the decimal frac tions in the table on page 85. Oral Work Without copying, state the results of the following : 2. 49^.50. 4. 63-^.14f. 6. 10^.' 1. 7-5-.12|. 3. 126 -f- .33J. 5. 8-4-.06|. 7. 15-^.25. 9. 13.63 ^.1( 11. 3.249 -^ .50, 13. 63.98-*-. 2. 8. 1627^.20. 10. 1.43^.25. 12. .023-5-.08J 14. .043h-.16|, SHORT METHODS 87 72. Aliquot Parts which are not Unit Fractions. State a short method of multiplying by .37 J ; by .66| ; by .75 ; by .871. State a short method of dividing by .37 J; by .66^; by .75; by .87^. When dividing by one number and multiplying by another, observe the following directions: Divide first if the division results in an integer. If the division would result m a mixed number^ multiply first. Examples. 1. Multiply 32 by .37i. Solution. .37^ = |. 32 - 8 = 4. * 4 X 3 = 12. Since 8 is a factor of 32, the division is performed first. 2. Divide 16 by .37|. Solution. Substituting the equivalent common fraction, we have 16-4-1 = ? or 16 X f = ? Inverting the divisor. 16 X 8 = 128. 128 -^ 3 = 42|. Since 3 is not a factor of 16, the multiplication is per formed first. What advantage is there in observing these directions ? Written Work Without recopying, find the results of the following : 1. 64 X .375. 2. 96 X .66f. 3. 480 X .75. 4. 168 X .875. 5. 248 X .87|-. 6. 3260 X .75. 7. 4864 X .37J. 8. 639x.66f. 9. 42-^.37^. 10. 56 -.871 11. 40^.66|. 12. 36 ^ .75. 13. 1462 -.662. 14. 465 -.375. 15. 11322 -.75. 16. 994 -.875. 17. 426 X .875. 18. 143 X .371. 19. 1347 X .75. 20. 539 X .66f. 21. 3.29 X .75. 22. 1.267 X .875. 23. 139 -^.87J. 24. 1426-^.37^. 25. 139 ^.66|. 26. 46-f-.75. 27. 46.9 -^.37^. 28. .429 -f-.66t. 88 ALIQUOT PARTS 73. General Table of Aliquot Parts. The following table shows the most frequently used decimal parts of 1, 10, 100, and 1000. Fractions i § § i i i i of 1 .50 .331 .66f .25 .75 .125 .375 of 10 5. 3.33^ 6.66 1 2.5 7.5 1.25 3.75 of 100 50. 33.33i 66.66f 25. 75. 12.5 37.5 of 1000 500. 333^ 666| 250. 750. 125. 375. Fractions i 1 1 A A iV h f of 1 .625 m .875 .081- .061 .06i .161 .141 of 10 6.25 8.33i 8.75 ■m .625 IM 1.42 of 100 62.5 83.3i 87.5 8.3i 6.25 16f •14.28 of 1000 625. 833.3^ 875. 83i 62.5 166| 142.8 Study this table until you can recognize quickly these fractional parts of 1, 10, 100, and 1000. 74. Rules for Multiplication by Aliquot Parts of 1, 10, 100, and 1000. a. To multiply by fractional parts of 10. Multiply by the equivalent fraction ; multiply this product by 10, by moi>- ing the decimal point one place to the rights annexing a zero, if necessary. Examples. 1. Multiply 16 by 2^. Solution. 2| is I of 10. ^ of 16 = 4. Multiply by 10, by annexing a zero ; the result is 40. 2. Multiply 26 by 1.25. Solution. 1.25 is ^ of 10. \ of 26 = 3.25. Move the decimal point one place to the right; the result is 32.5. b. To multiply by fractional parts of 100. Multiply by the equivaleyit common fraction; multiply this product by 100. I SHORT METHODS 89 Examples. 1. Multiply 24 by 871. Solution. 87^ is | of 100. I of 24 = 21. 21 X 100 = 2100. 2. Multiply 4252 by 12.5. Solution. 12.5 is | of 100. I of 4252 = 531.5. 531.5 X 100 = 53,150. Oral Work State a short method of multiplying by each of the following : .06i; 2.50; 6|; m-' 250; 87J; 6.25; 37 J; 7.60; 5; 3831; 75; 125; 8^; ^■' 12.50; H' 62|; H' 8|; 25; 66*; 375; 750; 875; 37.50; 7500; 12,500. Find the products of the following. Do the work orally when possible. Be prepared to explain how the short" method was ap- plied in each example. 1. 32 X 25. 2. Ill X 3f 3. 390 X 66|. 4. 648 X 250. 5. 724 X 75. 6. 832 X 1^. 7. 96 X 871. 8. 108 X 83f 9. 3264 X .625. 10. 144 X 8J. 11. 80 X 875. 12. 48 X 375. 13. 464 X 12.50. 14. 24 X 71 15. 3.20x25. 16. .27 X 6f . 17. 8.4 X 3.75. 18. 640 X 6.25. 19. 3.612 x.83f 20. 208 X 3f . 21. 143 X 250. 22. 1936 X 62.50. 23. 1721 X 7.50. 24. 1239 X 125. 26. 426 X 750. 75. Interchanging Multiplicand and Multiplier. When the mul- tiplicand and multiplier are abstract numbers, they may be inter- changed. Example. Multiply 25 by 428. Solution. Interchanging, 428 x 25 i of 428 = 107. 107 X 100 = 10,700. 90 ALIQUOT PARTS Written Work Perform the following multiplications as indicated. Explain how the short method was applied in each example. 1. 924x12.50. 2. 864x750. 3. 125x488. 4. 264 X .12|. 5. 45 X .06|. 6. 250 x 3288. 7. 62.50x648. 8. 8J x 3.60. 9. 342x87.50. 10. 375 X 112. 11. 6| X 456. 12. 1468 x 250. 13. 875 X 88. 14. 1250 x 96. 15. 1776 x .625. 16. 7.2 X 8f. 17. li X 104. 18. 125 x 1.248. 19. 66 X 875. 20. 83^ x 9.6. 21. 62^ x 20. Find the cost of the following: 22. 12 articles at $.50 each 16 articles at .25 each 18 articles at .33 J each 30 articles at .40 each 16 articles at .75 each Total 23. 64 doz. articles at $ .62^ per dozen 76 doz. articles at 8.75 per dozen 58 doz. articles at .75 per dozen 125 doz. articles at .16 per dozen 6^ doz. articles at .32 per dozen ____^ Total 24. 72 lb. at I .83^ per pound 52 lb. at 1.25 per pound 44 lb. at .37 J per pound 90 lb. at .12J per pound 112 lb. at .06 J per pound Total 25. 80 yd. at I .621- per yard 66| yd. at 1.20 per yard 86 yd. at 1.25 per yard 25 yd. at .78 per yard 75 yd. at ,66^ per yard ^^^ Total SHORT METHODS 91 26. 83^ yd. at 11.80 per yard 12^ doz. at 1.60 per dozen 8| lb. at 1.60 per pound 6| yd. at 2.10 per yard 3 J yd. at 1.80 per yard Total 27. 135 yd. at 1. 06 J per yard 56 yd. at .08| per yard 96 yd. at .16| per yard 152 yd. at .12|- per yard 24 yd. at .07 J per yard Total 76. Rules for Division by Aliquot Parts of 1, 10, 100, 1000. a. To divide by fractional parts of 1. Divide by the equivalent common fraction. Example. Divide 13 by .121 Solution. .12\ = I 13 -^ i = 13 X f = 104. b. To divide by fractional parts of 10. Divide by 10 ; divide this quotient by the equivalent common fraction. Example. Divide 80 by 2.50. Solution. 2.50 is \ of 10. 80 - 10 = 8. 8 - J = 8 X f = 32. c. To divide by fractional parts of 100. Divide by 100 ; divide this quotient by the equivalent common fraction. Oral Work . 1. State a rule for dividing by fractional parts of 1000. 2. 1 100 will pay for how many articles at i .33^ each ? 3. 112 will pay for how many yards of cloth at $.25 per yard? 4. Which is easier — 14-^.75=? or 14--|=? 5. State how to find the total cost of some articles, when the number of articles bought is given and the cost of each is S^^ ; uy-, siy; wy-, uy-, 62y; siy. 92 ALIQUOT PARTS Without copying, state results for the following examples. State the method of operation in each. 6. 15-^.121. 7. 14-f-.061. 8. 9^.25. 9. $6-^1.75. 10. 114 ^1.87 J. 11. $8^$1.33J. State the quotients of each of the following : ] Dividend Divisor Quotient Dividend Divisor Qxtotibnt 12. 42 .331 13. 13 .25 14. 22 .66f 15. 36 .75 16. 5 * .061 17. 45 .371 18. 17 .125 19. 28 87.5 20. 15 1.25 21. 900 6.25 22. 400 8. 33 J 23. 150 Written Work .06| Complete the following : Total Cost Pkicb Each 1. $ 5.25 $ .371 -^ NUMBKB PtTKCUASED 2. 20.25 .75 3. 56.00 .66f 4. 40.00 1.25 5. 77.00 .871 6. 212.50 2.50 7. 97.50 3.75 8. Divide each of the following by .12| : .37^; .33J; .625; .871; .25: ; 1.14f 9. Find the sum decimally. of J, |, |, |, |, and J and express the sum 10. Divide 36 by each of the following : .37J; .12^; .14?; .50; .06f SHORT METHODS 93 11. How many yards can be bought in each case : Total Cost Cost per Yard Numbbe of Yards 116 $ .25 24 .33i 36 .371 • 20 .621 32 .50 26 .66| 56 1.25 44 1.33-1 24 2.66f Review of Short Methods Perform the following operations, telling what ; short method was used in each case : 1. 360-^.37 J. 2. f + |. 3. 436 X 11. 4. 65 X 25. 5. 463 X 287. 6. 1016 X 1005. 7. 3654 X 2700. 8. 105 X 126. 9. 95 X 87. 10. i-i- 11. 48{ X 63 1. 12. 611 X 121. 13. 109 X 113. 14. A + tV 15. 463 X 416. 16. 96 X 94. 17. 1015 X 1014. 18. 13 X 18. 19. 61 X 4J. 20. 825 X 927. 21. .000825x100. 22. 17x12. 23. 724 X 999. 24. 116 X 104. 25. i^h 26. 113 X 102. 27. 1026 X 1003. 28 i + h 29. 5362 X 111. 30. 433 X 99. 31. 109 X 112. 32. 976 X 990. 33. 331 X 121 34. 17 X 19. 35. 131 X 14f . 36. f + f 37. f-l- 38. 151x181 39. 96 X 88. 40. 905.387 X 3000. 41. 986 X 993. 42. 16 X 18. 43. 874 X 1236. UNITS OF MEASURE AND THEIR APPLICATIONS CHAPTER X DENOMINATE NUMBERS Tables of Weights and Measures 77. Long Measure. 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 5|^ yards, or 16J feet = 1 rod (rd.) 320 rods, or 5280 feet = 1 mile (mi.) 1760 yards = 1 mile Architects, carpenters, and mechanics frequently write ' for foot, and " for inch. Thus 8' 7" means 8 ft. 7 in. In engineering it is customary to divide the foot and the inch into tenths and hundredths, instead of into halves and fourths. There is a growing tend- ency to use the decimal division of the units. Other measures of length are : 1 hand = 4 in. Used in measuring the height of horses. 1 fathom = 6 ft. Used in measuring depths at sea. 1 knot, nautical or geographical mile = 1.1526f mi. or 6086 ft. The knot is used in measuring distances at sea. It is equivalent to 1 min. of longitude at the equator. 78. Square Measure. 144 square inches (sq. in.)= 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30 J square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) Sq. ' and sq. " are frequently used for square foot and square inch. Thus, 15 sq. ' 6 sq. " means 15 sq. ft. 6 sq. in. A square is 100 sq. ft. It is used in measuring roofing. 94 TABLES OF WEIGHTS AND MEASURES 95 79. Cubic Measure. 1728 cubic inches (cu. in.)=s 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 128 cubic feet = 1 cord A cubic yard (of earth) is considered a load. 24| cubic feet = 1 perch (P.) A perch of stone or masonry is 16J ft. (1 rd.) long, IJ ft. wide, and 1 ft. high. 80. Avoirdupois Weight. 16 ounces (oz.)= 1 pound (lb.) 100 pounds = 1 hundredweight (cwt.) 2000 pounds = 1 short ton (T.) 2240 pounds = 1 long ton (T.) Avoirdupois weight is used in weighing all ordinary substances except precious metals, jewels, and drugs at retail. The long ton is used in mining and in the United States custom- house. 81. Liquid Measure. 4 gills (gi.) = lpint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal.) A gallon contains 231 cu. in. 31.5 gal. are considered 1 barrel (bbl.). 63 gal. = 1 hogshead (hhd.). 82. Dry Measure. 2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.) A bushel contains 2150.42 cu. in. A dry quart contains 67.2 cu. in. A liquid quart contains 57.75 cu. in. 96 DENOMINATE NUMBERS 83. Measures of Time. 60 seconds (sec.)= 1 minute (min.) 60 minutes = 1 hour (hr.) 24 hours = 1 day (da.) 7 days = 1 week (wk.) 30 days = 1 commercial month (mo.) 52 weeks = 1 year (yr.) 12 months = 1 year 360 days = 1 commercial year 365 days = 1 common year 366 days = 1 leap year 100 years = 1 century 84. Counting. 12 units = 1 dozen (doz.) 12 dozen =1 gross (gro.) 12 gross = 1 great gross (gr. gro.) 20 units = 1 score 85. Wood Measure. A straight pile of wood, 4 ft. x 4 ft. x 1 ft., contains 1 cord foot. 8 cord feet, or 128 cubic feet = 1 cord. 86. United States Money. 10 mills = 1 cent 10 cents = 1 dime 10 dimes = 1 dollar 10 dollars = 1 eagle The mill is not a coin, but the term is frequently used in com- putations. The term " eagle " is not common in business. 87. English Money. 4 farthings (far.) = l penny ((?.), (plural, "pence") 12 pence = 1 shilling (s. ) = $ . 243+ 20 shillings = 1 pound sterling (£), $4.8665 DENOMINATE NUMBERS 97 88. French Money. 100 centimes (c.)= 1 franc (fr.) A franc is worth about 1 .193. 89. German Money. 100 pfennigs (pf.)= 1 mark (M.) A mark is worth about f 0.238. Written Work 1. Draw a line 1 foot long at the blackboard. Try to form a. very definite mental picture of this length so that you may be able to estimate lengths with a fair degree of accuracy. 2. Draw lines of the following lengths without any aid, then check each estimate. ^ft, 2 ft., 3 ft., I ft., 1| ft., 7 ft., 3 in., 9 in., 15 in. 3. Estimate the length and width of your desk ; the length and width and height of the classroom ; the dimensions of the school building and grounds. Check your estimates. 4. Practice estimating and stepping off various distances until you can do so with a fair degree of accuracy. 5. Lay off on the school grounds a square rod and, if possible, an acre. Estimate the areas of various lots, parks, or fields, and check your results, when possible. 6. By lifting various units of weights and then checking your own estimates of the weights of numerous objects, you can acquire the ability to estimate certain weights with but a small error. 90. Changing to Lower Denominations. Example. How many quarts in 3 bu. 3 pk. 5 qt. ? • Solution. 3 bu. = 12 pk. 12 pk. + 8 pk. = 1.5 pk. 1.5 pk. =120qt. 120 qt. + 5 qt. = 125 qt. Therefore, 3 bu. 3 pk. 5 qt. = 125 qt. After studying this solution, state a method for reducing measured quantities to lower denominations. 98 DENOMINATE NUMBERS Oral Work Reduce as indicated ; do as much of the work orally as possible. 1. 15^ yd. to feet. 2. 4| ft. to inches. 3. 5 gal. 3 qt. 1 pt. to pints. 4. 4 bu. 3 pk. 5 qt. to quarts. 5. 5 lb. 9 oz. to ounces (avoir.). Example. Reduce .345 mi. to lower denominations. Solution. 1 mi. = 320 rd. .345 mi. = 110.4 rd. 1 rd. =■ 5.5 yd. .4 rd. =: 2.2 yd. 1 yd. = 3 ft. .2 yd. = .6 ft. 1 ft. = 12 Id. .6 ft. = 7.2 in. Therefore, .345 mi. = 110 rd. 2 yd. ft. 7.2 in. After studying this solution, state a method for reducing frac- tions of a large denomination to units of lower denominations. Written Work Reduce : 1. I mi. to rods. 2. .236 mi. to feet. 3. .89 bu. to quarts. 4. ^ sq. mi. to square rods. 5. 62 rd. to feet. 6. .85 gal. to pints. 7. 4.3 mi. to feet. 8. A man bought an acre of land and sold it in building lots of 10 sq. rd. each. How many lots did he sell ? 91. Changing to Higher Denominations. When a quantity is expressed in a low denomination, it may be desired to express it in higher denominations. DENOMINATE NUMBERS 99 Examples. 1. Express 1316 pints in higher denominations. Solution. Since 2 pints = 1 quart, 1316 pints = 658 quarts. Since 4 quarts = 1 gallon, 658 quarts = 164 gals., and 2 qt. remaining. Therefore, 1316 pints = 164 gal., 2 qt. After studying this solution, state a method for reducing quan- tities to units of higher denominations. 2. Reduce 3 qt. 1 pt. to a decimal part of a peck. Solution. 3 qt. 1 pt. = 7 pt. 1 pk. = 16 pt. Therefore, 3 qt. 1 pt. = j\ pk. f J pk. = .4375 pk. Written Work Reduce to units of higher denominations : 1. 367 pints (dry measure). 2. 133 in. 3. 47 ft. 4. 12 yd. 5. 216 oz. (avoir.). 6. 31 pt. (liquid measure). 7. 2369 sq. in. 8. Reduce 4 sq. ft. 68 sq. in. to a decimal part of a square rod. 9. Reduce 1 qt. 2 pt. to a decimal part of a gallon. 10. Reduce 7 oz. to a decimal part of a pound (avoir.). 11. Reduce | yd. to a decimal part of a rod. 12. Reduce 2^ ft. to a decimal part of a yard. 13. Reduce 47 sq. rd. to a decimal part of an acre. 14. Reduce 8 J in. to a decimal part of a foot. 15. Reduce 2 J qt. to a decimal part of a gallon. 16. Reduce 4 ft. 7 in. to a decimal part of a rod. 92. Addition of Denominate Numbers. Example. Find the sum of 2 yd. 2 ft. 9 in. and 4 yd. 1 ft. 7 in, Solution. 2 yd. 2 ft. 9 in. 6 yd. 3 ft. 16 in. •7 « \ (i 4 " State a method for adding denominate numbers. 100 DENOMINATE NUMBERS Written Work Add: 1. 2yr. 5 mo. 18 da. 2. 5 gal. 3 qt. 1 pt. 5 " 8 " 19 " 4 " 2 " 1 ^' 6 " 11 " 13 " 5 " 1 u 1 u 3. 2 1b. 5 oz. 17 pwt. 4. 5 A. 126 sq. rd. 3 " 8 " 19 " 16 " 249 " " 4 " 9 " 12 " 13 » 168 " " 3. 7 mo. 12 da. 6. 12 mi. 4rd. 5 " 5 " 8 " 9 " 7. A rectangular field is 18 rd. 2 yd. 2 ft. long, and 13 rd. 1 yd. 2|- ft. wide. What length of wire will be required for a fence 6 wires high ? 8. A dealer bought 17 gal. 3 qt. of milk from each of two men, and 29 gal. 3 qt. 1 pt. from a third man. What was the entire cost at 19 cents a gallon ? 93. Subtraction of Denominate Numbers. If it is required to subtract 1 mi. 42 rd. 13 ft. from 3 mi. 25 rd. 14 ft., we write the numbers as follows ; 3 mi. 25 rd. 14 ft. 1 " 42 " 13 " When, as in this problem, the number of units of some denom- ination of the minuend is smaller than the number of correspond- ing units of the subtrahend, combine one unit of the next larger denomination with the number of units of the minuend. The problem thus becomes : 2 mi. 345 rd. 14 ft. 1 " 42 " 13 " 1 " 303 " 1 " DENOMINATE NUMBEI^ ,>, i - .,,,,,^.101 ' > 5 1 ) ^ - Written Work Subtract as indicated : 1. 13 bu. 3pk. 2qt. 2. 7 A. 5 sq. rd. 6 sq. ft. g 44 Y 44 44 2 '' '' 6 " 2 " 7 " 27 rd. 13 " 4 yd. 5 " 1ft. 19 1b. 7 " 12 oz. 14 " 4. 14 gal. 2 qt. 1 pt. 5 " 3 " 6. A man owned a field containing 1| A. From it he sold two lots each having an area of 11| sq. rd. What was the area of the part remaining ? 7. From a cask which contained 31 gal. 3 qt. 1 pt. of vinegar, 19 gal. 3 pt. were drawn out. How much remained ? 94. Multiplication Involving Denominate Numbers. Example. Multiply 3 yd. 2 ft. 7 in. by 4. Solution. 3 yd. 2 ft. 7 in. 12 yd. 8 ft. 28 in. or 15 yd. 1 ft. 4 in. Written Work Multiply as indicated : 1. 5 gal. 3 qt. 1 pt. by 7. 2. 7 lb. 5 oz. by 12. 3. 5 cu. yd. 19 cu. ft. 364 cu. in. by 13. 4. 4 mi. 19 rd. 3 yd. by 18. 95. Division Involving Denominate Numbers. Examples. 1. Divide 4568 inches by 8. Solution. 4568 in. -^ 8 = 571 in. 571 in. = 2 rd. 8 yd. 2 ft. 7 in. 2. Divide 17 gal. 2 qt. 1 pt. by 3. Solution. 17 gal. 2 qt. 1 pt. = 141 pt. 141 pt. -r- 3 = 47 pt. 47 pt. = 5 gal. 3 qt. 1 pt. 102 DENOMINATE NUMBERS 3. How many times is 4 gal. 2 qt. contained in 1 barrel ? Solution. 4 gal. 2 qt. = 18 qt. 1 bbl. = 126 qt. 126 qt. contains 18 qt. 7 times. Explain the method used in this illustration. Written Work Divide as indicated: 1. 27 cu. yd. 15 cu. ft. -^6. 2. 584 A. 8 sq. rd. -^ 8. 3. 1 sq. ft. 48 sq. in ^ 16. 4. How many times are 4 yd. 2 ft. 7 in. contained in 29 yd. 6 in. ? 5. Reduce to the decimal part of a mile: 5 rd.; 7 J rd.; 5 ft.; 13 yd.; 5 ft. 9 in. 6. An automobile traveled 1 mi. in 3|^ min. What was the rate per hour ? 7. If a man sells 17 loads of wheat, each containing 53 bu. 8 pk., at 97^ cents a bushel, how much should he receive ? 8. Fifteen cans hold an average of 10 gal. 2 qt. 1 pt. How much do they all hold ? 9. Change .427 sq. mi. to units of lower denominations. 10. A cubic foot of water weighs 62.5 lb., cast iron weighs about 7.2 as much as water; what is the weight of 2| cu. ft. of cast iron ? 11. Determine whether the window space in your school room is as much as J of the floor space. It should be at least ^ in a well-lighted room. 12. A train leaves a city at 4 : 30 p.m., and reaches a certain station 87 J mi. distant at 6 : 20 p.m. Allowing 12 min. for station stops, what is the rate of travel per hour ? 13. There are twenty-four students in a class and each needs 2J cups of hot water for a cooking lesson. How much water must there be in a kettle to supply all the class at one time, allowing 4 cups to a quart ? CHAPTER XI THE METRIC SYSTEM The metric system of weights and measures originated in France about 1800. An international convention met at Paris in 1799 and adopted the system, but it was not until forty years later that it came into general use in France. Since that time its use has become universal in scientific measurements, and it is estab- lished as the commercial system in a large part of the civilized world. The United States made the metric system "lawful" in 1866, and obligatory in Porto Rico and the Philippine Islands about 1900. The advantage of the metric system lies in the fact that it is based on a decimal scale. The only multiplier or divisor used is 10 or a power of 10. All reductions are made by merely changing the position of the decimal point. 96. Definitions of Terms. The unit of length is the meter. It is approximately 39.37 inches. The unit of capacity is the liter (leter), which is equivalent to a cube having an edge one-tenth of a meter long. The unit of weight is the gram, which is the weight of a cube of distilled water having an edge of ^o o ^^ ^ meter. 97. Fractions and Multiples of Units. Fractional parts of these units are expressed by Latin prefixes, as follows: ,^illi. _ ^^^ thousandth centi- = one hundredth, deci- = one tenth. Multiples of the units are expressed by Greek prefixes, as follows: ^^k^. ^^^^^ hekto- = one hundred, kilo- = one thousand, myria- = ten thousand. 103 104 THE METRIC SYSTEM Thus, a millimeter is .001 of a meter, a milligram is .001 of a gram, a centigram is .01 of a gram, a dekaliter is 10 liters. The prefixes and their meanings should be learned. 98. Measures of Length. 1 millimeter (mm.) 1 centimeter (cm.) 1 decimeter (dm.) 1 METER (m.) 1 dekameter (Dm.) 1 hektometer (Hra.) 1 kilometer (Km.) 1 myriameter The table may be expressed as 10 millimeters 10 centimeters 10 decimeters 10 meters 10 dekameters 10 hektometers = .001 of a meter. = .01 of a meter. = .1 of a meter. = 1 meter. = 10 meters. = 100 meters. • = 1000 meters. = 10,000 meters. follows: = 1 centimeter. = 1 decimeter. = 1 meter. = 1 dekameter. = 1 hektometer. = 1 kilometer. The following rule is 10 centimeters, or 1 decimeter, long. The smallest subdivisions are millimeters. Illllllllilllllllllllllll llllllllllllllllllllllllllll lllllllll mMH MI CENTIMETERS INCHES ilililiMlilililililililililililililililililili'ililiiililihli The meter is used for measuring certain merchandise and for otner purposes where the foot and yard would be used in the English system. It is also used in engineering and constructions. The kilometer is used for measuring distances which would be expressed in the English system in miles. THE METRIC SYSTEM 105 The centimeter is used instead of the inch in certain measure- ments such as in expressing the size of paper and books. The millimeter is used for very fine measurements in machine con^ struction and similar work. Examples. 1. Reduce 473 m. to Km. Solution. 473 m. = ,473 Km. 2. Reduce .54 Km. to m. Solution. .54 Km. = 540 m. Oral Work 1. Reduce 734 m. to Hm.; Km.; dm. 2. Reduce .042 Km. to cm.; Hm.; mm. 3. Reduce 5427 cm. to m.; Km. 4. Reduce .0037 Km. to cm. 5. Reduce 4.72 Km. to dm. 6. Reduce .034 m. to Km. 7. Reduce 1^ cm. to mm. 8. Reduce .0842 Km. to m. The advantage of the metric system is well illustrated in the measurements of distances. A distance of 1 kilometer, 6 deka- meters, 4 decimeters, 8 centimeters, is expressed as 1060.48 meters, and is read "ten hundred sixty meters and forty-eight centi- meters, just as we would say "ten hundred sixty dollars and forty-eight cents." 99. Measures of Area. The table of area is formed by squaring the units of length, as in the English system. 100 sq. millimeters (sq. mm.) = 1 sq. centimeter (sq. cm.). 100 sq. centimeters = 1 sq. decimeter (sq. dm.). 100 sq. decimeters =1 sq. meter (sq. m.). 100 sq. meters = 1 sq. dekameter (sq. Dm.). 100 sq. dekameters = 1 sq. hektometer (sq. Hm.). 100 sq. hektometers = 1 sq. kilometer (sq. Km.) 106 THE METRIC SYSTEM The abbreviations of the system are not uniform, mm. 2 is fre- quently used instead of sq. mm.; etc. The more commonly used denominations of square measure are square kilometer (sq. Km.), square meter (sq. m.), square centi- meter (sq. cm.), and square millimeter (sq. mm.) The square meter is used to measure such surfaces as those to which the square yard would apply; the square centimeter is used to measure smaller surfaces. 100. Land Measure. The are is ten meters square. It has a side about 33 feet long. The hektare, containing 100 ares, is about 2| acres. The hektare is the unit of land measure. A quarter section (160 acres) is almost exactly 64 hektares. Examples. 1. Reduce .4867 sq. m. to sq. Hm. Solution. 4367 sq. m. = .4367 sq. Hm. 2. Reduce .0547 sq. Dm. to sq. dm. Solution. .0547 sq. Dm. = 547 sq. dm. Oral Work 1. Reduce 427 sq. m. to sq. Dm; sq. Hm. 2. Reduce 87 sq. cm. to sq. m. ; sq. mm. 3. Reduce .0854 sq. Hm. to sq. m.; sq. Dm. 4. Reduce .1 sq. m. to sq. cm.; sq. mm. Written Work Complete the following, carrying results to three decimal p aces ; -j^ square meter = ? square inches. 1 square meter = ? square yards. 1 square meter = ? square feet. 1 square centimeter = ? square feet. 1 square foot = ? square meters. 1 square yard = ? square meters. 101. Measures of Volume. The cubic meter is the unit of volume. It is sometimes called the stare. THE METRIC SYSTEM 107 1000 cu. millimeters (cu. mm.) = 1 cu. centimeter (cu. cm.) 1000 cu. centimeters = 1 cu. decimeter (cu. dm.) 1000 cu. decimeters = 1 cu. meter (cu. m.) 1000 cu. meters = 1 cu. dekameter (cu. Dm.) 1000 cu. dekameters = 1 cu. hektometer (cu. Hm.) 1000 cu. hektometers = 1 cu. kilometer (cu. Km.) The abbreviations mm. 3, cm. 3, etc. are sometimes used. Examples. 1. Reduce 4386 cu. m. to cu. Dm. Solution. 4386 cu. m. = 4.386 cu. Dm. 2. Reduce .0427 cu. cm. to cu. mm. Solution. .0427 cu. cm. = 42.7 cu. ram. Oral Work 1. Reduce 37864 cu. m. to cu. Dm. 2. Reduce .04276 cu. cm. to cu. mm. 3. Reduce 742863 cu. dm. to cu. Dm. 4. Reduce .0476 cu. m. to cu. cm. Written Work A meter is approximately 39.37 inches. Complete the following table of comparisons : 1 cubic meter = ? cubic inches. 1 cubic meter = ? cubic feet. 1 cubic meter = ? cubic yards. 1 cubic foot = ? cubic meters. 1 cubic yard = ? cubic meters. 102. Measures of Capacity. The unit of capacity is the liter, which is a cubic decimeter. It equals 1.05668 liquid quarts or 0.9081 dry quart. 10 milliliters (ml.) = 1 centiliter (cl.) 10 centiliters = 1 deciliter (dl.) 10 deciliters =1 liter (1.) 10 LITERS = 1 dekaliter (Dl.) 10 dekaliters = 1 hektoliter (HI.) 10 hektoliters = 1 kiloliter (Kl.) 108 THE METRIC SYSTEM The liter serves the same purpose in measuring capacities as the quart and gallon. The hektoliter is used for measuring quantities commonly measured by the bushel in countries where the English system is used. Oral Work 1. Reduce 427 1. to DL; HI.; cl. 2. Reduce .043 Dl. to dl.; cl. 3. Reduce .04278 Kl. to. 1. ; dl. ; HI. Written Work Complete the following table of comparisons : 1 peck = ? liters. , 1 bushel = ? liters. 1 bushel = ? hektoliters. 1 hektoliter = ? bushels ? 103. Measures of Weight. The gram is the unit of weight. A liter of water weighs a kilogram, or 1000 grams. 10 milligrams C^g-) = 1 centigram (eg). 10 centigrams = 1 decigram (dg.) 10 decigrams = 1 gram (g.) 10 grams = 1 dekagram (Dg.) 10 dekagrams = 1 hektogram (Hg.) 10 hektograms = 1 kilogram (Kg.) Oral Work 1. Reduce 4736 g. to Kg.; eg.; mg. 2. Reduce .03 eg. to mg.; g.; Dg. 3. Reduce .07428 Kg. to g.; dg.; eg. Written Work A kilogram = 2.204622 pounds avoirdupois. Complete the following table of comparisons : 1 gram = ? pound avoirdupois. 1 gram = ? ounce avoirdupois. 1 kilogram = ? ounces avoirdupois. 1 pound = ? kilograms. THE METRIC SYSTEM 109 The kilogram and the " half kilo " are the common measures used in trade. A half kilo = ? pounds. The metric ton or tonneau (1000 kilograms) is used for larger weights. 1 metric ton = ? pounds 1 metric ton = ? short tons. 1 metric ton = ? long tons. 104. Comparative Table of Weights and Measures. The following table of comparisons will be useful in reducing measurements stated in the English system to equivalent metric measures, and vice versa. It is not to be memorized. 1 inch = 25.4001 millimeters, or 2.54001 centi- meters. 1 foot = .304801 meter. 1 yard = .914402 meter. 1 mile = 1.60935 kilometers. 1 square inch = 945.16 square millimeters, or 6.452 square centimeters. 1 square foot = .09290 square meter. 1 square yard = .8361 square meter. 1 square mile = 2.59 square kilometers. 1 cubic inch = 16,387.2 cubic millimeters or 16.3872 cubic centimeters. 1 cubic foot = .02832 cubic meter. 1 cubic yard = .7646 cubic meter. 1 acre = .4047 hectare. 1 liquid quart = .94636 liter. 1 liquid gallon = 3.78543 liters. 1 dry quart = 1.1012 liters. 1 peck = 8.80982 liters. 1 bushel = .35239 hectoliter. 1 grain = .06480 gram. 1 ounce (avoir.) = 28.3495 grams. 1 ounce (Troy) = 31.10348 grains. 1 pound (avoir.) = .45359 kilogram. 1 pound (Troy) = .37324 kilogram. 1 millimeter = .03937 inch. no THE METRIC SYSTEM 1 centimeter 1 meter 1 meter 1 meter 1 kilometer 1 square millimeter 1 square centimeter 1 square meter 1 square kilometer 1 cubic centimeter 1 cubic meter 1 hectare 1 milliliter 1 liter 1 liter 1 hectoliter 1 gram 1 kilogram = .3937 inch. = 39.37 inches. = 3.28083 feet. = 1.093611 yards. = .62137 mile. = .00155 square inch. = .155 square inch. = 10.764 square feet or 1.196 square yards, = .3861 square mile. = .061 cubic inch. = 35.314 cubic feet, or 1.3079 cubic yards. = 2.471 acres. = .03381 liquid ounce or .2705 apothecaries' dram. = 1.05668 liquid quarts, or .26417 liquid gallon. = .9081 dry quart. = 2.83774 bushels. = 15.4324 grains, or .03527 ounce (avoir.), or .03215 ounce (Troy). = 2.20462 pounds (avoir.), or 2.67923 pounds (Troy). Exercise State the result in each of the following in metric units. (Use a meter stick in making the measurements.) 1. Measure the edges of the cover of this book. 2. How many square centimeters in the surface of the cover? 3. How tall are you ? 4. Find the dimensions of the top of your desk. 5. What is the length of your classroom ? What is its width? Estimate its height. 6. What is the area of the floor ? (Other measurements may be suggested by the teacher). 7. Make a cube from cardboard which will contain 1 liter. THE METRIC SYSTEM 111 Using the table of comparative weights and measures, make the following reductions : 8. 1 ft. 8 in., to meters. 9. 3| meters to feet and inches. 10. 6 sq. ft. to square meters. 11. 14 square meters to square yards. 12. 36 cubic inches to cubic centimeters. 13. 130 cubic centimeters to cubic inches. 14. A bin is 8 ft. x 16 ft. x 7 ft. How many cubic meters will it contain ? 15. A horse weighs 715 kilograms. How many pounds does he weigh ? 16. The distance from Boston to Chicago by rail is 999 miles. How many kilometers ? 17. What is the cost of 16 yards of cloth at il.35 per meter? 18. A barrel (31.5 gal.) will contain how many liters? 19. If a stere is -^j of a cord, how many steres are there in a wood pile 4 ft. X 4 ft. x 17 ft. ? 20. How long would a tank 4 feet wide and 3 feet high have to be to contain 6 cubic meters ? (State your result to the near- est foot). 21. The Eiffel tower in Paris is about 300 m. high. State this height in feet ? 22. Olive oil weighs .92 as much as an equal volume of water. What is the weight of 1 liter of olive oil ? 23. If a stream flows at the rate of 1|^ Km. per hour, what is its rate of flow per second ? Express the result in centimeters. 24. A liter of mercury weighs 13.596 Kg. How many mm^. of mercury weigh 3 g. ? 25. Fifty-four miles are how many kilometers, to the nearest unit? 26. 428 ft. are how many meters, to the nearest unit ? 27. Sound travels 332 m. per second, how long will it take it to travel 4.5 Km. ? CHAPTER XII PRACTICAL BUSINESS MEASUREMENTS Plane Figures 105. Rectilinear Figures. An angle is the opening between two lines which meet. Thus the angle AOB is formed by the lines AG and OB^ which meet (intersect) at 0. The lines which intersect are called the arms of the angle and their point of intersection is called the vertex of the angle. Thus AG and GB are the arms of the angle and G is the vertex. Two angles which have the same vertex and a common arm between them are called adjacent angles. Thus the angles ^ OX and XOFare adjacent angles. i A right angle is an angle formed when one straight line meets another straight line so as to make the ad- jacent angles equal. The lines forming the angles are said to be ^ perpendicular to each other. Thus the angles MGX and XGA are right angles and the lines AM _j^ and GX are perpendicular to each ^ other. An acute angle is an angle less than a right angle. An obtuse angle is an angle greater than a right angle. Thus the angle ADB is acute and the angle BDO'i'^ obtuse. A surface has length and breadth but no thickness. A plane, or plane surface, is a level surface such as that of still water. 112 PRACTICAL BUSINESS MEASUREMENTS 113 A plane figure is a figure all of whose points lie in the same plane. A quadrilateral is a plane figure bounded by four straight lines. A parallelogram is a quadrilateral whose opposite sides are parallel. A rectangle is a parallelogram whose angles are right angles. A square is a rectangle whose sides are all equal. Parallelogram Rectangle A diagonal of a quadrilateral is the straight line connecting two of its opposite vertices. A triangle is a plane figure bounded by three straight lines. A right triangle is one that has a right angle. The hypotenuse of a right triangle is the side opposite the right angle. A triangle which has three sides equal is called equilateral. If two sides are equal it is called isosceles. If it has no equal sides it is called scalene. The perimeter of a plane figure is the sum of its sides. A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center. 114 PRACTICAL BUSINESS MEASUREMENTS The diameter of a circle is a straight line passing through the center and terminated by the circumference. ^,*cxxnifere^„ The ladlus of a circle is the straight line ©from the center of the circle to the circumfer- ence. It is equal to one half of the diameter. An arc of a circle is any part of the circum- ference. The base of a plane figure is the side on which it is supposed to stand. The altitude of a plane figure is the perpendicular distance from the highest point above the base to the base or to the base pro- duced. An area is always expressed in terms of some square unit, such as square inch, square foot, or square yard. To find the area of any figure is to find the number of square units it contains. A square whose side is one unit is said to have an area of one square unit. Thus, a square whose side is one inch has an area of one square inch. Oral Work 1. Into how many squares 1 in. on a side can you divide a rectangle 5 in. long and 1 in. wide ? 2. Into how many squares 1 in. on a side can you divide a rectangle 5 in. long and 3 in. wide ? 3. How many square feet in the area of a rectangle 7 ft. long and 3 ft. wide ? Areas of Plane Figures Tlie number of square units in the area of a rectangle is equal to the number of units in the length times the number of units in the width. Find the areas of the rectangles having the following di- mensions : 4. 12 ft. by 8 ft. 5. 3| rd. by 6 rd. 6. 25 rd. by 25 rd. 7. 11 in. by 15 in. 8. 15 in. by 15 in. 9. 35 rd. by 35 rd. 10. 16 ft. by 12 ft. 11. 3.5 ft. by 3.5 ft. PRACTICAL BUSINESS MEASUREMENTS 115 Written Work 1. How many acres are there in a rectangular field 130 rd. long and 80 rd. wide ? 2. Find the cost of painting a rectangular floor 30 ft. long and 18 ft. wide at 80 cents a square yard. 3. A rectangular floor 24 ft. long and 22 ft. wide is to be covered with tiles 8 in. square. How many tiles will be required? 4. A football field is 120 yards long and 53^ yards wide. How many acres does it contain ? 5. A tennis court is 78 ft. long and 36 ft. wide. What part of an acre does it contain ? 6. A field 96 rd.'by 130 rd. produces 2340 bu. of wheat. What is the average yield per acre ? 7. Find the area of a square field whose perimeter is 128 rd. 8. A rectangular field is 42 rd. long and 26 rd. wide. Find the cost of fencing it at $1.20 a rod. 9. Find the cost of painting the four walls of a room 14 ft. long, 10 ft. 6 in. wide, and 9 ft. high at 8 cents per square yard, no allowance being made for openings. The parallelogram ABCB may be shown to be equivalent to the rectangle AMRD by cutting off the area H and placing it in the position H' It is evident that the rule for finding the area of a parallelogram is the same as for finding the area of a rectangle. State the rule. A triangle may be shown to be equivalent to one half the area of a rec- tangle with the same base and altitude. The number of square units in the area of a triangle is equal to one half the number of units in the base times the number of U7iits in the altitude. 116 PRACTICAL BUSINESS MEASUREMENTS Oral Work State the area of the triangles whose bases and the altitudes are as follows : Bask Altitude Bask Altitude 2. 12 rd. 7 rd. 4. 101ft. 12 ft. 6. 1 ft. 4 in. 9 in. 8. 4 ft. 6 in. 20 in. 106. Circumference and Area of a Circle. Find the length of the circumferences of several circles of different sizes. This may be done as follows: Mark a point on the circumference and roll the circle along a level surface. Determine the distance between the places where the point comes in contact with the level surface. 1. 10 ft. 6 ft. 3. 4.2 rd. 20 rd. 5. 18 yd. 11 yd. 7. 3 yd. 1 ft. 2^ ft. In the figure above, the length of the line PB is equal to the length of the circumference of the circle. After the circumferences of several circles of different sizes have been measured, find the ratio of the length of the circumference of each circle to the length of its diameter. Find the average of these ratios. If the measurements were made with care you will find that, whatever the radius of the circle, the length of the circum- ference divided by the length of the diameter gives a quotient slightly larger than three. It is shown in geometry that the ratio is always the same and that it is approximately 3.1416 or ^^. This constant ratio is called tt (pronounced pi). Length of circumference -^ length of diameter = tt. C This is usually expressed as follows: — = tt, or C= ttD, PRACTICAL BUSINESS MEASUREMENTS 117 If the diameter of a circle is known, the circumferences may be found by multiplying the diameter by the value of tt. If the circumference is known, the diameter may be found by dividing the circumference by the value of tt. Note. For most practical purposes ^-^ may be used as the value of tt. Written Work Find the circumferences of the circles with the following diameters : 1. 16 ft. 2. 32 in. 3. 18 yd. 4. 3 ft. 4 in. 5. 9 ft. 2 in. 6. 110 yd. 7. 2 rd. 8. 6 ft. 8 in. 9. 2 rd. 1 yd. 10. 7 ft. 2.5 in. Find the diameters of circles with the following circumferences: 11. 110 yd. 12. 44 ft. 13. 5000 ft. 14. 5 ft. 6 in. 15. 1 mi. 16. A bicycle wheel has a diameter of 28 in. How many times will the wheel turn in going 1 mile ? 17. The inner circumference of a circular race track is one mile. The track is 90 ft. wide. How long is the outer circum- ference ? If a circle be divided as shown in the figure below, it is evident that the circle is composed of figures which are approximately triangles. The area of the circle is equal to the sum of the areas of the approximate triangles. The altitude of each of the triangles is equal to the radius of the circle, and the sum of the bases of the triangles is equal to the circumference of the circle. We may conclude, therefore, that the number of units in the area of the circle is equal to one half the number of units in the drcum- ference^ times the number of units in the radius. 118 PRACTICAL BUSINESS MEASUREMENTS Tins may be expressed as follows : area of circle = — , where Q represents the number of units in the circumference and It the number of units in the radius. Since (7= ttD, or 2 ttB, the area is equal to ^"^^ ^ ^ ^ or ttW. Hence, to find the area of a circle^ square the radius and multiply the result hy tt. Note. The parts into which the circle is divided are not exact triangles but it is proved in geometry that the area of the circle is the same as that of a triangle having a base equal to the circumference and an altitude equal to the radius. Written Work 1. Find the area of a circle the radius of which is 6 ft. 2. Find the area of a circle the radius of which is 12 ft. Com- pare with the preceding area. 3. Find the cost of painting a circular area fiaving a diameter of 1\ ft. at 75 cents per square yard. 4. Find the area inclosed by a circular running track with an inner circumference of | mi. 5. Find the area of a circular window 6 ft. in diameter. 6. Find the cost of refinishing the top of a circular table which has a diameter of 4 ft. 4 in., at 25 cents per square foot. Compute the areas of the following: 7. A triangle having a base of 11 in. and an altitude of 9 in. 8. A parallelogram having a base of 12 in. and an altitude of 3.5 in. 9. A circle having a radius of 3 ft. 7 in. 10. A circle having a circumference of 14 ft. 3 in. 11. A rectangle having an altitude of 7.5 ft., and a base of 3.45 ft. 12. A triangle having an altitude of 4 rd. 3 yd., and a base of 12.3 rd. PRACTICAL BUSINESS MEASUREMENTS 119 13. A square which has a perimeter of 14.72 in. 14. What must you know and what must you do to find the area of each of the following: circle; square; gram; rectangle ? triangle; parallelo- Land Measure 107. Description of Farm Lands. When the land of the Central and Western states was surveyed the following methods were employed : a. Imaginary lines running north and south were established and called principal meridians. These principal meridians were numbered from 1 to 24. The first runs through Ohio and the last through Oregon. h. Imaginar}^ lines running east and west were also established, and called base lines. N Base Line 6 mi." c. Lines were then run at intervals of six miles parallel to the principal meridians, and others at intervals of six miles parallel to the base lines. 120 PRACTICAL BUSINESS MEASUREMENTS d. The land was thus divided into tracts 6 miles square. Each such area is called a township. The townships are de- scribed by their relation to the principal meridians and to the base line. The township marked A is described in real estate records thus : Twp. 2 N, R 3 E of the * principal meridian. Twp. 2 N means that it is in the second row of townships north of the base line ; while R 3 E means that it is in the third row east of the specified principal meridian. Description of Qi Twp. 2 S, R 2 W. Describe townships marked D and B. What is meant by Twp. 3 N, R 1 W ? Twp. 3 S, R 2 E ? e. Each township is divided into sections, one mile square. Each section, therefore, contains 640 acres. The sections are numbered as shown in the following plot. 6 5 4 3 2 1 7 8 9 10 11 12 18 17 16 15 14 13 19 20 21 22 23 24 30 29 28 27 26 25 31 32 33 34 35 36 Assuming that this is a plot of township A in the figure on page 119, the 25th section would be described as follows : Section 25, Twp. 2 N, R 3 E of the principal meridian. Fractions of a section are often sold, and the following method of description is used. * Here is stated the number of the meridian. PRACTICAL BUSINESS MEASUREMENTS 121 The section is divided into quarters. M is described as the northwest \ of Section 25, Twp. 2 N, R3E. H is described as the southeast \ of Section 25, Twp. 2 N, R3E. Section 25 North North West M East 160 Aares Q South South West East H If iff and Q were sold together, they would be described as the north I of Section 25, Twp. 2 N, R 3 E. The following diagram shows a section divided into various farms, with their descriptions. Section 25 N W West V2 Section Westy2 of , N.E./^ N.E.H of N. E.h S.E.H of N.E.'4 Southeast 122 PRACTICAL BUSINESS MEASUREMENTS Written Work Since a section is a mile square, each side of the section is 320 rd. in length. S.tate the dimensions of each of the farms shown in the diagram on page 121 ; thus, The west ^ of Section 25 is 160 rods east and west by 320 rods north and south and contains 320 acres. 108. Measurements of Farm Lands. The unit of farm land measure is the acre, which contain 160 square rods. Thus, a piece of land 10 rods wide and 16 rods long contains an acre, or a strip of land 1 rod wide and 160 rods long contains an acre. Oral Work 1. Locate farms on plot of Section 25 having the following dimensions. How many acres in each ? a. 160 rods x 80 rods. h. 160 rods x 160 rods. c. 320 rods x 160 rods. d. 80 rods x 80 rods. 2. The owner of the southwest | sells a strip 20 rods wide along the south side of his farm. How much does he receive at il50 per acre? Describe the property sold. 3. The owner of the S. E. { of the N. E. ^ sells the north half of his farm for f 125 per acre. How much land did he sell ? Describe it. What was the total selling price ? Square Root and its Applications 109. Extracting the Square Root. The square of a number is the product obtained by using the number twice as a factor. Thus, since 3x3 = 9; 9 is the square of 3. The square root of a number is qne of the two equal factors of the number. Thus, the square of 4 is 16. The square root of 16 is 4. The square root of a number may be indicated by writing the number under the radical sign or by placing *' | " above and to the right of the number. Thus, both Vl44 and 144- indicate the square root of 144. PRACTICAL BUSINESS MEASUREMENTS 123 Oral Work What is the square root of each of the following : 36, 64, 81, 169, 225, 25, 49, 1, 256, 400, 100, 10,000? How many digits in the square of each of the following : 1, 9, 10, 99, 100,' 999, 1000, 9999? How does the number of digits in the square of a number com- pare with the number of digits in the number ? The square of 53 may be found as follows : 50 + 3 50 + 3 502 = 2500 (50x3) + 32 2(50 X 3) = 300 502 +(50x3) 32= 9 502 + 2(50x3) +32 * 2809 By squaring several numbers, as illustrated above, you will un- derstand that the square of a number is equal to the square of the tens, plus twice the product of the tens by the units^ plus the square of the units. This principle may be applied in finding the square root of numbers whose square root cannot be found by inspection. The square of a number contains twice as many digits, or one less than twice as many digits, as the original number. Hence, if an integer be separated into groups or periods of two digits each, from right to left, there will be as many digits in the square root as there are groups of digits in the original number. Example. Find the square root of 576. Solution. Beginning at the right, separate the digits into groups of two each. The greatest square in 5 is 4, and the square root of 4 is 2. .Two is therefore the tens digit of the root. q a Find the remainder and annex the next group (76). — — The result is 176. We have taken the square of the tens from the "^ '^ number, hence the remainder (176) must contain twice the product of 4 the tens by the units plus the square of the units. Twice two tens is 40' 176 four tens or 40. 40 is contained 4 times in 176. Hence, 4 is the units' 4 176 digit of the root. Twice the tens, times the units, plus the square of TT the units, is the same as the sum of twice the tens, and the units, ' times the units. Therefore, add 4 units to the 40 and multiply the result by 4. The result is then 176. Therefore, the square root of 576 is 24. 124 PRACTICAL BUSINESS MEASUREMENTS To find the square root of a number. Begin at the units and separate the number into groups of two digits each. Find the greatest sq^iare in the left-hand group, and write its square root for the first digit of the required root. Subtract the square of the root digit from the left-hand group and then annex the second group for a dividend. Annex a zero to the part of the root already found and multiply the re- sult by two. Divide the dividend by this product. Place the quotient as the next figure of the root. Add the quotieyit to the divisor and multiply the result by the digit of the root just found. Continue in like manner until all of the groups have been used. The result will be the square root. (It may not be the exact square root, as indicated in the note on page 125.) If the number contains a decimal fraction, begin at the decimal point and separate the number into groups of two digits each ivay from the decimal point. If the last group on the right of the decimal point has but one fig- ure, annex a zero. Each decimal group) must contain two figures. To find, the square root of a commoii fraction ivhose numerator and de- nominator are not perfect squares, first reduce the common fraction to a decimal, then extract the root. Examples. 1. Extract the square root of 16,641. Solution. 2 _?. _E 1 66 41 1 20 66 2 44 22 2241 240 9 249 2241 2. Extract the square root of 18.0625. Solution. 4. 2 5 18. 06 25 16 80 206 2 164 82 4225 840 5 845 4225 PRACTICAL BUSINESS MEASUREMENTS 125 Written Work Find the square root of : 1. 3325. 2. 9025. 5. 52.9984, 9. .0256. 6. .005476. 10. 3. 3. 89.25. 4. .1764 7. 5. -!■ "•!■ 12. 7. Note. If a number is not a perfect square, its approximate square root may be found by placing the decimal point in its proper place and annexing zeros to the right of ohe last digit. It is usually not necessary to find a root to more than two or three decimal places. 110. The Square and the Right Triangle. Since the number of units in the area of a square is found b}^ squaring the number of units in one side, it follows that the square root of the number of units in the area is the number of units in one side. It is proved in geometry that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. This is illustrated in the figure. The length of the hypotenuse is equal to the square root of the sum of the squares on the other two sides. To find the length of either side, extract the square root of the difference between the square on the hypotenuse and on the other side. 'c o, b Written Exercise A square field contains 9025 sq. rd. Find the length of one 1. side. 2. The base lines on a ball field are each 90 ft. in length, and are at right angles to each other. What is the distance from home plate to second base ? 126 PRACTICAL BUSINESS MEASUREMENTS 3. A tennis court is 78 ft. long, and 36 ft. wide. What is the length of the diagonal ? 4. A ladder 19 ft. long placed on level ground reaches 13 ft. up a wall. How far is the foot of the ladder from the wall ? 5. The rafters of a building are 25 ft. long. The ridge of the roof is 18 feet above a line joining the foot of the rafters. How wide is the building ? 6. A rectangular corner lot is 90 ft. long and 60 ft. wide. A path runs diagonally across it. What distance is saved by using the path? 7. A guy rope 80 ft. long is attached to a flagpole at a point 54 ft. above the ground. How far from the foot of the pole may the rope be made to touch the ground when stretched taut ? 111. To find the area of a triangle when the length of each side is known. When the altitude of a triangle is not known but the length of the sides is known, the area may be found as in the following : Example. Find the area of a triangle the sides of which are 12 ft., 14 ft., and 22 ft. Solution. 12 + 14 + 22 = 48. ^ of 48 = 24. 24 - 12 = 12. 24 - 14 = 10. 24 - 22 = 2. 24 X 12 X 10 X 2 = 5760. V5760 = 75.88, the number of square feet in the area. Rule. From one half the sum of the three sides subtract each side separately. Find the product of the half sum and of the three remainders. Extract the square root of this product. Tlie result is the number of units in the area. Written Work 1. Find the area of an equilateral triangle the sides of which are 8 inches. 2. The perimeter of an isosceles triangle is 28 inches. One of the equal sides is 9 inches. Find the area. PRACTICAL BUSINESS MEASUREMENTS 127 3. Compare the area of an equilateral triangle with a side of 4 inches with that of one with a side of 8 inches. 4. Find the value at $160 an acre of a triangular field having sides of 60 rd., 78 rd., and 84 rd. respectively. Roofing 112. Roofing is generally measured by the square of 100 square feet. Shingles average 4 in. in width, and are usually laid 4 in., 4J in., 5 in., or 5 J in. to the weather. A bunch of shingles contains 250. Part of a bunch is not sold. The following table shows the usual estimate per square. > TO Weathbb NUM] BER PER Square 4 in. 1000 41 in. 900 5 in. 800 51 in. 700 Slate varies in size. It is usually 16'^ by 24^', or Q" by 12". Written Work 1. When shingles are laid A" to the weather, how many 4-in. shingles cover a square foot ? How many to the square foot when they are 5^' to the weather ? 2. A roof is 42 ft. long and 28 ft. wide on each side. How many bunches of shingles will be required to cover it, if the shingles are laid 5 in. to the weather ? 3. At ^4.50 a square what will be the cost of tinning a roof 22 ft. by 18 ft.? 4. A roof is 40 ft. long and 30 ft. wide on each side. How many shingles, laid 5 in. to the weather, will be required to cover it? 5. How many bundles of shingles, li^id 5 in. to the weather, will be required for a roof 28 ft. by 21 ft. ? 128 PRACTICAL BUSINESS MEASUREMENTS The pitch of a roof is found by dividing the rise in the rafters by the width of the base of the gable. If the rafters rise 10 ft. Base of Gable 16 ft. and the base of the gable is 40 ft., the pitch of the roof is ^. pitch of I is called the Gothic pitch. Written Work Find the pitch of the roof in each of the following : Width of Bask Height 45 ft. 20 ft. 36 ft. 18 ft. 64 ft. 16 ft. 20 ft. 5 ft. 24 ft. 15 ft. 3ight of the gable. Width of Base Pitch of Eoof 50 ft. h 20 ft. i 32 ft. Gothic Flooring 113. Flooring is usually measured by the square or by the thousand square feet. There is some waste when lumber is "tongued" and "grooved." Dealers measure the width before the lumber is matched. The amount of waste depends upon the width of the lumber. It is customary to allow ^ for flooring 3 in. or more in width and J for flooring less, than 3 in. in width. Illustration. How many square feet of 4-in. flooring will be required for a room 28 ft. by 24 ft.? 28 X 24 = 672, the number of square feet to be covered. 1^ X 672 sq. ft. = 840 sq. ft., the quantity required. PRACTICAL BUSINESS MEASUREMENTS 129 Written Work 1. A room is 24 ft. by 36 ft. Find the cost of the 2|^-in. floor- ing at $ 50 per thousand square feet. 2. Compute the cost of flooring a hall 72 ft. by 50 ft., with 4-in. lumber at $ 30 a thousand, incidentals $ 28.40 extra. 3. How many feet of 4-in. flooring will be required for a hall 60 ft. by 42 ft.? 4. What will the 4-in. flooring for a hall 60 ft. by 42 ft. cost at $ 36 per thousand ? Plastering, Papering, Painting, Carpeting 114. Plastering is usually measured by the square yard. There is no uniform rule regarding allowances to be made for openings. To find the area of the walls, multiply the perimeter by the height. The dimensions of a room are usually stated in the following order: length, breadth, height. Thus the dimensions of a room 18 ft. long, 14 ft. wide, and 9 ft. 6 in. high would be indicated as follows: 18 ft. x 14 ft. x 9 ft. 6 in. or 18^ x 14^ x 9' 6". Wall paper is generally 18 inches wide. It is sold by the single roll of 8 yards or by the double roll of 16 yards. Complete rolls must be bought. There is no uniform procedure in making allowance for openings. Some paper hangers deduct the total width of all openings from the perimeter of the room, and cover the spaces about the openings with the parts of strips left from the rolls. Painting is usually measured by the square yard. It is not customary to make any allowance for openings. Carpet is sold by the linear yard regardless of its width. Ingrain carpets are usually 1 yard wide, other carpets are usually I yard wide. Carpets are generally laid lengthwise of the room. It is some- times more economical to lay a carpet crosswise. Fractional lengths, but not fractional widths, may be bought. Allowance must sometimes be made for matching designs. 130 PRACTICAL BUSINESS MEASUREMENTS Written Work The six rooms of a house have the following dimensions and openings: Living room, 20' x 16', 3 windows 3' x Q' 6'', and two doors 3' 6" x 1' &'. Dining room, 15' x 13' 6", 2 windows 4' x 6', and two doors 3' 6" x 7'. Two bedrooms, each 14' 6" x 12' 6", 2 windows 4' x 6' 6", and 2 doors 3' 6" x 7'. Kitchen, 15' x 15' 6", 3 windows 4' x 7', and 2 doors 3' 6" x 7'. Bathroom, 10' 6" x 8' 6", 1 window 3' x 5', 1 door 3' 6" x 7'. All rooms are 9 ft. high and the baseboards are 1 ft. wide. 1. Find the cost of plastering the walls and ceiling of eacli room at 35 cents a square yard, allowing for one half the openings. 2. Find the cost of papering the walls of the living room and the dining room at f'l.lO a double roll, making one half allowance for openings. 3. Find the cost of caicimining the ceilings of these two rooms at 60 cents a square yard. 4. Find the cost of papering the walls of the two bedrooms at 90 cents a double roll, making full allowance for openings. 5. How many square yards of linoleum will be required to cover the floors of the bathroom and the kitchen ? 6. Find the cost of painting the baseboards in the six rooms, at 40 cents a square foot, allowance being made for all openings. 7. How many gallons of paint will be required for two coats on a building 32 ft. by 24 ft. by 18 ft., if the first coat takes one gallon for 52 sq. yd. and the second one gallon for 74 sq. yd. ? Solids 115. Rectangular Solids. A solid has three dimensions: length, breadth, and thickness. A rectangular solid is bounded by six rectangular surfaces. Such a solid is called a prism. The bases of a prism are equal and parallel. A cube is a rectangular solid having six square faces. A cube 1 unit long, 1 unit wide, and 1 unit thick contains PRACTICAL BUSINESS MEASUREMENTS 131 1 cubic unit. Volumes are always measured in terms of some cubic unit. How many cubic inches in a block 1 in. long, 1 in. wide, and 1 in. thick ? In a prism 5 in. long, 1 in. wide, and 1 in. thick ? in a prism 5 in. long, 3 in. wide, and 1 in. thick ? in a prism 5 in. long, 3 in. wide, and 2 in. thick ? It is evident that the number of cubic units in the volume of a rec- tangular solid is equal to the product of the number of units in its three dimensions. Written Work Compute the volumes of the following; 1. A cube with an edge of 35 in. 2. A rectangular solid 7' x 8' X 5' &', 3. A piece of ice 2J^ x 1|' x 9^ 4. A piece of timber 22 ft. long, 1| ft. wide, and IJ in. thick. 5. How many cubic feet of earth must be removed in digging a cellar 20' X 18' x 7'? 6. Compute the cost of a stone wall 24 ft. long, 3.5 ft. wide, and 4 ft. high at $3.65 a cubic yard. 7. A swimming tank is 44' by 28' by 9'. How many cubic feet of water does it contain when filled to a depth of 4' ? 8' ? 8. A ditch for some sewer pipe is to be made 1200 yd. long, 3 ft. wide, and 7 ft. deep. Compute the cost of making the exca- vation at 28 cents per cubic yard. 9. Compute the number of cubic feet of air space allowed each student in your schoolroom. 10. Compare the volumes of two rectangular pieces of ice having the same length and breadth, the thickness of one being twice that of the other. \\, Compute the volume of a rectangular bin 18' x 16' x 7'. 12. Find the capacity in bushels of a grain elevator 60' x 42' X 24'. (A bushel is equivalent to 1\ cu. ft.) 132 PRACTICAL BUSINESS MEASUREMENTS 116. A cord of wood or stone is a pile 8 ft. long, 4 ft. wide, and 4 ft. high. It contains 128 cu. ft. In certain localities a cord of wood means a pile 8 ft. long, and 4 ft. high, the price varying with the length of the stick. Written Work 1. A pile of four-foot wood ten feet high and forty-two feet long was cut from a ten-acre tract. What was the average num- ber of cords per acre ? 2. How many cords of wood in a pile 30 ft. by 4 ft. by 9 ft. ? 3. How many cords of 4 ft. wood in a pile 16 ft. by 8 ft. by 12 ft. ? 117. A cylinder is a solid bounded by two bases which are equal parallel circles and by a uniformly curved surface. The curved surface of a cylinder is called its lateral surface. If the lateral surface of a cylinder be exactly covered with paper and the paper then removed, the paper will be seen to have the form of a rectangle the base of which is the length of the cir- cumference of the cylinder and the altitude is the height of the cylinder. Hence, the number of units in the lateral area of a cylinder equals the product of the number of units in the circumference by the number of units in the altitude. To find the entire surface of the cylinder the areas of the two circular bases must be added to the lateral area. It is shown in geometry that the number of units in the volume of a cylinder equals the product of the number of units in the area of the base and the number of units in the altitude. Written Work 1. Compute the entire surface of a cylindrical cup having a diameter of 3 in. and an altitude of 7 in. Determine the cubic contents of this cup. 2. A cylindrical cistern having a radius of 4|^' is filled with water to a depth of 9'. How many cubic feet of water are there in the cistern ? PRACTICAL BUSINESS MEASUREMENTS 133 3. A cylindrical tank 22 ft. in diameter is filled with water to the depth of 18 ft. What is the weight of the water (1 cubic foot of water weighs 62.5 lb.) ? 4. A man contracted to dig a cistern 7 ft. in diameter, 24 ft. deep at the rate of 11.20 per cu. yd. Find the entire cost. 5. Find the cost of cementing this cistern at $ 1.80 per square yard. 6. How many yards of sheet iron will be required for a smoke- stack 3 ft. in diameter and 24 ft. high, allowing 1 in. for the lap ? What will be the cost at 14 cents per square foot ? 7. If a steam roller is 5 ft. high and 7 ft. long, how many square feet of ground will it roll at each revolution ? 8. At 7J gal. to the cubic foot what will be the capacity of a cylindrical tank having a base of 6 ft. and an altitude of 14 ft. ? 9. A farmer has a roller 2-| ft. in diameter and 6 ft. wide. Allowing 4 in. for lapping, how far must the team travel in rolling a rectangular field 80 rd. long and 56 rd. wide ? 10. At 60 cents a square yard find the cost of polishing a cylin- drical monument 14 ft. high and 4 ft. in diameter. 118. The sphere. It is shown in geometry that the number of units in the surface of a sphere is equal to 4: ir times the square of the number of units in the radius; and the number of units in the volume of a sphere is equal to ^ tt times the cube of the number of units in the radius. Written Work Find the surfaces and volumes of spheres of radii: 1. 3'^ 2. 1". 3. 2.5'^ 4. 13'. 5. 24.2''. 6. 8.24'. 7. 6.3". 8. 14.1'. 9. 8.7'. lo. 12.3". 11. A ball with a radius of 18 in. is to be gilded. How many square inches of gilding will be required ? 119. Capacity. Grain is usually estimated by the stricken bushel of 2150.42 cu. in. ; fruits, vegetables, coal, and corn on the cob by the heaped bushel of 2747.71 cu. in. Since a stricken bushel is 2150.42 cu. in., and there are 1728 134 PRACTICAL BUSINESS MEASUREMENTS 1728 cu. in. in 1 cu. ft., therefore, 1 cu. ft. contains -^prrTr-ri) bushels or approximately .8 of a bushel. To find the number of bushels of grain a bin will hold, multiply its capacity in cubic feet by .8. 1728 A cubic foot of space will contain ^ heaped bushels, or .63 heaped bushels. To find the number of heaped bushels that a bin will hold, midtiply its capacity in cubic feet by .63. ' Written Work 1. How many bushels of potatoes will just fill a bin 18' x 7' x 5' ? 2. How many bushels of wheat will just-fill a bin 30' x & X 6'? 3. A wagon bed is 10' long, 4' wide, and 2^' deep. How many bushels of wheat will it hold ? 4. Mr. Williams wishes to build a bin that will store 250 bushels of wheat. He expects to make the bin 24' long and 6^' wide. What must be the depth ? 5. A car 34' long and 7' wide is filled with oats to a depth of 4^'. How many bushels of oats are in the car ? A gallon is equal to 231 cu. in. A cubic foot of space, there- fore, contains -J-^^- gallons, or 7.48 gallons. To find the number of gallons when the cxibic contents may be founds multiply the capacity in cubic feet by 7.48. (^In practice 1 cu. ft. is considered equal in capacity to 7 J gallons.) Written Work Find the capacity in gallons, of : 1. A cistern 12' in diameter and 18' deep. 2. A tank 12' long, 4^' wide, and 5' deep. 3. A cistern 14' in diameter and 20.5' deep. 4. What is the capacity in gallons of a cylindrical tank 18.5' in diameter and 32' deep ? 5. A cylindrical standpipe 60' high has a diameter of 14'. How many gallons of water will it hold ? PRACTICAL BUSINESS MEASUREMENTS 135 120. Board Measure. The board foot is the unit of lumber measure. It is a board 1 ft. long, 1 ft. wide, and 1 in. thick. The volume of a board foot is therefore, 144 cu. in. (except when the lumber is less than 1 in. in thickness). Boards having a thickness of less than 1 in. are considered as having a thickness of an inch. A board 16 ft. long, 12 in. wide, and 1 in., or less, in thickness contains 16 board feet. If the thickness were IJ in., the board would contain 24 board feet. In measuring boards that taper uniformly the average width is used. The width of boards, except in expensive lumber, is generally taken as the next smaller half inch. When no thickness is mentioned the thickness is understood to be 1 inch. It should be evident that the number of hoard feet is the product of the width in inches^ hy the thickness in inches^ by the length in feet^ by the number of pieces^ divided by 12. Illustration 1. How many board feet in 24 scantlings, 2" x 4'', 16'? 24 X 2 X 4 X 16 ^ 256, the number of board feet. 12 Illustration 2. How many board feet in 18 pieces, each ^" x 9'', 16'. 18 x4x 9 X 16 ^ gg^^ ^j^^ number of board feet. Oral Work Compute the number of board feet in each of the following : 1. A board 12 ft. long, 1 ft. wide, and 1 in. thick. 2. A board 7 ft. lohg, 2 in. wide, and 1 in. thick. 3. Two boards each 10 ft. long, 4 in. wide, and 1 in. thick. 4. Two boards each 14' x 4" x 12". 5. Twenty boards each 10' x 3" x |'^ 6. One hundred boards each 14' x 4" x 2". 7. Twenty-five boards each 9' x 2" x 1". 8. Three hundred boards each 15' x 4" x f ". 9. Fifty boards each 12' x 6" x 2". 136 PRACTICAL BUSINESS MEASUREMENTS Dealers sometimes use a table in determining the number of board feet in a given piece of timber. A portion of such a table is given below. Le>ngtu in Feet 10 12 14 16 18 2x4 ^ 8 n lOf 12 2x6 10 12 14 16 18 2x8 m 16 18| 21^ 24 2 X 10 16f 20 23i 26f 30 2 X 14 231 24 32f 37i 42 2^ X 12 25 30 35 40 45 2| X 14 29^ 35 40i 46| 52| 3x6 15 18 21 24 27 3x8 20 24 28 32 36 Written Work Determine the number of board feet in : 1. 40 pieces of white pine 2" x 10^ 18'. 2. 130 joists 2" X 8^ 16^ 3. 36 beams 4^' x 8^ 20. 4. 20 planks 2^" x 8^ 18'. 5. 80 joists 4." X 4'', 20'. 6. At $15 a thousand, find the cost of the following : 14 joists, 2''x 6'', 18' 24 joists, 2" X 10", 32' . 80 boards, |" x 4", 16' 30 scantlings, 2" x 4", 16' 20 beams, 8" x 9", 16'. CHAPTER XIII Bed Room ll'xl2' DRAWINGS AND GRAPHS Newspapers, magazines, and trade journals make frequent use of drawings or graphs in order to make clear the relations between magnitudes. A graph will often reveal a relationship much more quickly and more clearly than a table of statistics. 121. Purposes of Drawings and Graphs. Drawings and graphic representations are extensively employed for two purposes : a. For reference, to show quickly and conveniently the shape and dimensions of -^^__________^^^ fields, rooms, build- I | Q ings, furniture, ma- chinery, etc. Dimensional drawings and dia- grams, similar to this one, are of great value. An architect designs a building, and the contractor builds it in accordance with the plan shown by the drawing. Tools and machinery are usually constructed in accordance with drawings prepared by draftsmen and designers. h. To present sta- tistics in a manner Floor Plan of a Bungalow Scale ^=1' . 138 DRAWINGS AND GRAPHS which will show their meaning and their relationship more clearly than can be done by columns of figures. For example, the rela- tive importance of Louisiana as a producer of cane sugar is made clearer by the following graph than by the table of statistics. Value of Cane Sugar Produced in Certain States in 1909 State Dollars Louisiana 17,752,537 Georgia 2,268,110 Texas 1,669,683 Alabama 1,527,166 Mississippi 1,506,887 Florida 1,089,698 Millions of Dollars 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Louisiana ^■"' ^'^ "*" „^ ^^ ^^ ""^ ^^^ ■"" Georgia "" — "^ " Texas Alabama ^"* ■" Mississippi *^" ** Florida — 122. Drawing to Scale. The ability to read drawings and graphic representations intelligently depends somewhat upon a knowledge of how to draw figures to scale. The values represented by the lines in drawings and graphs can be easily determined because the lines are drawn to scale ; that is, a certain distance on the drawing represents a specified amount of the quantity represented. In the floor plan, on page 137, one foot of true distance is repre- sented by -^2 ^f an inch plotted distance on the drawing. All lines in the drawing correspond to this scale. In the graph showing the production of cane sugar, ^ inch represents a value of $ 1,000,000. 123. Types of Scales. The scale may be stated in various ways, the most common of which are : DRAWINGS AND GRAPHS 139 a. A fraction. For example, a scale of \ means that the true distances or values are four times as great as the plotted distances or values. h. Statement of equivalent dimensions or values. For example, V^=V . (Read 1 in. = 1 ft.) One inch of the drawing represents one foot of the real object. In the graph showing cane sugar production the scale is f = $1,000,000, that is, | inch rep- resents 11,000,000. c. A diagram or scaled rule accompanying the drawing. This is the method commonly used in map drawing. Thus, in the map shown here, the scale is indicated. Scale 3U Miles to 1 loch 5 10 15 20 25 d. The graph may be drawn on ruled paper, the distance be- tween the ruled lines representing a specified value. Exercise 1. A scale of 1'' = l^ is equivalent to what fractional scale ? 2. A scale of 1^' = 5'', is equivalent to what fractional scale ? 3. A scale of 1^' = 5^ is equivalent to what fractional scale ? 4. If the scale is J^^ what distance on the drawing would repre- sent 6' 3''? 4' 9^'? 5. If the scale is ^^, what plotted distance would represent 750 feet ? 750 inches ? 6. If the scale is 1" = 1000 bushels, what distance on a graph would represent 5125 bushels ? 8500 bushels ? 1750 bushels ? 140 DRAWINGS AND GRAPHS The following floor plan is drawn to a scale of Jg. 7. One inch of plotted dis- tance on the floor plan is equiva- lent to how many feet of true distance ? 8. One foot of true distance on the floor plan is represented by what part of an inch on the drawing ? 9. What are the true di- mensions of this room ? 10. Assume that this draw- ing is made to the scale,, | in.= 1 ft. (y = 1'). What are the true dimensions of the room? 11. The map on p. 139 is drawn to the scale 1'^ = ? miles. 12. ^' ' on this map represents what true distance ? 13. What is the true distance between each of the towns on the railroad ? Measure distances from centers of towns. 14. An electric railroad is in process of construction between Morton and Harritown. It is surveyed in a direct line. How much shorter will this road be than the one via Sterling ? 15. It is planned to locate a power house halfway between Sterling and Harritown. Indicate its position on the map and determine its distance from the two towns. How far will it be from the nearest point on the new electric line ? The following is an illustration of a graph drawn on ruled paper. The figures along the top of the graph indicate the num- ber of millions of bushels of wheat grown. Quantities smaller than 10,000,000 bushels can be approximated with sufficient accu- racy for general comparative purposes. For example, the wheat crop of 1870 is shown by the graph to have been about 236,000,000 bushels, and that of 1904, about 553,000,000 bushels. DRAWINGS AND GRAPHS 141 Millions of Bushels 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 1870 1875 1880 1885 1890 1895 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1 1910 Oral Work 1. What was the approximate crop of each of the years shown? 2. What was the record crop shown by the graph ? 124. Determining the Scale. When a drawing or a graph is to be made, it is first necessary to determine the scale. The scale de- pends, in general, upon three things : a. The size of the paper to be used. h. The largest dimension to be shown on the graph. e. Convenience in showing fractional parts of the scale. 142 DRAWINGS AND GRAPHS Example. A room is 15' 6" long by 10' 3" wide. What scale should be used to show a diagram of this room on a sheet of paper 8" by 10", leaving a margin of at least one inch around the drawing? Solution. The largest dimension of the room is 15' 6", or 186". The largest dimension of the paper is 10 inches. After deducting 2 inches for margins, there is a space of 8" available for the drawing. The largest scale possible, therefore, is 8" represents 186". This is equivalent to a scale of 1" = 2^1". (How was this determined?) For convenience in showing fractional parts of a foot, it will be better to use the scale of 1" = 24". Written '^ork 1. With the scale 1" = 2', what length lines would represent the dimensions of the room 15' 6" xlO' 3" ? 2. Use this scale to make a drawing of a room 12' G" by 9' 9". 3. A field is 120 rods by 80 rods. Scale, 1"=1 rod. How large a paper is needed to diagram the field, leaving a margin of 2 inches all around? Would this be a reasonable scale to use ? 4. If a scale 1 inch = 20 rods is used, what size paper is neces- sary in order to diagram this field and leave a margin of one inch on all sides ? 5. What is the largest scale that could be used to plot this field on a paper the size of this page, leaving margins of at least I" ? 6. It is desired to show by a graph the imports of coffee into various countries of the world. The year chosen is 1910. The United States was the largest importer, with an importation in round numbers of 804,000,000 pounds. The graph is to be placed on paper the same size as this page, with the same margins. How long a line would represent 100,000,000 bushels ? 7. If the names of the countries require one inch, the scale might be inch = 100,000,000 bushels. 8. Draw a diagram of your schoolroom, entering the dimen- sions as illustrated in the drawing on page 137. VARIOUS TYPES OF GRAPHS 143 9. Draw a diagram of a room in your home. Do not enter the dimensions but state the fractional scale used, and draw all lines very carefully in accordance with this^ scale. Note to Teacher. When these drawings are brought to class, they may be exchanged, and the students required to compute the dimensions in accordance with the scale stated. * 10. Draw a line graph (similar to the one on page 138) to ex- press the following statistics. Exports of Tea from Various Countries in 1910 Country Pounds British India 258,000,000 Ceylon 182,000,000 China 207,000,000 Dutch East Indies 33,000,000 Formosa 24,000,000 Japan 40,000,000 Singapore 2,000,000 Rule the paper thus : 10 20 30 40 50 60 70 80 90 100 110 Use the scale j" = 10 million pounds. (How large a paper will you need?) Arrange the countries so that the longest line will be at the top and the shortest at the bottom, the others being placed in the order of their lengths. Various Types of Graphs 125. Colored and Shaded Graphs. By the use of different colors of ink, or different shadings, comparisons may be made to show increase, decrease, or various changes in statistics from year to year. 144 DRAWINGS AND GRAPHS The following graph shows the average number of wage earners employed in manufacturing industries in 1899 and 1909. The graph is limited to the ten states employing the largest number of men. Average Number of Wage Earners, by States: 1909 and 1899 1 Oral Work 1. By referring to the graph, determine the approximate num- ber of wage earners in each state in 1899 and in 1909. 2. Which state shows the greatest increase in the number of wage earners between the years 1899 and 1909 ? 126. The Circle is frequently used for graphic purposes. It is particularly valuable because it shows two things very clearly : a. The relation of each magni- tude to each of the others. h. The relation of each magni- tude to the sum of all. This graph shows clearly that the states of the Middle Atlantic Division produce a greater value of manufactured articles than the states of any other division, and that they produce about one third of the entire value of the manu- factures of the country. The scale used in making cir- cular graphs is based on the degree. If the circumference of Value of Manufactured Products i 1 Reprinted by permission of the United States IBureau of the Census, Depart- ment of Commerce. VARIOUS TYPES OF GRAPHS 145 a circle were divided into 360 equal parts, each part would be one degree of arc. Degrees may be measured by an instrument called a protractor. The method of locating the lines in a circle graph may be ex- plained by showing how the apace occupied by the Middle Atlantic section was determined. This section produces .345 of the total value of manufactured products. It should, therefore, occupy .345 of the circle. .345 of 360° is 124.2°. Points as nearly as possible 124.2° apart are marked off on the circumference with the aid of the protractor, and lines are drawn from the center of the circle to these points on the circumference. Written Work 1. The total exports of coffee from all the countries of the world in 1910 were 2,163,764,874 pounds. Brazil exported 1,286,217,168 pounds or of the world's trade. It should therefore occupy what part of a circle designed to show the coffee exports of the world ? How many degrees of arc ? 2. The next largest exporter was the Netherlands, with 173,823,451 pounds. What part of the world's supply was pro- vided by this country? What part of the circle should represent the amount of coffee exports of the Netherlands? 3. Five departments of a wholesale store produced profits as follows : Dept, Profits I 12165.00 II 3297.00 III 794.00 IV 1719.00 V 4625.00 Prepare a circle graph showing what per cent of the entire profit was made by each department. 146 DRAWINGS AND GRAPHS 127. Graphic Pictures. Another kind of graph frequently used IS illustrated below : Workingmen's Expenditures FOOD RLNT CLOTHING <5UND111L5 - rUtLTLlGft> INSUR/^MCfc^Hfc/^LTH-- CW TWt* Food $385.82 Rent 161.36 Clothing 98.79 Sundries 60.28 Fuel and light 36.94 Insurance 18.24 Health 14.02 Carfares ; . . 10.53 From The Independent. These figures are based on a study of the wages of a number of workingmen, whose average annual income was $749.83 and whose average annual expenditure was $ 735.98. 128. The Graphic Curve. Graphs drawn on cross-sectioned paper are especially valuable when it is desired to show the varia- tion of statistics during consecutive intervals, as from month to month, or from year to year. The divisions on the vertical line may represent multiples of some unit of value and those on the horizontal line represent various intervals of time. The following graph shows the variations in the monthly sales of a store during two years. The unbroken line VARIOUS TYPES OF GRAPHS 147 indicates the sales for the year 1914 and represents the following statistics : Sales for January . $1426.80 Sales for July . . . . $1167.85 February . . 1638.80 August . . . . 1232.65 March . . . 1526.75 September . . . 1386.64 April . . . 1246.70 October . . . 1566.45 May . . . . 1147.10 November . 1626.30 June . . . . 1060.50 December . . 1575.25 It is sufficient for com- parative purposes to show the approximate sales in dollars. 129. How this Graph is Drawn. An unbroken line represents the data for 1914. A point was placed on the January line at a point repre- senting approximately $1425.00. A second point was placed on the February line at a point representing ap- proximately 11638.00. Other points were prop- erly located on the other lines, and an unbroken line, or curve, was then drawn connecting all the points. In the same way the dotted line was drawn to represent the data for 1915. 1750 1700 1G50 ICOO 1550 1500 1450 1400 1350 1300 123.) 1200 1150 UOO 1050 / / / / / \ \ 1 ''/ \ ■ \ \ 1 1 1 / \ / \ '^% 1 1 / \ / \ \ I \ / / / \ \ 4 ' / \ V \ / \ l\ \ \ / \ \ \ \ 1 \ \ \ / / / F \ / / / \ 1 / \ \ 1 Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Exercise Study the graph and answer the following questions : 1. Was there any uniformity of trade from year to year? That is, did the busy and the dull months follow in about the same order each year? 148 DRAWINGS AND GRAPHS 2. As a rule, during what seasons did this store have the largest trade ? 3. What was its "dullest" month? 4. How did the business of 1915 compare with that of 1914? 5. About how many more dollars' worth of goods were sold during August, 1915, than during August, 1914 ? 6. Estimate the sales for each month of the year 1914. If your answers are within $2.00 of the correct amount, they will be accurate enough for purposes of comparison. 7. Discuss the value of such a graph. 130. The following graph shows a slightly different use of the curve. The curves serve to compare the grades given by three teachers in a certain school, showing what per cent of the students in their classes received certain grades. This graph was made in the following man- ner : A table was prepared showing what per cent of each teacher's stu- dents received grades be- tween 40 and 50, 50 and 60, etc. For example : Eight students of teacher A received grades 60-70. This was 16% of the students in A's classes. m m ; \ / ; v \ \ / / \ / ; \ 1 1 ; // \ \ / ( /-- / / V >. '7 > f \ r ^^ // ^ A' / \\ s. \ 1 1 1 :>-' v^ 1 1 I '^ ' -v^ 1 1 1 y ^ 1 1/ / 'L 40-50 50-60 GO - 70 70 - cSO 80 - 90 90 - LOG VARIOUS TYPES OF GRAPHS 149 Teacher A Graub Teacher A Geade No. of Students Per Cent of Total Number No. of Students Per Cent of Total Numbei- 40-50 50-60 60-70 2 4 8 4 8 16 70-80 80-90 90-100 12 • 16 8 24 32 16 The curve for Teacher A was plotted thus : On the horizontal line above 40-50, a point was placed to indicate 4%. On the horizontal line above 50-60, a point was placed to indicate 8 %, etc. All of the points thus located to represent grades given by A were then connected. Oral Work Interpret the curves, stating what per cent of the students of each teacher received the grades specified. \ Written Review Use paper S'^" by 11'^ or larger, for the following graphs. 1. By a graph similar to the first one on page 144, show the following statistics of exports from the United States to the United Kingdom. Use black ink for the data of 1910; red ink for those of 1911. Cattle . . Bacon . . Hams . . Fresh Beef Lard . . Leather Machinery Copper . . Paraffin Wax Petroleum . Tobacco Fish . . . 1910 1911 £ 2,578,000 £ 3,056,000 4,453,000 5,067,000 2,329,000 2,712,000 1,070,000 397,000 4,201,000 4,014,000 4,057,000 3,828,000 2,287,000 2,894,000 2,568,000 3,027,000 871,000 617,000 3,745,000 3,370,000 2,815,000 3,278,000 1,021,000 702,000 150 DRAWINGS AND GRAPHS 2. Show graphically what part of the coinage of the years named in the following table was gold, what part silver, and what part other coin. Gold Silver Other Coin 1909 1910 1911 1912 88,776,908 104,723,735 56,176,822 17,498,522 8,087,852 3,740,468 6,457,301 7,340,995 1,756,389 3,036,929 3,156,726 2,577,386 3. By drawings of corn stalks, ears of corn, corn cribs, or any other suitable design, graph the following statistics of corn crops in the United States. Year Bushels Year Bushels 1870 1880 1890 1,094,000,000 1,717,000,000 1,489,000,000 1900 1910 2,105,000,000 2,886,000,000 4. By a graph similar to the illustration of monthly sales (p. 147), show the variation in the wholesale price of corn per bushel by months for the following years. January . February March April . . May . . June . . July . . August . September October . November December 1910 Cents 62.3 65.2 65.9 65.5 63.5 65.2 66.2. 67.2 66.3 61.1 52.6 48.8 1911 Cents 1912 Cents 48.2 62.2 49.0 64.6 48.9 66.6 49.7 71.1 51.8 79.4 55.1 82.5 60.0 81.1 65.8 79.3 65.9 77.6 65.7 70.2 64.7 58.4 61.8 48.7 VARIOUS TYPES OF GRAPHS 151 5. Show by a graph the data for the attendance at your school for a school year. (The principal can supply the data.) 6. Graph the temperatures for a certain hour of several succes- sive days. 7. Make a graph showing your progress in speed and accuracy in addition, subtraction, multiplication, and division for a given set of examples. 8. What is the largest scale that could be used to represent a square farm of 160 acres on a paper 18^' by 20' ^ leaving a margin of at least 1''? 9. Two cities known to be 60 miles apart are 21 inches apart on a map. What is the scale of the map ? PERCENTAGE CHAPTER XIV PERCENTAGE 131. Relation of Percentage to Common and Decimal Fractions. Percentage is the process of computing by hundredths. The symbol % stands for per cent. 15 Thus, 15 % means — — or .15. 8 8 % means — — or . 08. 300% means 1^ or 3.00. ^% means -~ or .00 J or .005. . 2 %% means-|- or .00?. ^ ^ 100 ^ 71 TJ% means -^ or .07| or .075. ^ 100 ^ Oral Work Express each of the following as a common fraction and as a decimal fraction: 3. 19% 4. 24% 7. J-5-% 8. 200% 11. -,l^% 12. 16f% Express with the symbol % : 13. .74 ' 14. .03 15. .07 J 16. 2.00 17. .32^ 18. .001 19. 1.00 20. .OOJ.C 152 1. 7% 2. 4% 5. 2i fo 6. i% 9. 184% 10. 5i% PERCENTAGE 153 21. .5 22. .005 23. .16| 24. .14|- 25. I 26. i 27. I 28. | 29. I 30. f 31. f 32. 1 33. 40% of a quantity is how many hundredths of it? What fractional part of it ? 34. 100 % of a number is how many times the number ? 35. 300 % of a number is how many times the number ? 36. 140 % of a number is how many times the number ? 37. 2 times a number is what per cent of the number ? 38. 5 times a number is what per cent of the number ? 39. What part of a number is: 20% of it? 12% of it? 13% of it? 80% of it? 75% of it? |^%ofit? 100 % of it? I % of it ? 121 % of it ? 37i%ofit? 871% of it? 50% of it? 6| % of it ? 621 % of it ? 66| % of it ? 40. Express each of the following as a decimal fraction and with the symbol %. 1115321324 1 5 73 2' 5' ^' 6' ■?' T' T' 2' 3' 5' 10' T2'' 8' 4* 41. The following table states the fractional part of the total number of colonies of bees in the United States owned in each section of the country. State what per cent of the colonies are owned in each section. New England 012 Middle Atlantic 085 East North Central 158 West North Central 159 South Atlantic 197 East South Central 147 West South Central 11 Mountain 05 Pacific 082 154 PERCENTAGE 42. The following table shows the per cent of the total value of live stock owned in each section of the United States. State these per cents as decimal fractions. New England 2 % Middle Atlantic 7.1 % East North Central 19.8 ^o West North Central 31.5% South Atlantic lA^Jo East South Central 7.5 % West South Central . 12 % Mountain l.^^o Pacific. . . . ■ 4.8 9i, 132. Terms Used in Percentage. Base. The number of which a given per cent is to be taken is called the base. Rate. The per cent of the base to be taken is called the rate. Percentage. The result obtained by taking a certain per cent of the base is called the percentage. Thus, 64 X.25 = 16; or base x rate = percentage. Fundamental Processes of Percentage Computations in percentage are based on the following : base X rate = percentage. 64 x.25 = 16. Since the percentage is the product of the base and rate, it is evident that, a. The percentage divided by the base equals the rate. For example : 16 -^ 64 = .25 = 25 %. h. The percentage divided by the rate equals the base. For example : 16 h- 25 % = 16 -^ .25 = 64. From these statements it is evident that if any two of the terms are known, the other one can be found. In the chapter on Decimal Fractions you learned how to multi- ply and divide by any number expressed decimally. Percentage FUNDAMENTAL PROCESSES 155 involves the mathematical principles of decimal fractions. The exercises in decimal fractions involved computations with tenths, hundredths, thousandths, etc. In Percentage, computation is by hundredths. All mathematical computations involved in percentage may be grouped under three headings: a. To find a given per cent of a number. b. To find what per cent one number is of another. c. To find a number when a certain per cent of it is known. 133. To find a given per cent of a number; that is, to find the percentage. Examples. 1. Find 1 % of 428. Solution. 1 % = .01. .01 of 428 = 4.28. 2. Find 7 % of 378. Solution. .07 x 378 = 26.46. 3. Find 14 % of 8360. Solution. $ 300 .14 1440 360 $ 50.40 To Ji7id the percentage, multiply the base by the rate. Oral Work 1. Find 1 % of each of the following: 18; 146; 198; 7; 03; 876; .045. 2. Find 5 % of each of the following : 80 ; 60 ; 25 ; 42. 3. Find 10 % of $ 18.20 ; of 478 mi. ; of 32 yd. ; of 648 A. 4. How many places should be pointed off in finding each of the following: 17% of 4762? 17% of 476.2? 17% of 47.62? 1.7 % of 4762 ? .17 % of 4762 ? 17 % of .4762 ? 5. Find 10 % of 400 : 560 ; 8.46. 156 PERCENTAGE 6. Find 3% of 40; 60; 15. 7. Find 100 % of 15 ; 40; 3. 8. Find 20 % of 80 ; 70 ; 60. 9. Find 50 % of 40 ; 2 ; 10. 10. Find 30 % of 30; 40; 80. ll. Find 12-i % of 480; 96; 640. 12. Find 371% of 24; 80; 72. 13. Find 200 % of 9; 32; 181. 14. Find 14f % of 21; 35; 350. 15. Find 25 % of 12; 17; 96. 16. Find j % of 120; 34; 18. Written Work Find : 1. 17 % of 472. 2. 92 % of $537. 3. 16f % of 1420. 4. 3 % of 48,729. 5. 200 % of 37 ft. 6. 1.8 % of 42,690. 7. 17.5 % of 479,362. 8. 250 % of il42. 9. 128 % of 346 yd. lo. 5 % of 83.6. 11. ^ % of 42.736. 12. 1 % of 8476. 13. 32 % of 14.76. 14. 19 ojo of .084. 15. 25 ojo of 264 sq. mi. ^ 16. 371- % of 24 A. 17. 121 oj^ of 1488. 18. 871 % of 648 mi. 19. 33J % of \. 20. 20 ojo of |. 21. 6f % of 32 cu. ft. 22. 40 % of 85 sq. rd. 23. 62J % of 40 A. 24. 33 J % of $36. 25. 66| % of 120 ft. 26. Vl\ % of 64 yd. 27. A school has an enrollment of 450 students. How many students are absent when 4 % are absent ? 28. What is 1 200 increased by 4 % of itself ? 29. In 1900 the population of a certain city was 52,840. In 1910 the population was 15 % larger than in 1900. What was the population in 1910? 30. A boy made a journey of 48 miles. He rode 85 % of the distance in an automobile and walked the remaining distance. How far did he walk ? 31. An architect's fees for designing a house are 4 % of its cost. The cost is $7360. What is the fee ? 32. A man whose salary is $3200 spends 19 % of it for rent. How much does he spend for rent ? FUNDAMENTAL PROCESSES 157 33. A clerk receives 2 % of the amount of his sales. If his sales for Monday were 1160.40, how much did he receive ? 34. The report of a school with an attendance of 400 showed the per cent of tardiness to be 1^. How many were tardy? 35. A man earns il400 a year and saves 18 % of it. How long will it take him to save i 756 ? 36. In a recent year, the following live stock was reported on farms in the United States : numbkr Cattle 61,803,866 Horses 18,833,113 The following table shows the per cents of the total number of cattle and horses, in terms of the above data, in each section of the country. Thus 5.2 % of 61,803,866 was the number of cattle in the Pacific States. Section New England . . Middle Atlantic . East North Central West North Central South Atlantic East South Central West South Central Mountain . . . Pacific .... Cattle HOESES 2.2 efa / &0S, WC DENNISTON CO- / OAO (fOsS- FUNDAMENTAL PROCESSES 161 18. The following table shows one of the ways in which mer- chants determine which clerk is selling the most goods. Rule a form similar to the model ; enter on the blank the facts which are given in the model ; find the total sales made by air of the salesmen. Find what per cent of the total sales was made by each salesman. Enter all of these facts on the blank. Table Showing Per Cent of Month'8 Sales Made by Various Salesmen SAirSMAJiriS J^AME SALES PERCENT or TOTAL i/ B.Drf/MY / / &6,iA ■9^ O.F.ALBRIGHT / Cf / 3 ^s. G.r.SLATrji / 7S& c<^ WriLIAM. WAJiXCR S-H /3 7^ C.B.WlLZr / Cf ^3 ¥^ H. WALKER / ^27 3S. rRAXK M'Grr / 6 q*& r 8 r.L.MOUTGOMSJiY- & / Ji8 ¥-S C.H.HrURY / 7&S ^4 • TOTAL i , 19. The following tabulation is a record of a week's sales in four departments of a store. Rule a blank similar to the model. Enter the statistics on the blank. Find the total sales for each day made in all departments ; enter these totals in the " total " column at the right. Find the total sales made during the week in each department ; enter these totals on the line at the bottom marked "total." Find (in two ways) the total sales made in all of the depart- ments for the entire week. Enter in the space marked Grand Total. 162 PERCENTAGE Find what per cent of the grand total sales was made eatih day ; enter these per cents in the column at the right. Find what per cent of the grand total sales was made in each department. Enter these per cents on the line at the bottom marked per cent. One of ■ the qualities which a business man desires in his employees is the ability to follow directions. This exercise will give you an opportunity to prove your ability along this line. Get a clear understanding of the instructions, and follow them by preparing the exercise without asking for any further directions. A Week's Sales in a Department Store Day Dept. 1 Dept. II Dept. Ill Deft. IV Total Per Cent Monday .... $362 50 $562 83 1862 94 $126 39 $ Tuesday .... 415 75 475 92 732 83 143 62 Wednesday . . . 896 21 415 60 769 42 129 38 Thursday . . • 472 96 516 29 640 20 145 17 Friday .... 387 29 429 36 721 32 96 27 Saturday. . . . 493 89 562 64 816 25 163 92 Total .... Grand Total Per Cent . . . 135. To find a number when a certain per cent of it is known; that is, to find the base. Method. Since the percentage is the product of two factors, the base and the rate, and since any product can be divided by one of its factors to find the other factor, it is evident that, percentage -^ rate = base. Therefore, to find the base, divide the percentage hy the rate ex- pressed as a decimal. Examples. 1. 18 is 25% of what number? Solution. 18 is the percentage, 25% is the rate; the base is not known. 18 -f- .25 = the required number, or base. • 18 H- .25 = 72. FUNDAMENTAL PROCESSES 163 2. 45 % of the number of students in a school are boys. If there are 135 boys, how many students are in the school ? Solution. 135 -=- .45 = 300, the total number of students. This may be explained as follows : Since 45 % of the number of students = 135, 1 % of the number of students = ^^ of 135 = 3 and 100 % of the number of students = 100 x 3 = 300. Oral Work Find the number of wliich : 1. 40 is 20%. 2. 12 is 4%. 3. 10 is 5%. 4. 86 is 2%. 5. f45 is 15%. 6. 40 is 80%. 7. 12is|%. 8. 42 is 100%. 9. 60 is 200% 10. 12 is 33 J %. 11. 35 is 7%. 12. 19is J%. 13. 8 is 1%. 14. 2700 is 66J%. 15. A boy lost 40 cents, which was 10 % of what he had. How much did he have? 16. A man sold 32 acres of land, which was 80 % of all that he owned. How many acres did he own? Written Work 1. In a certain school 5 % of the pupils are absent and 475 pupils are present. What is the enrollment? 2. By saving 28% of his salary a man saved $2240 in 5 years. What was his salary ? 3. 18.75% of a class failed. If 26 passed, how many were in the class ? 4. The distance from New York to San Francisco via the Panama Canal is 5278 miles. This distance is 60.44 % less than the distance via Cape Horn. What is the distance via Cape Horn ? 5. A boy paid f3 for a pair of shoes and had 70% of his money left. How much money had he at first ? 6. P^our partners engage in business. The first invests $4000; the second invests $3000; each of the others invests 25% of the total capital. What is the total capital ? 164 PERCENTAGE 7. The Washington Monument is 555 ft. and Eiffel Tower is 984 ft. high. The height of the monument is what per cent of the height of the tower? 8. The average velocity of wind is 18 mi. per hour and that of sound is 1090 ft. per second. The velocity of wind is what per cent of the velocity of sound ? 9. The mean annual rainfall in Denver is 14 inches, and that in New York City is 44.8 inches. Each is what per cent of the other ? 10. The length of the Hudson River is 280 miles ; the length of the Ohio is 950 miles ; and the length of the Mississippi is 3160 miles. The length of each is what per cent of the length of the others ? 11. The record for the 100-yard dash is now 9| sec. It was formerly 9|- sec. By what per cent was the record reduced ? 12. In 1776 there were 13 states in the Union. There are now 48 states. What has been the per cent of increase ? 13. A certain basketball player can shoot on an average 90% of his free chances. If there are 20 fouls called on his opponents in a game, how many points should he make on fouls ? 14. The United States Census divides persons engaged in manu- facturing into three classes : wage earners, clerks, and proprietors. The table on page 165 shows the number of persons in the first class; that is, the wage earners. It also shows the per cent of the total number engaged in each line of manufacturing who were wage earners. For example, there were 50,551 wage earners engaged in the manufacture of agricultural implements. The wage earners were 83.9% of the total number of persons engaged in this work. What was the total number of persons engaged in this work ? Rule a form and find the total number of persons engaged in such industries as the teacher directs. Since the per cents are only approximate, the results will be only approximate. Indicate the ten industries having the largest number of employees. Mark the industry with the largest number of employees " 1," the second largest " 2," etc. FUNDAMENTAL PROCESSES 165 Industry Wage Earners Av. Number Per Cent Total Employees Rank 6,615,046 86.1 50,551 83.9 75,721 88.7 198,297 91.8 40,618 89.4 100,216 69.4 18,431 58.5 59,968 83.3 69,928 84.3 282,174 93.7 43,086 91.5 23,714 85.3 239,696 88.3 153,743 85.9 44,638 81.4 73,615 84.7 378,880 97.7 87,256 82.6 39,453 59.7 531,011 86.3 128,452 89.1 37,215 73.0 129,275 94.9 38,429 89.2 240,076 92.1 34,907 80.2 62,202 92.7 6,430 77.2 54,579 81.8 695,019 88.5 65,603 84.9 17,071 80.2 14,240 65.0 75,978 93.3 22,895 55.7 13,929 8.37 258,434 66.5 99,037 94.1 89,728 82.5 15,628 92.8 7,424 92.1 13,526 86.4 166,810 84.4 168,722 96.3 1,648,441 86.0 All Industries Agricultural Implements . Automobiles Boots and Shoes .... Brass and Bronze . . . Bread Butter, Cheese .... Canning Carriages Cars and Shop Construction Cars, Steam Chemicals Clothing, men's .... Clothing, women's . . . Confectionery .... Copper, Tin Cotton Goods Electrical Machinery . . Flour Mill . Foundry Furniture Gas Hosiery Iron, Steel, Blast . . . I. and S. Steel Works . . Leather Goods .... Leather Liquors, Distilled . . . Liquors, Malt Lumber Marble Oil Paint and Varnish . . . Paper Patent Medicines . . . Petroleum Printing and Publishing . Silk Slaughtering Smelting, Copper . . . Smelting, Lead .... Sugar and Molasses . . . Tobacco Manufacture . . Woolen, Worsted .... All Other Industries . . 166 PERCENTAGE Percentage of Increase and Decrease Percentage is frequently employed to find the relation between numbers, or to find how much larger or smaller one number is than another. This does not involve any new mathematical principles. Example. What number increased by 20 %. of itself is 360? Solution. 100 % of the number = the number, 20 % of the number = the increase, 120 % of the number = 360, 1 % of the number = 360 -- 120 = 3, 100% of the number = 100 x 3 = 300, or we may say : 1.20 times the number =360, therefore the number = ;J-— =300. Oral Work (Use equivalent fractions if more convenient.) What number increased by 1. 20 % of itself is 240? 2. 25 % of itself is 250? 3. 121 cf^ of itself is 360? 4. 200 % of itself is 1800? 5. 142 ^^ of itself is 88 ? 6. 75 % of itself is 14? 7. 50 % of itself is 600? 8. 5 % of itself is 420? 9. 300 % of itself is 2400? lo. 87 J % of itself is 330? 11. 1 % of itself is 202? 12. 7 % of itself is 428? 13. 6| % of itself is 4800? 14. 661 % of itself is 40? 15. 60 % of itself is 64? 16. 100 % of itself is 600? 17. How much is 1^40 increased by 20 % of itself? 18. How much is 60 increased by 10 % of itself? 19. How much is $42 increased by 10% of itself? 20. How much is 3 increased by 100 % of itself ? 21. How much is 24 bu. increased by 37^% of itself? 22. How much is 12 yd. increased by 33J% of itself? 23. How much is 10 mi. increased by 7 % of itself? 24. How much is -118 increased by 200% of itself? 25. How much is 32 acres increased by 12^% of itself? INCREASE AND DECREASE 167 136. Per Cent of Increase. . To find the increase, multiply the base by the per eeyit of increase. Example. Mr. Smith, whose salary was 1)1200.00, received a 5% increase. How much was the increase? Solution. $ 1200 Base .Qd 1 60.00 Increase To find the per cent of increase, divide the increase by the base. Example. Mr. Smith, whose salary was #1200.00, received an increase of $60.00. What was the per cent of increase ? Solution. $ 60.00 - $ 1200.00 = .06, or 5 %. To find the base. a. Given the increase and per cent of increase. Example. Mr. Smith received a 5% increase in salary. The increase was 160.00. What was his original salary ? Solution. $60.00 - .05 = $ 1200.00. Increase -f- per cent of increase = base. b. Given the increase and the amount. Example. Mr. Smith's salary was increased f60.00, after which he received $1260.00. What was the per cent of increase ? Solution. $ 1260 - $ 60 = $ 1200, the base. $60-^^1200 = .05. Hence, the per cent of increase is 5 %. c. Given the per cent of increase and the amount. Example. After receiving a 5 % increase, Mr. Smith's salary was $1260.00. What was his original salary and what was the increase ^ Solution. His original salary was 100% of itself. His increase was 5% of the original salary. Therefore, the new salary was 105 % of the old one. $ 1260 H- 1.05 = $1200. 168 PERCENTAGE Written Work 1. A merchant's sales during 1914 were i 6238. 92. By adver- tising, he increased his sales f 2485.35 the following year. What was the per cent of increase, and what was the amount of the jales in 1915 ? 2. The deposits of the Wells Street Bank on June 30, 1914, were $365,894.56. On June 30, 1915, the deposits had increased to 1396,268.55. What was the increase and the per cent of increase ? 3. A factory produced 240 articles of a certain kind per day. By installing new machinery, the output was increased 12|-%. What was the amount of the increase, and how many articles were produced per day after the new machinery was installed ? 4. Williams paid $16.87 more taxes this year than he did last year; an increase of 7.8%. What was the amount of his taxes each year ? 5. The payroll of the Maynard Manufacturing Company for the week ending April 4, 1914, was $428.62. The payroll for the week ending April 3, 1915, was 13 % larger. What was the pay roll for the week in 1915, and what was the increase ? 6. A merchant built an addition to his store which increased the floor space 28%. After the addition was completed, the floor space was 1280 square feet. What was the number of square feet of floor space in the original store, and what was the amount of the addition ? 137. Per Cent of Decrease. To find the per cent of decrease, divide the decrease hy the base. Example. Mr. Smith's coal bill in 1914 was $80.00. In 1915 his bill was $4.00 less. What was the per cent of decrease ? Solution. Decrease -r- base = per cent of decrease. Thus, $4.00 -^ % 80.00 = 5 %. The decrease was 5 %. INCREASE AND DECREASE 169 Written Work 1. The proprietor of a retail grocery employed five clerks at a total annual expense for wages of $5000.00. In order to reduce the expense, he released one clerk whose wages were i 60.00 per month. How much did he decrease the cost of the clerk hire per year ? What was the per cent of decrease ? What was the annual cost of the clerk hire after one clerk was dismissed ? 2. A paper mill which burned 2400 tons of soft coal per year remodeled its furnaces and boilers and now burns 2000 tons of coal per year. How many tons less does this factory consume per year than formerly, and what is the per cent of decrease ? 3. Previous to 1914, Mr. Waterbury owned the only drug store in the town of X. When a new drug store was opened, the com- petition decreased Mr. Waterbury 's annual sales -11067.60, or 17%. What was the amount of Mr. Waterbury 's sales the year before the new store opened ? 4. In 1914 Mr. Snowden, a grocer, lost 1327.00 from bad debts. A credit-rating association was formed in the town; the merchants informed each other of persons who did not pay their bills; and the following year Mr. Snowden decreased his loss from bad debts 18%. How much did the credit-rating association save Mr. Snowden, and what was his loss from bad debts in 1915 ? 5. Ratlibun moved his store into a new building where the rent was 15.00 per month less than the rent of the building which he formerly occupied. The rent in the new location was $125.00 per month. What was the per cent saved? 6. Barnes said to his partner, " We cut down our delivery expense 30 % when we sold the horses and bought an auto truck. Our annual cost for making deliveries after we made the change was only 11645.00. When we delivered with horses, the cost per year was $ , so we are saving | ." 170 PERCENTAGE 7. The following table shows one of the uses which business men make of per cent of increase and decrease. This table compares the sales on the first Tuesday in June, 1914, with the sales on the first Tuesday in June, 1915. The merchant assumes that trade conditions were about the same on the two days. A table of this kind is prepared every day, comparing the business for the day with the business of the corresponding day of the previous year. Prepare a table similar to the model, and enter the facts given. Show increases and per cents of increase in black ink; decreases and per cents of decrease in red ink. What was the increase in business in department 1 ? What was the per cent of increase ? Complete the table. Comparative Sales Sheet Department Number Sales, Tuesday, June 2, 1914 Sales, Tuesday, June 1, 1915 Increase or Decrease Per Cent Increase or Decrease 1 2 1 826 1034 95 78 $ 914 1231 32 64 1 3 1237 62 1196 14 4 2643 80 2843 27 5 1413 80 1376 29 6 962 40 1235 96 7 2642 16 2927 92 8 1964 39 2129 80 9 1636 48 1596 27 10 1213 42 1723 96 11 1394 29 1146 92 12 415 75 496 25 13 3460 00 3246 29 14 2690 70 2889 00 15 878 25 794 60 Total 8. The following table shows the value of irrigating arid land. For example, the government records show that, in the regions where rainfall is insufficient, the potato crop on an acre of INCREASE AND DECREASE 171 irrigated land is worth $15.37 more than the crop grown on an acre of unirrigated land. This is an increase of 34.4% due to irrigation. What is the average value per acre of the potato crops grown on unirrigated land and on irrigated land ? Complete the table. Comparative Value of Crops Grown on Irrigated and Unirrigated Land Crop Potatoes Sugar Beets Wheat Alfalfa Oats Barley Corn Timothy and Clover, mixed Timothy alone .... Excess of Ayeragk Value OF Crop per Acre grown ox Irrigated Land, over THAT GROWN ON UNIRRI- GATED Land $15 5 8 5 7 6 3 3 3 34.4 % 10.4 58.6 35.2 63.2 55.1 24.0 27.6 24.1 AVRBAGB VaLXTE OF Crop per Acre on Unir- rigated Land Average Value OF Crop per Acre on Irrigated Land 138. Per Cent of Maximum. It is sometimes desired to com- pare a certain number with a larger number. For example, a certain packing plant is equipped to slaughter and pack a maxi- mum of 2000 hogs daily. On October 22, this plant packed 1882 hogs. The day's pack was Jiff of the maximum capacity, or 91.6 %. State a rule for finding per cent of maximum. Written Work The table on page 172 shows the number of wage earners em- ployed in coal mining in the United States in a recent year. The number of employees varies with the season. Some idea of the steadiness of employment in this industry may be formed by comparing the number of employees each month with the maximum. 172 PERCENTAGE During what month was the maximum number of persons employed in coal mining ? What per cent of this number was employed in January ? Complete the table. Wage Earners Employed in Coal Mining in the United States Month January February March . April May . . June . . July . . August . September October . November December Wage Earners Employed 691,244 686,322 679,791 649,870 646,592 652,894 659,434 667,146 685,234 704,939 720,341 729,273 Per Cent of Maximum 139. Per Cent of Average. Percentage is also used to show the relation between different numbers by comparing them with their average. Written Work The following table shows the monthly sales of a number of clerks : Clerk No. Sales Per Cent Clerk No. Sales Per Cent 201 202 203 204 $1412.32 1218.16 967.32 1046.89 205 206 207 208 $1836.24 1216.26 1375.85 1493.85 Find the average sales. The sales of Clerk No. 201 are what per cent of the average ? Complete the table. What is the value of such a table for the manager of a business ? INCREASE AND DECREASE 173 Review Work 1. If a merchant sells all goods at an advance of 10 % of the cost, what will be the selling price of an article which cost $ 3.40 ? What will be the profit on this article ? If this merchant's an- nual sales are $ 24,126.85, what is his gross profit ? He marked all goods at 25 % increase on the cost the following year and his sales dropped to f 15,625.90. What was the cost of the goods sold, and the gross profit ? 2. In 1910 the total area of the Indian reservations in the United States, exclusive of Alaska, was 77,446 square miles. In 1890 the area of such reservations was 243,991 square miles. What per cent did the area decrease in twenty years ? 3. In 1910 the Indian population was 300,121, in 1890 it was 243,524. What per cent did the population increase ? 4. What was the average number of acres of land in reserva- tions per Indian for each of the years named ? 5. What was the per cent of increase or decrease in the average acreage ? 6. Complete the following table showing the average size of farms in different divisions of the country. Division Average Size op Fabms (Acres) Increase (+) Decrease (-) 1910 1900 Acres Per Cent United States . . New England . . Middle Atlantic East North Central West North Central South Atlantic . . East South Central West South Central Mountain .... Pacific. .... 138.1 104.4 92.2 105.0 209.6 93.3 78.2 179.3 324.5 270.3 146.2 107.1 92.4 102.4 189.5 108.4 89.9 233.8 457.9 334.8 174 PERCENTAGE 7. The following table shows the amount of sugar produced in and imported to the United States. Complete the table. Long Tons , (2240 LB.) Sugar imported from Hawaii and Porto Rico .... 718,788 Sugar imported from other countries 1,674,776 Total imports x,xxx,xxx Domestic production of cane sugar 409,960 Domestic production of beet sugar 434,000 Total domestic production x,xxx,xxx Total consumption of sugar in United States . . x,xxx,xxx a. What per cent of the total consumption of sugar was imported ? b. What per cent of the sugar consumed was produced in this country ? c. What per cent of the sugar made in this country was cane sugar ? What per cent was beet sugar ? 8. Complete the following table. Pkrsons Engaged in Manufactures Glass 1904 1909 Per Cent of Number Per Cent of Total Number Per Cent of Total Increase, 1904-1909 Proprietors and firm members Salaried employees .... Wage earners (average number) 225,673 519,556 5,468,383 273,265 790,267 6,615,046 Total 140. Percentage Analysis of a Business. Mr. E. C. Barton is the proprietor of a wholesale store. At the end of each month he analyzes the records of his business. The following analysis was made June 30, 1915. Results should be approximate to the near- est liundredth of a per cent. 1. The purchases during June, 1915, were -18146.90. Some of the goods purchased were defective, and were returned. The value of goods returned was $123.60. The returned goods were what per cent of the purchases ? INCREASE AND DECREASE 175 2. Gross sales for June, 1915, were 111,216.29. Goods re- turned to the store by dissatisfied customers, $97.65. The re- turned sales were what per cent of the gross sales ? 3. Gross sales for June, 1914, were 19862.15. Returned sales, f 101.80. What per cent of the sales were returned in June, 1914 ? 4. What was the increase in the gross sales, and what was the per cent of increase ? 5. Gross Sales — Returned Sales = Net Sales. What were the net sales for June, 1914 ? For June, 1915 ? What was the increase in net sales, and the per cent of increase ? 6. The merchandise on hand June 1, 1915, was worth $ 14,162.45 at selling prices. The net sales for the month were found in problem 5. What per cent of the stock on hand at the beginning of the month was sold during the month ? 7. Net Sales — Cost of Goods Sold = Gross Profit. The gross profit for June, 1914, was $1688.54. The gross profit was what per cent of the net sales for the month ? (For net sales see results to problem 5.) 8. The gross profit for June, 1915, was 12001.36. The gross profit was what per cent of the net sales for that month ? 9. The expenses of the business in June, 1914, were $ 1015.60. The expenses had increased in June, 1915, to $1140.26. What was the per cent of increase in the expenses ? 10. Net Sales — Gross Profit = Cost of Goods Sold. What was the cost of goods sold in June, 1914 ? What was the cost of goods sold in June, 1915 ? 11. Gross Profit — Expenses = Net Profit. What was the net profit for June, 1914 ? What was the net profit for June, 1915 ? 12. What was the per cent of increase or decrease in the net profit ? 13. Net Profit -h Net Sales = Per Cent of Net Profit on Sales. What was the per cent of net profit for June, 1914 ? What was the per cent of net profit for June, 1915 ? TRADING ACTIVITIES. PROFIT AND LOSS CHAPTER XV BUYING AND SELLING MERCHANDISE 141. The Invoice. When a merchant sells goods, he usually gives the customer a bill or invoice. The invoice states the fol- lowing facts : The date of the sale. The name and address of the seller. The name and address of the purchaser. The terms of the sale. A detailed list of the articles sold, including the price of each item and the total of the invoice. If prepaid freight is to be charged to the purchaser, the amount of freight is added to the invoice. If the invoice has been paid, a statement of the receipt of pay- ment is made by the seller. Study the following invoice and state as many as possible of the facts enumerated above. TtltPHONE, MAIN 1340 PRIVATE EXCHANfiE A. B. HUGHES DEALER IN STAPLE AND FANCY GROCERIES. 211-213-215 Lake Street, terms: ChicgoJlHooi. June 10,1915 2?^ Cash in 10 days , SOLD TO Scobey & Company, Net 30 days. Fayette, Iowa 2 Cases Tomato Catsup 4doz. 1.30 5 20 6 Cases Elgin Canned Corn 12 doz. 1.10 13 20 5 Cases Echo Peas 10 doz. 1.25 12 50 30 90 176 BUYING AND SELLING MERCHANDISE 177 142. What the Purchaser Does. After the purchaser receives both the goods and the invoice, he inspects the merchandise to see if it agrees with the items for which he has been charged on the invoice. If stock of the correct kind and quantity is received, a check mark is entered on the invoice opposite each item in the column at the left. The invoice is next checked to ascertain : a. Whether the correct prices have been charged. h. Whether any error has been made in the extension of the cost of each item, or in the total of the invoice. 143. Credit Memorandum. In case an error is found, notice is sent to the firm from which the goods were purchased. When credit is to be given by the seller on account of an error in the invoice, or for imperfect goods, or for any other cause, the pur- chaser will usually receive a credit memorandum, notifying him of the amount of credit entered to his account. CREDIT MEMORANDUM A. B. HUGHES CHICAGO. June 17, 19 15. TO Williams & Co., Albany, New York Your account has been credited $1,25 On account of overcharge on invoice of June 10, 1915 Written Work Check the invoice on page 176. If the multiplications are found to be correct, enter a check mark at the right of each item. If the total is correct, check it also. When an invoice has been checked and found to be correct, the exten- sions and footings are checked as shown in the illustration. $16 50/ 23 00/ 4 80/ $44 30 • 178 BUYING AND SELLING MERCHANDISE Written Work Find the totals of each of the following sales Apply short methods when possible. 1. 4 doz. Men's Irish Linen Handkerchiefs 5 doz. Men's Hemstitched Handkerchiefs 14 doz. Men's White Initial Handkerchiefs 9 doz. Women's Imported Swiss Embroidered Handkerchiefs 22 doz. Cliildren's Linen Handkerchiefs 7 doz. Women's Swiss Lawn Handkerchiefs 13 doz. Children's Mull Handkerchiefs 2. 17 doz. Men's Leather Gauntlets 11 doz. Men's Buckskin Gloves, sizes 8 to 10 16 pairs Men's Leather Automobile Mittens 4| doz. Men's Suede Gloves, sizes 7| to 10 3^ doz. Men's No. J 264 Kid Gloves 6| doz. Imported Kasan Cape Gloves 3. 16 Silk Taffeta Umbrellas 28 8 Rib Pure Silk Taffeta Umbrellas 32 Men's Suit Case Umbrellas 12 Extra Size Umbrellas 4. 3 doz. pairs Walton Cotton Blankets 1 doz. pairs Cotton Crib Blankets 8 doz. pairs Wool Filled Gray Blankets 7 doz. pairs Douglass Wool Finish Plaids 4 doz. pairs All Wool Plaids 10 doz. pairs " Canada Camp " Blankets 5. 20 Assorted Pattern Smyrna Rugs, 36 x 72 80 Scotch Jute Rugs 3 doz. Cotton Bathroom Rugs, 27 x 54 doz. 14.431 doz. 5.38 doz. 3.23 doz. 2.16| doz. 1.231 doz. .67^ doz. .72i doz. $ 7.68 doz. 9.49 pair 1.361 doz. 4.44 doz. . 10.50 doz. 13.50 each 12.15 each 4.25 each 2.25 each .87| pair $ .82 J pair .57^ pair 3.85 pair 1.891 pair 6.00 pair 1.12J each 12.25 each .371 each 1.12J BUYING AND SELLING MERCHANDISE 179 6. 3 doz. Size 6 Children's Fast Black Hose 2 doz. Size 6| Children's Fast Black Hose 4 doz. Size 7 Children's Fast Black Hose 5 doz. Size 7^ Children's Fast Black Hose 6 doz. Size 8 Children's Fast Black Hose 8 doz. Size 8J Children's Fast Black Hose 7 doz. Size 9 Children's Fast Black Hose 6 doz. Size 9| Children's Fast Black Hose 5 doz. Size 10 Children's Fast Black Hose doz. il.171 doz. 1.21-1 doz. 1.24-1 doz. 1.27-1 doz. 1.311 doz. 1.421 doz. 1.491 doz. 1.61 doz. 1.66| 7. 20 No. B 645 Silk Woven Waist Patterns (each pattern 31 yd.) yd: |.16§ 25 No. B 493 Dresden Silk Mull Waist Patterns (31 yd. pieces) yd. .211 18 bolts Irish Linette, 10, II2, 12, 103, ni^ ns^ 121, 113^ 103, 12, 10, 103, 101, 112^ 12, 113, 102, 103 yd. J4I 20 bolts French Gauze Chiffon, 14, 133, 123, 141, 14, 132, 13, 123, 13^ 131^ 142^ 133^ 142^ 141, 133, 123, 14^ 133^ 132^ 123 yd. .371 NoTK. The small figures mean quarter yards. Thus 11- means 11| yards. Explanation of Grocery Orders The sign f if placed before figures means " number " ; if placed after figures it means pounds. Articles sold in cases [cs.] are usually priced by the dozen. The total num- ber of dozens in the cases is therefore given after the name of the commodity, and the price is the price per dozen. Some articles sold in barrels and cases are priced by the pound ; in such instances the total number of pounds in all the barrels or cases appears immediately before the price. Sugar is sold by the hundred pounds (cwt.). The net weight of each barrel is given. Find the total nunjber of pounds ; point off two places to the left to find the number of hundred pounds, and multiply by the price per hundred. 180 BUYING AND SELLING MERCHANDISE 7 cases Acme Peas 14 doz. Price .11.40 3 boxes Peona Soap 4.95 7 bbh Northern Salt 2.10 15 bbL Winter Wheat Flour ^ sacks 7.10 12 bbl. H. & E. Granulated Sugar 329, 335, 347, 351, 344, 347, 350, 331, >342, 355, 349, 333 6.15 per cwt, 5 sacks H. & E. Granulated Sugar 500# 6.10 per cwt. 9 cases Acme Peas 18 doz. 1.45 17 cases Acme Corn 34 doz. 1.70 6 boxes Dried Apples 150# .08f 2 bbl. 10 # sacks Northern Salt 1.95 6 cases Algonac Tomatoes 12 doz. 1.37^ 9. 1 cs. 25 # Macaroni $2.10 5# Cream of Tartar .40 1 cs. Acme Peas 2 doz. 1.30 5 cases Hawthorne Pears 10 doz. 2.95 11 cases Hawthorne Peaches 22 doz. 2.50 12 cans Pimento .14 15 cs. H.L. Shredded Pineapple 2.40 10 cases Tall Salmon 40 doz. 2.10 12 cases F. & B. Tomatoes 24 doz. 3.75 85 sacks Yellow Corn Meal 850# .03 8 cases 25 ^j^ Macaroni 2.10 5 cases 15 # Spaghetti 2.10 7J doz. pkgs. Seeded Raisins 1.40 125 # Rice .07 25 quarts Olive Oil .75 gah 18| gal. Sweet Pickles 1.06^ 6J gal. Olives |^ 1.30 25 cases 4 oz. Grd. Pepper 125# .30 6 cans Paprika 2.25 doz. 14 cases G. M. Soap 2.85 BUYING AND SELLING MERCHANDISE 181 12 cases Soda Crackers 12 Cracker cans 1 tub Peanut Butter 621 bbL I sacks Spring Wheat Flour 49f bbl. I sacks Winter Wheat Flour 16 cases #2 Algonac Lima Beans 14 cases #2 Algonac String Beans 10. 10 doz. W/W 6 in. Plates 131 doz. W/W 4 in. Plates 5 doz. /S/ 21 in. Butter Chips Tk. 8^ doz. #13 Cups 6 doz. W/W 4 in. Ice Creams 15 doz. #64 /G/ Nappies 8 doz. A.C. 1 Tk. 30's L/F Bowls I doz. #211 Tea Pots 21 doz. #0 /S/ Custard Pots 17 doz. #1352 Tumblers 12 doz. #1296 Finger Bowls If doz. # 3234 Oil Bottles 31 doz. 12-199 Salts 3i doz. 12-200 Peppers 21 doz. 444 A Pitchers J doz. Punch Glasses 121 doz. 3404 Dessert Forks 121 doz. 3405 Dessert Knives 16 doz. 3413 Tea Spoons 8 doz. 3406 Dessert Spoons 2.25 doz. Rule invoices and enter the following sales, assuming that you a^e the selling merchant. 11. To W. K. Sears, Elgin, Illinois. Sept. 10. 45 No. R 721 Body Brussels Rugs 6x9 ft. each f 13.25 32 No. R 731 Body Brussels Rugs 8 x 10 ft. each 19.75 m* Prick $ .09 .50 48i# .121 5.80 6.25 32 doz. 1.40 28 doz. 1.371 f .82 doz. .62J doz. .22 doz. .87.1 doz. .44 doz. 1.121 doz. 1.28^ doz. 1.25 doz. .98 doz. .45 doz. 1.331 doz. 2.25 doz. 1.50 doz. 1.50 doz. 5.00 doz. .75 each 2.35 doz. 2.30 doz. 1.371 doz. 182 BUYING AND SELLING MERCHANDISE Prick 36 No. R 741 Body Brussels Rugs 9 x 12 ft. each $22. 87 J 25 No. R 751 Body Brussels Rugs 11 x 13 ft. each 30.80" 12. To C. B. Perkins, Amherst, Minn. Sept. 12. 20 H 20 Family Coffee Mills each $1.35 16 sets H 33 Sad Irons set .73 12 doz. H 545 Flour Sifters doz. 1.83J 25 doz. H 463 Carpet Beaters doz. .89 8 doz. H 6646 Galvanized Clothes Lines, 20 gauge wire. doz. .92| 10 doz. H 6546 Galvanized Clothes Lines, 18 gauge wire, doz. 1.52| 13. To Owen & Hendersen, Cedar Rapids, Iowa. Sept. 13. 35 F 384 Plush Library Chairs each $14.75 28 F 376 Reed Rockers each 3.10 18 F 394 Bedroom Rockers each 4.85 26 F 465 Roman Chairs each 7.88 19 F 414 Morris Chairs each 18.95 CHAPTER XVI COMMERCIAL DISCOUNTS Cash Discount 144. Purpose of Cash Discount. In order to encourage prompt settlement of accounts, merchants frequently offer to deduct a cer- tain per cent of the bill if it is paid within a fixed number of days. This deduction for prompt payment is called cash discount. 145. Terms. The terms state the discounts offered and the time when the bill is due. The terms are often expressed by an arrangement similar to the following : 2/10; 1/30; N/60. The figures at the left of the line indicate the rate of discount offered; the figures at the right indicate the number of days within which payment must be made in order to obtain the dis- count. Thus, the terms stated above mean : 2 % discount from the face of the bill, if paid in 10 days ; 1 % discount from the face of the bill, if paid in 30 days ; Net Amount (no discount is allowed, and bill is due) in 60 days. 146. Definitions. The amount of the purchase before subtract- ing the discounts is called the list price. The amount of the purchase after subtracting the discounts is called the net price. The Rate of Discount is stated as a per cent of the list price. 147. Cash Discount Illustrated. The terms of the invoice on page 176 were 2/10 ; N/30. In order to obtain the discount, Scobey & Co.'s payment must be made on or before June 20, 1915. The bill is due and payment is expected in full on July 10, 1915. No discount is allowed if payment is made between June 20 and July 10, 1915. 183 184 COMMERCIAL DISCOUNTS 148. Computing the Discount and the Net Price. First Method : 195.25 List price .02 Rate of discount $1.9050 Discount $95.25 List price 1.91 Discount $93.34 Net price State a rule for finding discount and net price by this method. (Note that five mills or more in the discount are considered a cent. Thus, $1,905 is considered $1.91.) Second Method : 100 % List price 2<^ Rate of discount 98 % Per cent of bill to be paid $95.25 List price .98 $93,345 Net price or $93.34 State a rule for computing the net price by this method. 149. The Advantages of Cash Discount. Cash Discounts may benefit both the purchaser and the seller. Merchants offer cash discounts because they encourage prompt payments, and thus decrease : a. the loss from bad debts ; 5. the cost of collecting accounts ; c. the amount of capital tied up in outstanding accounts. It is usually good business for the purchaser to "take his dis- count" (pay the bill before it is due), even though the rate of discount may be small. An illustration will show this fact. Suppose the terms of the sale are. Cash less 1 % ; net 30 days. If the purchaser pays cash, he receives 1 % for the use of his money for one month. 1% a month is 12% a year; a high rate of interest. CASH DISCOUNT . 185 The rates of cash discount are usually small, varying from 1 % to 5%. Small discounts are offered if the bill is due in a short time. For example, 1/10 ; N/30. Larger discounts are offered if the bill is due after a greater length of time. For example, 5/30 ; N/4 months. As a further means of insuring payment of invoices, merchants frequently charge interest on bills which are not paid when due. Written Work Find the list price, the discount, and the net price of each of the following purchases, and answer the following questions about each invoice. a. What is the last day on which payment can be made and the discount secured ? h. When is the invoice due ? 1. Invoice dated April 4. Terms 2/10 ; N/80. 7 cases Acme Peas $1.40 3 cases Osea Soap 4.95 7 bbl. Northern Salt 2.10 15 bbl. i sacks A. D. Flour 7.10 2. Invoice dated October 26. Terms 1/15; N/80. 12 bbl. H. E. Granulated Sugar, 329, 335, 347, 351, 344, 347, 350, 331, 342, 355, 349, 333 # $6.15 5 sacks H. E. Granulated Sugar, 500 # 6.10 3. Invoice dated January 5. Terms 2/10 ; 1/20; N/80. 16 bolts White Dress Linen, 10, 12, 11^, 122, iqs, ip^ 103,12,101,112,12,111,102,113,121,102 ... yd. ^.44^ 12 bolts Persian Lawn, 248, 25i, 232, 95, 242, 248, 252, 241,238,248,252,25 yd. .171 48 bolts French Nainsook, 12-yard pieces .... yd. .18^ 36 bolts Mercerized Lingerie Batiste, 24-yard pieces . yd. .21 24 bolts Imported Linen Lawn, 10-yard pieces ... yd. .43| Note. There will be two possible net prices for this invoice. 186 COMMERCIAL DISCOUNTS 4. Complete the following table. Combine the dollars in the column at the left, with the cents in the row near the top, to form the list price. Deduct the discount shown above the cents, and enter the net price in the table. The two results entered in the table show the method. Thus, $26.10 the list price .02 the discount $ .52 the discount at 2 % 126.10 ^ $25.58 Xet price $641.67 .025 $ 16.04 the discount at 2| % $641.67 16.04 $ 625.63 Net price Less 2 % Less 5 % Lkss 3 % Less 2^ % 10 45 75 67 $26 00 $25 58 14 00 73 00 19 00 261 00 112 00 317 00 216 00 641 00 $625 63 In this exercise and in many which follow, it is not expected that each student will complete the entire table. The work may profitably be distributed among the students. Trade Discount 150. Purpose of Trade Discount. In some lines of business merchants sell both at wholesale and retail. They advertise their goods at a certain price, but when they sell to dealers, they fre- quently deduct a part of this price. The amount deducted is called a Trade Discount. Trade discounts are most common in businesses which issue catalogues. When the catalogue is sent to a dealer, a discount sheet is inclosed. TRADE DISCOUNT 187 Specimen Discount Sheet Discount Sheet The following discounts are offered on articles listed in catalogue No. A 23. Pages 1 to 15 20 % Pages 16 to 3.9 28 % Pages 39 to 67 40 % Pages 68 to 90 Net Pages 91 to 136 14f % Do not show this discount sheet to your customers. Note. "Pages 68 to 90 Net" means, no trade discount is offered for goods listed on these pages. Not Responaible for aoods Lost or Damaged in Transit. Claims for Allowance must be made upon Receipt of Ooods. Address all Communications to Abworombie A Co., Chicago ABERCROMBIE & COMPANY PUBLISHERS & BOOKSELLERS 245 WABASH AVENUE CHICAGO. March 3, 19 15 SOLD TO W. M. Rickert Co., Home, jQ^j^ YOUR ORDER NO. 121 TERMS. ,2/10; N/30 CONVEYANCE, U. S. Ex. IN REFERRING TO THIS ORDER MENTION NO. 4336 ENTERED W. B.3/3/l5. 12 21 Copies H.& J. SecondYear English .85 »• Beeman's Algebra .90 Less 1836 10 18 20 90 23 86 29 5 10 24 188 COMMERCIAL DISCOUNTS Class Discussion 1. Why do merchants offer trade discounts ? 2. What is the catalogue price of the H. & J. Second Year English per copy ? 3. How much does each copy of the English book actually cost the retail dealer ? 4. If Mr. Rickert sells this book for the catalogue price, 85 cents, how much profit does he make on each book ? 5. Trade discounts are usually larger than cash discounts. Why do you think this is the case ? 151. Computing Trade Discounts. Trade discounts are com- puted in the same manner as cash discounts. Example. What will goods cost a dealer if they are sold to him for $46, less a trade discount of 25% ? Solution. $46.00 List price .25 Rate of discount $11.50 Trade discount $46.00 List price 11.50 Trade discount $ 34.50 Price to dealer Written Work Complete the following table, deducting the Trade Discount. Enter the price to dealer after Catalog iTB Price Trade Discount $27 85 $126 39 $96 45 14?% 18% 20% 22% 25% 15% • 17% 28% 16f% 10% TRADE DISCOUNT 189 152. Series of Two Discounts. Invoices are often subject to a cash discount in addition to the trade discount. Two or more dis- counts are called a " Discount Series." Example. What is the smallest amount of money that will pay a bill of tf 236, subject to a trade discount of 20% and a cash dis- count of 2 % ? Solution. if 236.00 List price .20 Rate of trade discount $ 47.20 Trade discount $236.00 List price 47.20 Trade discount $188.80 Price to the trade $188.80 Trade price .02 Rate of cash discount $3.7760 Cash discount $ 188.80 Trade price 3.78 Cash discount $ 185.02 Net price The cash discount is computed on the trade price, not on the list price. Therefore, 20 % trade discount and 2 % cash discount are not the same as a single discount of 22 % . Written Work Complete the following table. From each list price deduct the trade discount indicated above the list price; and from the trade price thus found, deduct the cash discount shown at the left. Cash Discount Facts to bk Found Trade Discount, 2S%- Trade Discount, 25% Trade Discount, List Price $36 45 $68 40 $239 64 Trade Discount 2% Trade Price Cash Discount Net Price List Price 205 08 333 95 47 30 Trade Discount 3% Trade Price Cash Discount Net Price List Price Trade Discount 35 00 713 20 609 49 5% Trade Price Cash Discount Net Price 190 COMMERCIAL DISCOUNTS • Quantity Discounts 153. Purpose of Quantity Discounts. In some lines of business, particularly in manufacturing, it is customary to give a larger rate of discount on a large order than on a small one. A mail order firm advertises : 1 % discount on an invoice of |10 ; 2 % on 120 ; 5 % on $B5. What is the purpose of such quantity discounts ? A printer advertised the following rates: f 10 per thousand for the first thousand copies. On an order of more than 1000 copies, a discount of 15 %. This discount is offered because the work of typesetting, making up the forms, and making ready the press must all be done, although only one copy is to be printed. The cost of printing 2000 copies, there- fore, is not twice as much as for 1000 copies. Written Work 1. The following prices were quoted by a manufacturer of lockers: No. 6094. Each $6.30. Discounts : Orders of from 50 to 100 — Less 8 %. Orders of from 101 to 300 — Less 10 %. Orders of from 301 to 500 — Less 12^ %, Find the total cost and the cost per locker of an order of 75 lockers; 140; 475. 2. A paper manufacturer quoted the following prices: No. 020 note paper, cut to size 8 by 10, $.55 per ream. An extra charge of 3 cents per ream will be made for wrapping in packages of 500 sheets. (500 sheets considered 1 ream.) On orders of 100 reams or more a discount of 4 % will 'be allowed. Terms, 1/10 ; N/30. Find the cost and state what discounts were allowed : a. An order of 50 reams, unwrapped, payment made 20 days from date of sale. TRADE DISCOUNT 191 h. An order of 150 reams, unwrapped, payment made 15 days from date of sale. c. An order of 150 reams, wrapped, payment made 18 days from date of sale. d. An order of 240 reams, wrapped, payment made 7 days from date of sale. e. An order of 60 reams, wrapped, payment made 8 days from date of sale. Fluctuation Discount 154. Purpose of Fluctuation Discounts. Another important discount is that offered to change the cata- logue price of an article to meet the changes, or fluctuations, in the market price. Fluctuation discounts are used by establish- ments which sell goods made from raw material the price of which frequently changes. For example, suppose an article made from steel (the market price of which varies at frequent intervals) is quoted in the catalogue at $8. When the market price of steel drops and the article can be sold for $ 7, a discount of 12 A % can be offered. If raw steel should drop in price so that the article could be sold for ^6, a discount of 25 % could be offered. The fluctuation discount sheet is a means of economy to the manufacturer, because he can issue new discount sheets much more cheaply than complete catalogues. 155. Computing Fluctuation Discounts. Example. What discount will change a catalogue price of 13 to a market price of $ 2.50 ? Solution. $3.00 Catalogue price 2.50 Price at which article is to be sold $ .50 Amount to be deducted by discount f .50 -4- 13.00 = 16| %, rate of discount to be offered State a rule for finding the rate of discount by this method. When the quotient obtained by the division involves a frac- tional per cent, the next lower whole number is sometimes taken as the per cent. Thus, a quotient of lb\ % may be regarded as 15 % ; a discount of 18.27 % may be regarded as 18 %. 192 COMMERCIAL DISCOUNTS Example. An article is listed at 124.50. The market condi- tions are such that it should sell for about 121.30. What rate of discount should be offered ? Solution. $24.50 List price 2L30 Market price $ 3.20 Amount to be deducted by discount ^3.20 H- $24.50 = 13.06%. 13 % would therefore be offered. This discount would make the net price $ . ? ' Written Work Complete the following table, showing what rate of discount would be offered to reduce the list prices at the left to the market prices shown at the top of the table. Express results to the nearest per cent. Market Prices List Pkices $8 50 $7 75 $8 00 $7 60 $6 00 $10 12 11 9 10 00 00 50 80 50 Discount Series 156. Trade and Fluctuation Discounts Combined. Some business concerns offer an unchanging trade discount and a changing fluctuation discount. This slightly increases the task of determining what fluctuation discount to offer. Example. An article is listed at $ 12 less a trade discount of 25%. The market value drops so that the real net price should be f 6. What additional discount must be offered ? Solution. $12 x .25 = $3, Trade discount. $ 12 - $3 = $ 9, Price less trade discount. ,^9 - 16 = $3, amount to be deducted by 2d discount. $3 H- $9 = 33^%, rate of fluctuation discount. tra.de discount 193 Written Work Complete the following table. The columns at the left show the list price and the trade dis- count offered. Find what fluctuation discount must be offered to reduce the price to market values. Approximate results, correct to the nearest hundredth of a per cent. Trade Discount Market Values 124 00 $23 50 $22 00 $20 00 ^28 33 30 40 00 00 50 00 10% 15 12 28 Written Review 1. An implement dealer purchased the following invoice : Dated April 17. 4 No. 364 Plows, $38.75, less 20 %. 7 Self Dump Hay Rakes, $ 20.50, less 18 %. 7 No. 264 Hay Stackers, $41.50, less 15 %. Terms, 2 % for Cash in 20 days. Net 90 days. On May 2, he paid the bill with a check for $ . 2. Which of the following prices is better for the purchaser : 145, less 25 %, 18 %, and 2 % ; 160, less 28 %, 25 %, and 1 % ? 3. A merchant's discounts were 25 % and 15 %. A clerk sold an invoice of 172 and gave a single discount of 40%. How much did his error cost his employer ? 4. A merchant lists a desk at $45 less 20 %. A competitor sells a similar desk for $48 less 33^ %. In order to exactly meet his competitor's price, the first merchant decides to give an addi- tional discount of — %. 194 COMMERCIAL DISCOUNTS 5. Hewett paid an invoice in time to secure a discount of 3 %. If the check sent was for f 208.55, what was the list price of the invoice ? 6. Graff Brothers sent a check to a wholesale house to pay an invoice. The check was for f 801.90. What was the list price of the invoice if the discounts taken were 10 % and 1 % ? 157. A Short Method of Finding a Single Discount Equivalent to a Discount Series. A single discount equivalent to two discounts may be found as follows: From the sum of the two discounts subtract their product. The rule may be easier to remember if stated thus: Add the two discounts; multiply the two discounts; subtract the second result from the first. Example. What single discount is equivalent to a trade dis- count of 20 % and a cash discount of 2 % ? Solution. .20 + .02 = .22 .20 X .02 = m^ Single discount = .216 or 21.6% The buyers in some large business houses prepare an elaborate table similar to the one which follows. When manufacturers quote prices subject to a discount series, the buyers can tell by a glance at the table what single discount the series equals. Written Work Complete the following table, using the method just explained to find single discounts equivalent to the discount series. Trade Discount 18% 15 20 25 33i Cash Discount, 8% Cash Discount, 6% Cash Discount, 5% Cash Discount, 1% Cash Discount, 10% TRADE DISCOUNT 195 With the aid of the table, find the net price of the following: a. An invoice of §215, less 18 % and 5 %. h. An invoice of 8464.20 less 18 % and 10 %. c. An invoice of 1 12.40 less 20 % and 6 %. d. An invoice of -f 23.87 less 83^ % and 3 %. 158. Series of Three Discounts. It sometimes happens that a bill is subject to several discounts. Explain how this might be the case. To find the net price of a bill subject to three discounts, find the discount equivalent to two of the discounts stated, then find the discount equivalent to this result and the third discount. Example. What discount is equivalent to three discounts 25 %, 20%, 10%? Solution. First find the discount equivalent to discounts of 25 % and 20%; the result is 40%. Find the discount equivalent to discounts of 40 % and 10 % ; the result is 46 %. Therefore a discount of 46 % is equivalent to discounts of 25 %, 20 %, 10 %. Written Work Find the net cost of the following bills : 1. {5> 45 less discounts of 20%, 15%, and 10 %. 2. 128 less discounts of 25 %, 10 %, and 5 %. 3. $ 70 less discounts of 30 %, 20 %, and 2 %. Find a single discount equivalent to each of the following series: 4. 20 %, 121 %, and 8 %. 5. 15 %, 10 %, and 4 %. 6. 28%, 14%, and 2%. 7. 25 %, 20 %, and 10 %. 8. 40%, 20%, and 10%. 9. 33^ %, 20 %, and 121 %. 10. 371 %, 10 %, and 20 %. CHAPTER XVIT RECORDING PURCHASES AND SALES 159. The Purchases Book. Merchants usually keep a record of purchases and sales. There are several different kinds of books used for this purpose. The following illustration shows a com- mon form of the Purchases Book. PURCHASES BOOK Date of Invoice From Whom Purchased Amount Termt Discount terra Expire. Csh Diicount Due Date When & How Peid /f/S » M^U^t,^^^^^^ S.3 8/(, ^/<5;^A ^e^ /^ iAH a/t^ i^ m^ /A 2/^-^ The entries in the purchases book are made from the invoice received at the time of the purchase. The model shows proper record of the purchase made from Abercrombie & Co., as shown by the invoice on page 187. Notice that $23.86 is the amount of the invoice after deducting the trade discount of 18%. The cash discount is not deducted until the bill is paid. The terms are taken from the invoice. The discount term expires March 13. It is important to have this date recorded in the purchases book, as it is the last date on which payment may be made and the discount secured. April 2 is the day when the bill is due and payment is ex- pected. No discount is allowed when payment is made between March 18 and April 2. 160. How to find the Date when an Invoice is Due. If the terms are stated in days, count the actual number of days. Thus, 30 days from March 3 is April 2. 196 RECORDING PURCHASES AND SALES 197 If the terms are stated in months, calendar months are counted. Thus, if the terms had been 2/10 ; N/1 month, the invoice would have been due on April 3. No entry is made in the " When and How Paid " column until the invoice is paid. It is not necessary to enter the items in the purchases book, because the invoice can be kept on file to supply this information. 161. The Sales Book. The following illustration shows a page from a commonly used form of sales book. The entries were made from the invoice on page 187. ^%;;Z>fc<5^^. /^/^ ^^9&.^^^. ^..^. <=£^.^ 1 cA^..^<^.^/o. ^/3o /2*g^^*.^^P^^.g^..^>*^^^^^(^^:^^.^ ^S /O 2^ ^f /. SS^^-rrz^,^,^ C^l^^J-i-.^ .^^ /3 ^ ^ '^^ JP.C7 /O ^,^.UU /g% ^ d^ ^.7^ S(^ 162. Loose-leaf Sales Book. Many merchants record their sales in a loose-leaf sales book. At the time the invoice is made, a carbon copy is also made. This requires very little extra labor, and the carbon copies, called "Charge Sheets," having holes punched at the side, can be bound together in a binder. The loose-leaf sales book has several advantages. Both the in- voice and the charge sheet, which forms the sales book, can be made on the typewriter at the same time ; and fraud is prevented because the invoices are numbered, and a clerk cannot sell goods and make an invoice without also making a charge slip. He cannot keep the money and destroy the charge slip because one of the num- bered sheets would be missing, and the fraud would be apparent. The following illustration shows the charge sheet made as a carbon copy of the invoice shown on page 187. 198 RECORDING PURCHASES AND SALES terms: 2^ C&8h in 10 days, Net 30 days. CHARGE June 10, 1915 Scobey & Company, Fayette, Iowa 2 Cases Tomato Catoup 4 doz. 6 Cases Elgin Canned Corn 12 doz. 5 Cases Echo Peas 10 doz. 1.30 1.10 1.25 30 90 Written Work Rule a Purchases Book and record the following purchases, making proper extensions. 1. From Eaton & Dunham, 213 Main Street, Indianapolis, Indiana. Date, June 5, 1915. Terms, 1/15 ; N/60. 6 doz. Silk Four-in-hand Ties 3 doz. White Lawn Ties 38 doz. Assorted Style Amoryth Linen Collars 18 doz. Policeman's Suspenders 9 doz. Khaki Overalls 6 doz. Boys' Flannelette Waists (ages 4 to 13 yr.) doz. 10 doz. Men's Flannel Work Shirts (sizes 14 to 18) 2\ doz. Men's Negligee Shirts doz. each t .371 gross 2.94 doz. 1.92 doz. 4.374 doz. 8.97 doz. 2.16| doz. 8.761 16.40 doz. 14.29 doz. 4.78 doz. 6.93 each 2.17 each 2.98 doz. 6.93^ doz. 4.69. doz. 4.25 RECORDING PURCHASES AND SALES 199 2. From J. B. Clark, Aurora, Illinois. Date, June 8, 1915. Terms 2/20 ;" N/3 months. 7 doz. Assorted Sizes Men's Silk Half Hose 19^ doz. Mercerized Lisle Hose 3 doz. Men's Black Overgaiters 18 Women's Taffeta Silk Waists (sizes 34 to 42) 24 Navy Blue Silk Chiffon Waists 5 doz. Embroidered Lace Coat Sets 2 doz. Amoskeag Gingham Aprons 2J doz. Lace Jabots 3. From Bishop & McGee, Independence, Iowa. Date, June 10, 1915. Terms, 1/5; N/20. 10 doz. Defiance Food Choppers each 1 2. 85 9 doz. Climax Food Choppers each .72 14 doz. No. 7 size Skillets each .22i 30 sets Enamel-lined Iron Kettles, each set con- taining 3 2 quarts at .21 4 4 quarts at .29| 6 6 quarts at .34| 4 8 quarts at .39| 2 10 quarts at .46| 2f doz. H 921 Waffle Irons 61 doz. H 922 Waffle Irons doz. $7.84| each .93 each .55 each ,65% 25 H464 Soapstone Griddles (round) 12 doz. H465 Soapstone Griddles (oval) 4. From A. D. McHaughtoir, Fairchild, Missouri. Date, July 14, 1915. Terms, 3/30 ; N/90. 5 doz. H 731 Wire Waste Baskets doz. I .89 15 doz. H 732 Wire Letter Baskets doz. 1.23 28 H 881 Spring Seats each .88 200 RECORDING PURCHASES AND SALES 15 sets H 393 Cobblers' Outfits set I .96 19 doz. H 242 Curry Combs doz. .6T 14 F 272 Upholstered Rockers each 8.75 25 F 279 Oak Rockers each 12.65 20 F 212 Turkish Rockers each 12.75 Rule a Sales Book, and record the following sales, making proper extension. 5. To J. D. Preston, Monmouth, Illinois. July 7, 1915. Terms, 1/10 ; N/40. 47 No. L 601 Royal Worsted Wilton Rugs 8 x 10 ft. each $ 29.25 52 No. L 602 Royal Worsted Wilton Rugs 6x7 ft. each 19.75 38 No. L 603 Royal Worsted Wilton Rugs 9x12 ft. each 32.35 65 No. L 661 Worsted French Wiltons 9 x 12 ft. each 44.60 50 No. L 662 Plain Color Wiltons 8 x 10 ft. each 31.75 6. To R. J. Noble, Dubuque, Iowa. July 8, 1915. Terms, 1/15 ; N/60. 25 doz. Half-bleached Cotton Towels 16 doz. Linen Monogram Towels 20 doz. Bleached Turkish Bath Towels 14 doz. No. T 291 Cotton Face Cloths 7. To Oscar Hamilton, Reynolds, North Dakota. July 9, 1915. Terms, 2/5 ; N/2 months. 15 doz. Palmetto Fiber Scrub Brushes 22 doz. H 221 Kitchen Spoons, 10 inch 19 doz. H 241 Kitchen Spoons, 12 inch 26 doz. H 251 Kitchen Spoons, 1*4 inch 38 doz. H 333 Kitchen Forks, 13 inch 36 doz. H 334 Kitchen Forks, 15 inch 12 doz. H 341 Perforated Steel Spoons 8 doz. H 691 Kitchen Sets 16 doz. H 692 Kitchen Sets 24 X 54 doz. 1.98 22 X 39 doz. 4.95 23 X 52 doz. 2.37| 10x13 doz. .421 doz. 1 .86 doz. .23 doz. .27 doz. .33 doz. .19 gross 3.20 doz. .84- doz. 8.75 doz. 3.95 RECORDING PURCHASES AND SALES 201 Marking Goods 163. Method of Marking Goods. When stock is placed on the shelves in the salesroom, the cost of each article should be marked either on the goods, on the package which contains them, on tags attached to the goods, or on card lists placed near the goods. 164. Advantage of Marking. In some lines of business it is necessary to have the selling price, or both the cost and the selling price, marked on the goods. When the stock becomes low and the buyer wishes to purchase a new supply, he can compare the price paid for the goods on the shelves, with quotations of prices made to him by the salesmen from the wholesale houses. It would also be a convenience to know the cost of an article if it proved to be a slow seller, and the manager determined to sell at a reduced price to unload the stock. One of the chief advantages of cost marking is in taking inventory of stock and finding its value at cost prices. In marking goods, the cost price is taken from the invoice. 165. "Blind Price Lists." It would be unwise to mark the cost in figures, as this would disclose the cost and the profit to purchasers. It is, therefore, customary for merchants to adopt a set of symbols, called a cipher, or blind price list. Any symbols may be chosen, but they will be more easily written if letters are used, and these letters will be more easily remembered if they form a word or phrase. The word or phrase selected must not contain the same letter twice. Otherwise the same letter will represent two different numbers. The following will illustrate : admonisher mah 1234567890 318 Fitzaubrey izy 1 2 345 6 7 8 90 240 166. The Repeater. To further conceal the cost a " repeater " should be adopted. When the same figure is repeated, as in f^l.55, the repeater sign is used for the repeated figure, "x" is frequently 202 RECORDING PURCHASES AND SALES used as a repeater, but because it is so commonly used, some other repeater would perhaps be preferable. Words or phrases with eleven letters are frequently chosen as keys, one of the letters being used as a repeater. Using "t" as the repeater, and "admonisher" as the key, $3.88 would be written mht. Written Work Using " blacksmith " as the key word, and " d " as the repeater, indicate the following costs : 1. $9.82. 2. I .09. 3. $ .25. 4. $ 1.64. 5. 11.00. 6. 16.20. 7. I .27. 8. $ 7.47. 9. $2.45. 10. I .55. 11. 11.33. 12. $ .39. 13. 18.23. 14. 15.00. 15. il.17. 16. 112.47. 17. $6.62. 18. $2.24. 19. $ .36. 20. $ 1.44. Many articles are bought by the dozen and sold by the piece. In marking goods bought in this way it is necessary to divide the cost by 12. This division will be facilitated if the decimal equivalents of the 12ths, from -^^ to \^ inclusive, are memorized. Make such a table of equivalents and memorize it. Thus, Example. What is the cost of one hat at the rate of $29 a dozen ? Solution. /^ of $ 29 = | 2^^ = % 2.41f . Oral Work What is the cost per article when the cost per dozen is : 1. $27? 2. $34? 3. $64? 4. $11? 5. $ 3.40? 6. $14.30? 7. $7.50? 8. $19.50? 9. $46.60? lo. $37.40? 167. Showing Cost and Selling Price. When both the cost price and the selling price are shown, it is customary to write the cost price above and the selling price below a line, thus: RECORDING PURCHASES AND SALES 203 Cost of an article, §6.25. Selling price, 18.00. Key word, Fitzaubrey. uia Price mark, 8.00 Key words or phrases are sometimes used to mark the selling price as well as the cost, thus : Cost key, " purchased it " 123456789 " t " is the repeater. Selling key, " studying her" 12345678 90 "r" is the repeater. Cost, 13.14. Selling price, f4.25. Mark, 4^. dty Written Work Using the above keys, show markings for the following : Cost Selling Price 1. $1.15 11.50 2. f .65 $ .90 3. $1.30 il.75 4. $2.18 - $2.50 5. $1.25 $2.60 What per cent of profit would be realized from selling goods marked as follows, using " purchased it " as the cost key and " studying her " as the selling key ? phi „ ah - „ dh ^ at 6. —rz' 7. 8. 9. 1.75 ge sty ny Mark the cost of each of the following articles, using " Now Pay Quick " as the purchase key. , 10. $3.00 per dozen. li. $ 185.00 per hundred. 12. $11.52 per gross. 13. $8.64 per case of 4 doz. 204 RECORDING PURCHASES AND SALES Mark both the cost and the selling price of the following. Devise a cost key of your own, and mark the selling price by using the key "importance." 14. Cost i 2.60, marked to gain 22 %. 15. Cost •$ 1.75, marked to gain 18%. 16. Cost $ 25.00, marked to gain 20%. The following is a list of key words and phrases : Buy for Cash Our Last Key Equinoctial Now Be Quick The Big Four Republican No Suit Case You Mark His Black Horse Charleston Frank Smith Now Be Sharp Buckingham Bridgeport Big Factory He Saw It Run Authorizes Cumberland Don't Be Lazy Hard Moneys United Cars Dozen Black Market Sign What Prices 168. Adding the Buying Expenses to the Cost of the Goods. Since the buying expenses are considered a part of the cost of the goods purchased, many merchants add a portion of the buying expenses in marking the cost of each article. Records of total purchases and buying expenses per year are kept for several years, and the average per cent of buying expenses is determined, as shown by the following illustration : To determine a rate per cent of buy- ing expenses for purchases made in 1915. 1912, Buying Expenses, $ 785.75 Purchases, $16,240.00 1913, Buying Expenses, 835.50 Purchases, 19,360.00 1914, Buying Expenses, 923.90 Purchases, 21,365.00 Total Buying Expenses, f 2545.15 Purchases, 156,965.00 12545.15^ 156,965.00 = 4.46^.%, the per cent of buying ex- penses. In marking costs, 4.4 % of the cost of each article should be added as buying expenses. Note, Probably 5 % might be used for convenience. Written Work 1. Compute the per cent of buying expenses to be added to the wholesale cost of goods purchased in 1916. to the nearest whole per cent. Carry the result RECORDING PURCHASES AND SALES 205 Ybar Pttbchases Bitting Expenses 1913 $10,246.80 1534.50 1914 12,726.95 592.90 ■ 1915 14,825.75 615.45 2. Find the marked cost of each of the following articles after adding the baying expenses. Use the per cent of buying expenses found in Problem 1. a. Wholesale cost, $16.20. h. Wholesale cost, 15.75. c. Wholesale cost, 2.35. 3. At what price should each of these articles be sold to gain 23 % on the total cost including buying expenses ? 4. The purchases made by a store in 1915 were $3287.20; the buying expenses for the same year were % 327.90. On the basis of these figures, what per cent should be added for buying expenses on purchases made in 1916 ? Approximate result to the nearest per cent. 5. What objection do you see to determining a per cent of buying expenses from the data of only one preceding year ? 6. Find the marked cost of each of the following purchases, after adding the per cent of buying expenses. Use the per cent of buying expenses found in Problem 4. a. Wholesale cost, % 2.45. h. Wholesale cost, 1.60. c. Wholesale cost, 34.50. 7. At what selling price should each of the articles in Prob- lem 6 be marked to gain 16| % of the total cost ? CHAPTER XVIII PAYING FOR GOODS 169. Making Change. The payment of debts between persons in the same community is usually made with either cash or checks. When cash is the medium of payment, it is often necessary to " make change." Speed and accuracy in making change are very desirable. The following method is generally used by experienced tellers and cashiers. Beginning with the amount of the purchase, take from the cash drawer enough small coins to bring the total to even dollars, using as few coins as possible, then take out dollars or larger denominations until the total equals the payment made. Example. A five-dollar bill was given in payment for a pur- chase of i.39. How should change be made? Solution. Take 1 penny, 1 dime, 1 fifty-cent piece, 4 dollars. As a check on the accuracy of the change, say as you give the customer the money : " 39 cents, 40, 50, $ 1, $ 5.00." Oral Work Following the method above, state what coins and bills should be given to make change for the following purchases, using the largest denominations possible ; Purchase Payment PURCHASK Payment 1. $ .07 $ .50 2. $ .21 $ .50 3. « .56 $ 1.00 4. $ .63 $ 2.00 5. $1.36, $ 5.00 6. $2.79 $ 5.00 7. $3.66 $ 5.00 8. $4.24 $10.00 9. $5.70 $10.00 10. $6.32 $20.00 11. $ .98 $ 5.00 12. $2.77 $10.00 206 PAYING FOR GOODS 207 PXTECHASB 13. $ 3.46 15. $14.42 17. $11.13 Payment $20.00 $20.00 $20.00 Purchase Payment 14. $11.87 $15.00 16. $ 7.37 $ 8.00 18. $ 1.13 $20.00 170. Payments by Check. The payment of all bills by the actual transfer of money would be so inconvenient that the giving of checks has been substituted, and it is said that about 90 % of all bills are now paid by checks. 171. Deposits and Withdrawals. Business men keep the greater part of their cash funds on deposit in banks or trust companies. When money is deposited, a deposit slip similar to the illustration below is filled out by the depositor, showing his name, the date, the item, and the amount of the deposit. DEPOSITED BY IN THE STATE BANK OF OAK PARK OAK PARK, ILU. i nm.n DOLLARS H-0 CENTS OO 35 00 35 snvKR 7 "6/ ^IT.LS Total A Deposit Slip The depositor, wishing to pay a bill, draws a check ordering the bank to pay from the funds on deposit the sum of money stated on the check to the person named thereon. If the depositor wishes to draw cash from his account, he may make the check payable to " Self " or to " Cash." 208 PAYING FOR GOODS 70-1742 OKDBR OI' /7L Jt. LffiuL i^JSSlM— 3'i^ixtnaj ruir DOIJ^ARS PAYABLE IN CHICAGO EXCHANGC. C . <^ QjtpAr(/n/ijor\) A Check C. L. Stevenson, the drawer of this check, is paying M. R. Cole, \hQ fayee^ f 15.65. Depositors are credited by the bank with their deposits, and are charged with the checks drawn by them. Checks received from other people may be cashed at the bank, or they may be deposited the same as cash. All checks cashed or deposited must be indorsed ; that is, they mast be signed on the hack by the per- son cashing or depositing them. Checks must also be indorsed when they are transferred to another person before being cashed at the bank. Indorsement should be made on the back of the left end of the check. 70-1742 fOCf — I>01iI^//, y^^-s- MouTf T Vkrnou, Iowa ^ jLZ. VSISL No_i^ Mount Vernon Bank .or order $4£l ..so j1££_ Dollars Written Work 1. Using the following information, rule a check and stub similar to the preceding illustration, enter the necessary facts, and draw the check. PAYING FOR GOODS 211 Name of bank, Fourth National, your city. Balance from yesterday, f 103.27. Deposit of $ 19.38. Check No. 6, drawn by you to-day, payable to G. D. Fitzgerald and Co., in payment of the invoice purchased from them eight days ago. Amount of invoice, 873.28; terms, 2/10; N/60. Write the check and stub. What is the new balance ? 175. The Bank's Accounts with its Depositors. All banks keep a depositors' ledger. Usually a page is devoted to the deposits and checks of each depositor. l/OHl/io'ifva' %^ /i-a/i/oio^ DATE DEPOSITS CHECKS BALANCE /Cff.^ Un.. 6 /fi^ A Bane Draft 218 PAYING FOR GOODS h. Bank drafts are drawn on banks in large cities, while checks may be drawn on banks in small towns. There is less expense, therefore, incurred in collecting a bank draft than in collecting a check, and banks seldom charge exchange when cashing bank drafts. Explanation. D. B. Carpenter is the cashier of the State Bank of Eudora. This bank has funds on deposit in the National Bank of the Republic, Chicago. When the National Bank of the Republic pays this draft, it will deduct the amount from the bal- ance of the Eudora Bank. S. F. Simonds lived in Eudora and wished to send i 16.25 to F. E. Craig of Bloomington, Illinois. When he purchased the draft from his bank, he had it made payable to himself. He might have had it made payable to F. E. Craig, but if he had done so, his (Simonds's) name would not have appeared on the draft, and if it had become separated from the letter accompany- ing it, Craig might have had difficulty in telling from whom he received it. After receiving the draft, Simonds indorsed it as follows; Pay to the order of F. E. Craig. S. F. Simonds. and sent it to Mr. Craig. Mr. Craig indorsed it and cashed it at the Corn Belt National Bank of Bloomington. We will now follow the steps by which the Corn Belt National collected the draft. This bank deposits funds with the Conti- nental National Bank of Chicago, which is called its "corre- spondent," and it therefore sent this draft, with others paid the same day, to the Continental National bank as a deposit. The Continental National sent the draft to the Clearing House, which collected it from the National Bank of the Republic. After paying the draft, the National Bank of the Republic charged the amount to the State Bank of Eudora. PAYING FOR GOODS 219 The preceding statement may be summarized as follows : State Bank of Eudora sells the draft to S. F. Simonds, who paid for it either with cash or a check ; and sent it to I F. E. Craig, who gave Simonds credit for il6.25; and deposited the draft at I Bloomington Bank, which gave Craig $ 16.25 ; and sent the draft to Continental National, which gave the Bloomington Bank credit for $16.25; and collected the draft through the Clearing House from I National Bank of the Repub- lic, which paid the Continental National $16.25, and charged Eudora Bank 116.25. Indorsements on the Model Bank Draft ^ ^ ^-^>«e..^ J^ £. (yi^^^j^^ Pay to the order of Continental National Bank. All prior indorsements guaranteed. Corn Belt National Bank, Bloomington, III., F. A. Frend, Cashier. Pay to the order of Any Bank, Banker, or Trust Co. Prior indorsements guaranteed. July 12, 1915. Continental National Bank, M. B. Jones, Cashier. These indorsements indicate the successive owners of the draft. The last two indorsements are made with rubber stamps. The last one is made payable to "any Bank, Banker, or Trust Company," for convenience in collecting through the Clearing House. 220 PAYING FOR GOODS 181. The Cost of Bank Drafts. When a bank sells a draft, it gives the purchaser the benefit of its deposit relations with a large city bank. For this convenience it may make a charge called "Exchange." It will be noted that exchange on a check is paid by the person receiving and cashing it, while the exchange on a draft is paid by the person purchasing and sending it. When ex- change is charged, -^-^^o with a minimum of 10 cents is a custom- ary fee. The following is a copy of the check given by S. F. Simonds to the State Bank of Eudora to pay for the draft purchased. There was a charge of 10 cents for exchange. =F I^lTDO JCA \^ ORUEIl OF Il/g-gPOLAARS ^c.^cJ^td^-'^Z-i^.^ Written Work 1. You owe H. J. Palmer, of Toledo, Ohio, $ 27.35. You buy a draft, payable to yourself for this amount, from the Merchants' State Bank of your city, of which A. R. Burton is the cashier. The draft is drawn on the Home National Bank of New York City. Exchange, 10 cents. Draft is made payable to you. Write a draft similar to the one which the bank would give you, and the check which you would give the bank in payment. Indorse the draft. How soon can Mr. Palmer get his money ? 2. Mr. Palmer cashed the draft at the High Street National Bank of Toledo, B. F. Ohren, Cashier. The High Street National sent it to the Bankers' National Bank of New York, G. B. Martin, Cashier. The Bankers' National collected it through the Clearing House. Show the indorsements on the draft. PAYING FOR GOODS 221 3. Find the cost of a draft sent to pay an invoice of i 246.50, less a cash discount of 2 %. Exchange, ^ % of the face of the draft; minimum, 15 cents. 4. On October 8, you purchased from Benedict & Meredith, Pittsburgh, Pennsylvania, an invoice amounting to $794.86. Terms, 2/15 ; N/60. On October 16, you paid the invoice by a draft purchased at the Claim Street State Bank of your city, J. D. Haines, Cashier. The draft was drawn on the First National Bank of New York. Exchange, ^3^ %. Write the draft which you received, the indorsement, and the check you gave to pay for the draft. 182. Postal Money Orders. A postal money order is an order drawn by one postmaster on the postmaster at some other office, calling for the payment of a stated sum of money to the person named on the order. Postal money orders are commonly used to make payments by mail. They are issued in any amount from $.01 to $100.00. As a means of protection, no order is issued for more than $100.00. If it is desired to send more than this amount, additional orders may be purchased. Fees for money orders paj^able in the United States (which in- cludes Hawaii and Porto Rico) and its possessions, comprising the Canal Zone, Guam, the Philippines, as well as in Bermuda, British Guiana, British Honduras, Canada, Cuba, Mexico, Newfoundland, at the United States Postal Agency in Shanghai (China), in the Bahama Islands, and in certain other islands in the West Indies, are as follows : from $ 0.01 to $ 2.50 . 3 cents from 2.51 to 5.00 . 5 cents from 5.01 to 10.00 . 8 cents from 10.01 to 20.00 . 10 cents from 20.01 to 80.00 . 12 cents from 30.01 to 40.00 . 15 cents from 40.01 to 50.00 . 18 cents from 50.01 to 60.00 . 20 cents from 60.01 to 75.00 . . 25 cents from 75.01 to 100.00 . . 30 cent? 222 PAYING FOR GOODS Examples. 1. What is the cost of an order for $27.35 ? Solution. $27.35 lies between $20.01 and $30.00, and the rate is 12 cents. Total cost of order, $27.35 + .12 = $27.47. 2. What is the cost of sending $ 267.95 by postal money orders ? Solution. Two orders for $100.00 each, and one order for $67.95, will be purchased. Fees of two $100.00 orders, 60 cents. Fee of $67.95 order, 25 cents. Total fees, 85 cents. Total cost of orders, $267.95 + .85 = $268.80. 183. Bank Drafts and Postal Money Orders Contrasted. Note the following differences between a bank draft and a postal money order : A bank draft may be indorsed as many times as desired. A postal money order may be indorsed only once. A bank draft may be cashed at any bank. A postal money order must be presented to the post office on which it is drawn, or to a bank which can cash it at that post office. A bank draft is payable as soon as it is presented to a bank. At the time of issuing a money order the issuing postmaster sends a notice to the paying postmaster. A postal money order will not be paid until the paying office has received this notice. However, this does not usually cause any delay. 184. Express Money Orders. Express money orders are similar in many respects to postal money orders. They can be purchased from the agent of the express company, and are payable from the funds of the express company on deposit in various banks specified in the order. No order is issued for an amount larger than $30. If it is desired to send a larger amount, additional orders must be purchased. Express Money Order Rates. The rates for express money orders are the same as for postal money orders, although no order is issued for more than $50. Example. What will be the total fee for the transfer of 8241.75 by express money orders ? PAYING FOR GOODS 223 Solution. Four $50 orders at the rate of 30 cents per hundred will cost 60 cents. One order for $41.75 will cost 18 cents. Total, 78 cents. 185. Telegraph Money Transfers. Money may be transferred by telegraph when there is an urgent necessity for immediate payment. The rates for this service between points in the United States are determined as follows : To the tolls for a fifteen-word message between the office of deposit and the office of payment add the following charges: For 1 25.00 or less .... 25 cents 25.01 up to 150 . . . . 35 cents 50.01 up to 75 .... 60 cents 75.01 up to 100 . . . . 85 cents For amounts above §100 add (to the f 100 rate) 25 cents per hundred (or any part of ilOO) up to 13000. For amounts above §3000 add (to the §3000 rate) 20 cents per hundred (or any part of §100). Exam'ples. 1. What is the charge for sending §25 or less to a point where the fifteen-word rate is 65 cents ? Solution. $ .25 Minimum charge .65 Tolls on 15-word message $ .90 Total charge 2. What is the total charge for transfer of §105 if the tolls on a fifteen-word message are 65 cents ? Solution. | .85 Charge for first $ 100 .25 Charge for fraction of second $ 100 .65 Tolls on 15-word message $1.75 Total rate Written Work 1. Assuming that you owe the following bills: F. G. Young, §39.40; P. S. Sanborn, §112.75; H. L. Colwell, §416.25, less 3%; determine the fees for the purchase of either postal or express money orders for transferring money to make payments. Com- plete the following blank form. 224 PAYING FOR GOODS Namb Net Amount OF Bills Fees for Money Orders Total Cost Denomina- tions of Orders Received FROM Ex. Co. Denomina tions of Orders Received from P.O. 2. What is the charge for a telegraph money transfer of $23.15 to a point where the fifteen- word message rate is 85 cents ? 3. What is the charge for a telegraph money transfer of $52,85 to a point where the fifteen- word message rate is $1.30? 4. What is the total cost of a telegraph money transfer for $215 to a point where the fifteen- word rate is 65 cents ? CHAPTER XIX COLLECTING BILLS 186. Statements. At periodical intervals, usually on the first day of each month, merchants send a statement to their customers. STATEMENT ACCOUNT NO. 5422 WEBSTER & MCCLELLAN 16 JEFFERSON STREET F. B. Turner, CHICAGO, May 1 , La Grange, 111.. 1915 Airbills are due the fint of the month after purchase. This statement Is Intended to show you the condition of your account on our books. If this statement does not correspond with your accounts please notify us. If correct, please remit. To balance, as per former statement 17.65 To.Mdse, as per invoice Apr 11^3 23.78 April 15 19.65 April 23 Credits 27.84 88.92 April 20 By Udse returned . 2.85 April 26 By Cash 75.00 77.85 Balance 11.07 This statement shows the date and amount of each purchase, the date and amount of each payment, and the balance due. The items sold are not enumerated in the above statement because the invoices ma}^ be consulted to obtain this information. 225 226 COLLECTING BILLS HENDERSON & BISHOP 143 WEST MONROE AVENUE R. F. Bailey West Union, Iowa. CHICAGO. July 1 , 19 15 Intereet charged on overdue aooounti. All claims for correction must be made on receipt of statement > DATE ITEM DEBIT CREDIT BALANCE June 1 Balance, May 31 75.60 June 2 Cash 75.00 .60 June 5 Mdse 34.55 •35 .15 June 11 Mdse 17.26 52.41 June 15 Returned goods 4.35 48.06 June 24 Mdse 5.96 54.02 Another Form of Statement Written Work 1. Rule a statement similar to the first illustration, and enter the following : Your transactions with S. J. Smith, Fayette, Missouri. Balance, August 1, 1127.86. Purchases, August 3, 172.85 ; August 11, $23.89 ; August 14, $75.23; August 20, 1 14.76 ; August 28, I 38.97. Payments, August 2, Cash f 126. 00; August 13, Returned merchandise, $15.00. Statement rendered September 1. 2. Rule a statement similar to the second illustration, and enter the following transactions with Beardsley & Russel, Montgomery, Alabama. Balance, October 1, 1915, $32.11. Purchases, October 5, $45.89; October 9, $23.87 ; October 12, $243.87; October 15, $65.00; October 21, $52.57; October 26, $40.50 ; October 29, $50.25. COLLECTING BILLS 227 Payments, October 7, 150.00; October 21, J^ 125.00; October 24, $40.00. Returned merchandise, October 20, $5.50. Statement rendered November 1. 187. Commercial Drafts. Commercial drafts offer an effective method of collecting accounts. A commercial draft is an order drawn by the party to whom money is due, requesting the debtor to pay a stated sum of money either to the drawer of the draft or to a third party mentioned in the draft. Two and Three Party Drafts. If a draft requests the debtor to pay money to the drawer, it is called a two-party draft. Such drafts are collected through a bank. If a draft requests the debtor to pay money to a third party, it is called a three-party draft. Sight and Time Drafts. If a draft requests immediate payment, it is called a sight draft. Such a draft is payable at once, without acceptance. If a draft is to be paid after a stated time, it is called a. time draft. 188. Parties to a Draft. The drawer is the person who draws the draft. The drawee is the person on whom the draft is drawn, and who is requested to pay the money. The payee is the person to whom the money is to be paid. In case of a two-party draft, the drawer is also the payee. 189. Reasons for Drawing Drafts. (a) To effect prompt payment of invoices. 1. How a sight draft is used : Wholesale houses often make terms similar to the following : '' Sight draft in ten days, less 2 %." At the expiration of ten days from the date of sale, the selling merchant sends a sight draft for the net amount of the bill, to the purchasing merchant's bank. The bank presents it to the purchaser for collection. 2. How a time draft is used : If the terms of the sale were " Thirty-day draft," the selling merchant would, at the time of 228 COLLECTING BILLS making the sale, draw a thirty- day draft on the purchaser and send it to him for acceptance. After the draft has been accepted, it has the same value as a note because the purchaser has agreed to pay it when due. The seller may borrow money from a bank, giving the accepted draft as security. (5) As a means of collection. When a bill is overdue, and the debtor is slow in making settlement, a draft, to be collected by his bank, will often bring about a settlement. ((?) To make C. O. D. shipments by freight. When a mer- chant sells goods to be shipped by freight, he receives a bill of lading from the railroad company. This bill of lading is the railroad's receipt for the goods. To make a C. O. D. shipment the seller obtains an Order Bill of Lading from the railroad. The purchaser cannot get the goods from the railroad without surrendering the bill of lading. Therefore, a selling merchant, instead of sending the bill of lading direct to the purchaser, attaches it to a sight draft and sends the draft and the bill of lading to a bank in the purchaser's town. In order to get the goods the purchaser must have the bill of lading ; in order to get the bill of lading he must pay the draft at the bank. (c?) To avoid the transfer of money. If Jones owes Smith, and Smith owes Brown, Smith may collect the debt from Jones and pay his own debt to Brown, or he may request Jones to send the money direct to Brown. If Jones and Brown live in the same town, both debts can be paid without sending the funds through the mail, even though Smith lives in a distant city. A three-party draft is used for this purpose, Smith requesting Jones to pay Brown. 190. Two-party Sight Draft. Benjamin Osborne of Madison, Kansas, owes J. B. Dunham of Toledo, Wisconsin, 8 28.65. In order to collect this bill, Mr. Dunham draws the following draft on Mr. Osborne. COLLECTING BILLS 229 £ ^ IZK^rrisO'rustandSamngsBaxk CRCDIT lYOriNAO ^^-^^^^^ FOREIGN MONEY AND EXCHANGE 237 Banker's Bill 201. Commercial Bills. A commercial bill of exchange is a draft drawn by a shipper of merchandise upon a foreign buyer or his representative. Commercial bills are made payable either at sight or after a certain time. If such a bill is payable in less than thirty days, it is known as a short hill; if in thirty days or more, it is known as a long MIL If the bill is accompanied by a bill of lading and other shipping papers, it is known as a documentary hill; if no papers accompan}^ it, it is known as a clean hill. ^^^^^>5: (Tc /A_yML- Commercial Bill 238 FOREIGN MONEY AND EXCHANGE A documentary hill is accompanied by the bill of lading, the invoice of the goods, and usually by the insurance certificate. 202. Sending Money by Banker's Bill. When it is desired to send money abroad, a banker's bill may be purchased from the bank in much the same manner that a domestic bank draft is purchased. In fact, bankers' bills are frequently called foreign bank drafts. The banker's bill is sent abroad by the purchaser in payment of his debt. 203. Collecting Accounts by Using Commercial Bills. When it is desired to collect an account from a foreign debtor, a merchant may draw a commercial bill and leave it with his bank for collec- tion. The method of collecting the bill is similar to that em- ployed by banks in the collection of domestic sight or time drafts. 204. Securing Immediate Payment for Goods by Using Documen- tary Bills. Exporters often obtain immediate payment for goods sent abroad by the following method. The goods are delivered to the transportation company and a bill of lading is received by the shipper. The goods are insured against loss in transit, and a certificate of insurance is received from the insurance company. The shipper draws a bill of exchange on the foreign importer, and attaches the bill of lading and the certificate of insurance to the bill of exchange, thus creating a documentary bill. The three papers are indorsed to the order of a bank which purchases the draft. The exporter thus receives payment for his goods at the time of shipment. If the bill cannot be collected, the goods are taken in payment. If the goods are lost, the certificate of insurance guarantees that the bank will receive payment from the insurance company. The bank, in turn, indorses the docu- ments and sends them to some foreign bank, receiving credit for the bill of exchange. The foreign bank collects the bill from the exporter. The following summary illustrates the method of collecting a documentary bill of exchange : American Exporter sells the documentary bill to an American Bank, and receives cash. FOREIGN MONEY AND EXCHANGE 239 American Bank sends the documentary bill to a foreign bank, and receives credit against which it can draw bankers' bills. Foreign Bank collects the documentary bill from the foreign importer. 205. Rates of Exchange. The amount which a bank will pay for a commercial bill and the amount which it will charge for a banker's bill, depend upon the rate of exchange existing between the countries involved in the transaction. The mint par of exchange, as shown by the table on page 234, is the actual value of the coin of one country stated in terms of the coin of another country. It remains comparatively constant. The rate of exchange is the market value of a bill of exchange. These values or rates of exchange are constantly fluctuating, because the value of a bill of exchange, like the value of other property, varies with the supply and demand. As we have seen, bankers buy documentary bills to send abroad to create a deposit against which they can draw bankers' bills. At a time when American exporters are shipping large quantities of goods abroad, documentary bills on London will be plentiful. American bankers can easily procure all of these bills they desire in order to keep up their balance in foreign banks. Supply will be relatively much greater than demand, and the price will there- fore be low. Exchange on England will be below par, or at a discount. Par is f 4.8665. If the rate of exchange is below par, gay at $4.84, the man who sells a documentary bill on London may re- ceive for it less than its face ; while the man who wishes to buy a banker's bill payable in London may buy it for less than its face. On the other hand, let us assume a condition when American imports greatly exceed exports. While imports are being made in large quantities, American banks will have frequent demands for bankers' bills to send abroad in payment for goods. In order to issue these bills, American banks must maintain a large deposit in the foreign banks. To keep up this large balance, they will require numerous documentary bills payable in London. But since exports are low, the supply of these documentary bills will 240 FOREIGN MONEY AND EXCHANGE be small, and bankers will bid against each other to obtain them. This will cause the rate of exchange to go above par. This means that the American exporter can obtain more than $4.8665 per pound sterling for documentary bills on London which he has for sale ; while the importer who wishes to send money abroad will have to pay more than $4.8665 per pound sterling for bankers' bills. 206. Quotations of Rates of Exchange. Exchange on Great Britain is quoted at the number of dollars to the pound sterling. 4.87 means that a pound bill on London will cost $4.87. Exchange on the Latin Countries (France, Spain, Switzerland, and Italy) is quoted at the number of foreign coins per dollar. Exchange on France, quoted at 5.15|^, means that 5.15|^ francs can be purchased for il.OO. . Exchange on Germany is quoted at the number of cents per four marks. 95 means a banker's bill for four marks can be pur- chased for 95 cents. Many banks receive daily the quotations of foreign exchange. The following is an extract from such a quotation : London Cables 4.8915 London Demand 4.8865 Sixty Day Grain 4.8625 Paris Checks 5.15 Berlin 95f To find the cost of a banker's bill on London. Example. What is the cost of a £600 draft on London, pur- chased at 4.8675? Solution. $ 4.8675 Cost per pound ^600 Number of pounds $ 2920.50 Cost of £ 600 draft To find the cost of a draft on Paris. Example. What is the cost of a 300-franc draft on Paris, pur- chased at 5.15? Solution. 5.15 francs cost $ 1.00. 300 francs will cost as many dollars as 5.15 is contained in 300; therefore the cost is ^58.25. FOREIGN MONEY AND EXCHANGE To find the cost of a draft on Berlin. 241 Example. What is the cost of a 1000-mark draft purchased at 951? Solution. 1000 -r- 4 = 250, number of lots of 4 marks purchased. ^.95i X 250 = ^238.13. Reverse these processes to find the value in foreign coinage of drafts purchasable with a specified amount of United States money. 207. Travelers' Checks. Travelers' checks are issued by the express companies and by the American Bankers Association. These checks are issued in denominations of United States money, but show on their face their cashable value in the coinage of foreign countries. The purchaser signs the checks when pur- chased, and again when cashed, as a means of identification. The cost of the checks is the face plus ^ % commission. 208. Letters of Credit. A letter of credit is a circular letter addressed to the correspondents of the issuing bank, introducing the holder, certifying that he is authorized to draw a certain sum of money, and requesting that his drafts be honored up to that amount. By depositing cash or securities with a bank, a traveler can obtain a letter of credit. This document is drawn by the bank in which the cash has been deposited. When a bank issues a letter of credit, it thereby authorizes its correspondents (banks in 242 FOREIGN MONEY AND EXCHANGE which it has money on deposit) to pay drafts drawn by the traveler up to a specified sura. The bank also furnishes the pur- chaser a Letter of Indication containing his signature ; when the (Eirrulm* JPrltrr uf (Hxtbxt. c^.OOOO Harris Trust and Samngs Bank ORGANIZED AS ^.W:HAIUaS & CO.,1882. INCORPORATED 1907. (Qj^/i^T/un^ '^am/t^^i ^ /^ha^ traveler presents a draft to one of the foreign banks specified in the letter of credit, the signature on the draft is compared with that on the letter of indication. If the signatures are identical^ FOREIGN MONEY AND EXCHANGE 243 OBLIGATION. FOREIGN LETTER OF CREDIT. fonn4S-B. tu:07. VAT ^ / ^5 It /^ ungrantinsto L'ZZZTL^ a circular LETTER Chicago HARRIS TRUST AND SAVINGS BANK.^>^ 'Dear Sirs: In consideration of ydurjjsrantinr *" ' '^'^ OF CREDIT onJ^:^S:::±^ No Q..^.. ...Jn fayorffL^^Lh.......y ..^„^^ — ..■ ^ .. for. ^^.:^.09,,Z.,..:^^^ of which Ciiik-.... acknowledge redeipt, ^..._ hereby engage to pay on presentation,^ in United States Currency {at the current ratSaf exdmnge), any and all sums that may from time to time be drawn under said Letjer of Credit, and also a commission of one per cent; or .?r-fL ........authorize you todklrgetkesame to /i^-<^ account with you. As coltnteral security for the prompt faymepif at maturity of any oj/tbe obligations contemplated above S>i...... ^have deposited with ^^CDOO vtng described properly : W^^.^Js...^- which youy or your asVipns, ^It hereby authorized to sell in whole or in part upon the non- performance of this promise or the nffta^aymen/at maturity of any of the obligations contemplated above, or at any time or times thereafter jGJ puNu or private sale, without advertising the same or demanding payment, or giving notice, and to\npl/i^uch of the proceeds thereof to the payment of such indebtedness as may be necessary to pay the same with all interest due thereon, and also to the payment of all expenses attending the sale of said property, returning the over- plus to the underisgned, who shall remain liable for the prompt payment of any deficiency or deficiencies arising on account of such sale. Yours tr the foreign bank pays the draft, charges the amount to the bank issuing the letter, and indorses the amount of the draft on the letter. Thus, the letter of credit shows at all times the balance remaining subject to draft. When a draft is drawn which exhausts the balance, the letter is surrendered, and sent, together with the draft, to the issuing bank. Letters of credit are issued in an amount equivalent to the exchange value of the cash or securities deposited, minus a percentage charged for the ac- commodation. HARRIS TRUST AND SAVINGS BANK INCORPORATCO 1607 Chicago, u. s. a. To Messieurs The Kinks and Bankers hiamed Herein: The Bearer of this Letter, «5 been supplied with our Circular * Letter of Credit No. OO HARRIS TRUST AND SAVINGS BANK 244 FOREIGN MONEY AND EXCHANGE Written Work 1. Find the total cost of a postal money order for |585, payable in Hongkong. 2. Find the total cost of a postal money order for $ 215.65, pay- able in Paris. 3. What would be the cost of a London draft for £ 115, ex- change being quoted at 4.8675 ? 4. A man had f 500 which he wished to remit to his mother in Paris. How many francs did she receive, the rate of exchange being 5.15? 5. A man residing in this country wished to send his nephew in Berlin a birthday present of $10. What was the amount of the draft in marks, exchange being at 95 J ? 6. M. Le Count, traveling in America, presented to a Chicago bank a draft on the Credit Lyonnais, Paris, for 2000 francs. How much American money did he receive, exchange being quoted at 5.16? 7. The Western Milling Co. sold a Glasgow customer three hundred barrels of XXXX flour at 19s. per barrel. The Milling Co. sold its sixty-day time bill, with bill of lading attached, to its banker for 4.86|- per pound sterling. What was the amount of the draft in English currency, and how much per barrel United States currency did the company receive for its flour ? 8. The Lincoln Grain Co. sold three cars of wheat to a Liver- pool miller at 4s. per bushel. The net weight of the cars was : 58,950#, 59,040#, and 64,360#. The bank, as agent for the grain company, sold the draft with bill of lading attached at 4.8555. How much did the Grain Company receive ? CHAPTER XXI ACCOUNTS An account is an orderly record of the transactions pertaining to any one person or thing. 209. The Cash Account. In keeping a record of cash, All cash receipts are entered on the left, or debit side ; All cash payments are entered on the right, or credit side ; The difference between the total receipts and total payments is the balance of cash on hand. The following transactions are recorded in the model cash ac- count in the illustration. April 6, 1915, C. D. Smith invested 15000 in business; April 7, he paid $1640 for goods; April 9, he paid his store rent, $75; April 10, he received $275 for merchandise ; April 13, he received $36 from John Appleton; April 14, he paid F. G. Barton $128; April 16, William Hobart paid him $60 on accoujit ; April 28, he paid D. F. Hilton $30 on account. K^^.^^ ^^ ^ ^^^^.:^. ^CC \^111/ ■^ ■^^^yS^^'A^A^^ /6^ ' /r> ^g^^.^3^^. 2a s — /27 a^^.,^a>.y- /■>, (L-A^^^^A/b,^ <^ /iJ. /2 ^ ^yy.^^B^:^^. ^ ^ j ^/? s^^^^C'j^.. 3 -^n ^^.Z.,,z^^ _i26fc i? <5i2 . . ^2-? 1/- ^^«^ / ^^y^^j-^. ^£2 5 ^ y 210. Personal Accounts. Transactions with persons are re- corded in personal accounts. Persons to whom goods are sold are debited for all goods sold to them on account; they are credited for payments made by them on account. 245 246 ACCOUNTS Persons from whom goods are bought, are credited for goods purchased from them on account ; they are debited for payments made. to them on account. The two illustrations which follow will show the two common rulings for personal accounts. May 1, 1915, purchased from Harold Booth, merchandise, -f 260. May 7, purchased merchandise from him, $37.90; May 10, paid him for the invoice of May 1, less 1 % discount. Cash #257.40, Discount $2.60; May 17, paid him for the invoice of May 7, less 1% discount, Cash $36.52, Discount $.38; May 20, pur- chased merchandise, $271.25. .%;>,.^.^^u^ /f/^ %^^^ AS-y 2.i,o &£o M^ ^^.^-^ £^£ 7^^ ^^<^-^ ^^ rZ^- 2^£. June 1, 1915, sold to B. A. Newcomber, goods amounting to $345.70; June 4, sold to Newcomber merchandise amounting to $38.45 ; June 11, received payment for invoice of June 1, less 2%, Cash $338.79, Discount $6.91; June 12, sold Newcomber an in- voice amounting to $83.92; June 14, received payment for the invoice of the 4th, less 1%, Cash $38.07, Discount $.38. (^ C^, yZc^:<^-c^^^^.^/^ yt^ Date Sale Cash Discount Balance 3AC^ n ^¥^ ^ /^ Z^ J^^ .A^ 6L5. ^ ^.3^5 .^3. 7^ ^ ^s_ A5. ACCOUNTS 247 211. Accounts Receivable and Accounts Payable. If a person's account is larger on the debit side, it shows a balance owed hy that person ; it is .therefore an account receivable, and the balance is a resource. If a person's account is larger on the credit side, it shows a balance owed to that person ; it is therefore an account payable, and the balance is a liability. Written Work 1. Rule a cash account and enter the following transactions ; find the balance, and rule the account. August 2, you invest 15000 in a grocery business; August B, purchase merchandise, paying cash for the same, $1345.75 ; August 6, receive cash for merchandise sold, $127.50 ; August 10, receive cash for goods sold, §50.25 ; August 12, pay for advertis- ing, $5.60 ; August 17, receive cash for merchandise sold, $23.74 ; August 18, pay cash for an invoice 'of merchandise, $56.35; August 21, receive cash from Henry Belmont on account, $45.80 ; August 23, pay cash to Oscar Haines on account, $54.85 ; August 31, pay store rent, $30, and clerk hire, $35. 2. Rule a personal account similar to the illustration of Harold Booth's account, page 246, and enter the following transactions : September 3, you purchase from R. G. Henderson, on ac- count, 2/10; N/60, an invoice of goods amounting to $237.40; September 9, purchase an invoice of goods from Henderson, $58.35, terms 1/15; N/2 months; September 11, purchase an invoice of merchandise from Henderson, $123.60, terras 2/5; N/30 ; September 12, pay the invoice of the 3d, less the dis- count ; September 14, purchase goods amounting to $25; Sep- tember 16, pay the invoice of the 11th, less the discount. What is the balance of Mr. Henderson's account ? Is this an account receivable or an account payable ? Is the balance a resource or a liability ? 3. Rule an account similar to the illustration of B. A. New- comber's account, page 246, and enter the following transactions ; 248 ACCOUNTS July 2, sold R. S. Clark, terms 1/5; N/30, merchandise amount- ing to $57.82; July 5, sold Clark goods to the value of 123.95, terms 2/10 ; N/60 ; July 7, received payment for the invoice of the 2d, less the discount; July 9, sold Clark an invoice of $75, less a trade discount of 10%, terms 1/10; N/30; July 11, sold him a bill of goods amounting to $40 ; July 15, received cash for the invoice of the 5th, less the discount. Is this account an account receivable or an account payable ? Is the balance a resource or a liability? CHAPTER XXII TAKING INVENTORY At certain regular intervals an inventory is taken to determine the value of the stock on hand. Two clerks usually work to- gether in taking the inventory. One counts the number of items of each kind, and reads aloud the cost price marked on the goods. The second clerk records these facts. The inventory is then sent to the oflQce, where the value of each item is extended and the total value of the stock on hand is determined. Inventories are entered in various forms, depending upon the details of information desired. 212. Periodic Inventories, may be used : A simple form like the following QVAIfTITY NAME on T£M COST COST rXTEAS/OU /^Ul. ^.^.t^t/^ C^^lC^^^yt. S Co / oC ¥0 34'^ff' /— ^&^^ ^6 2^ JO &8]^^ ^^&'^/&-ft^ C^^^^ ¥^ /:2 zt^ Written Work Rule an inventory similar to the preceding form, enter the fol- lowing items, find the cost of each item, and the total cost. This is one of several inventory sheets used in taking stock in a grocery. 87 lb. Mexican Java Coffee lb. % .23- 136 lb. Ceylon Tea lb. .42 167 Pkg. Half-pounds Ceylon Tea lb. .47 2 cases Boneless Herring (4 doz.) 249 doz. 1.10 250 TAKING INVENTORY Salt Mackerel Cans Corn Cans Tomatoes Cans Peas Cans Beans . Bottles Olives Bottles Olives (18 oz.) doz. Bottles Stuffed Olives (10 oz.) Evaporated Apricots Evaporated Apples Dried Prunes Dried Peaches Seedless Raisins case Currants (36 lb.) A more elaborate form of inventory similar to the following may be used when desired. 83 lb. 8f doz. doz. doz. H doz. H doz. H doz. 345 doz. lb. 163 lb. 109 lb. 230 lb. 67 lb. 1 case lb. $ .22 doz. .85 doz. .95 doz. 1.25 doz. 1.35 doz. 1.00 doz. 3.20 doz. lb. lb. lb. lb. .821 .08} .07i .05J .07| lb. lb. .09i .08J Add Deduct Lot No. Size Name and Quantity Cost Price Cost Extension % Dep. Loss As- turned c4 M^ 6 3 S2*«^^*«^ ^*«.%«^&^ O^.^^^ £ so S ¥c / ■:^ t/^^ d'A ^^2*^^ ,*^ C 8o g ^0 ¥ c/ vs. 7 ^9PaU^ ,.>^^^ (Z,..i>^^^^J^^^:7^2^:^:Jt^ J^ ^ % ^ ^ 3 ^ .. .^^^wv-^^ ^%.^^ S-^g^^g^^^^^^zx?^^ Promissory Note 257 258 INTEREST If the borrower is a person of small means, or if, for any other reason, it may be unsafe to loan him money, he may be requested to have some person of recognized financial standing sign the note with him. Such notes are either joint notes, or joint and several notes, depending upon the wording. OO ¥-00"^ . ^m^6(or/e>. >^ /. /,^^ m:S_ .^ 'yj^^^ ^^..t^<^ y{:i/^di^!CMZl6^^^^y^^»^n^^^/tu^ ^^fc^ffr ~~~ <^^.^. ^r^^,..^!^ S^_ ^^y ^iijAtW TlfbuviiJlL taVSdtkAnjrarTft* Joint and Several Note ^^r7^A^yMe/^y:^/Y^yrf/^(Z^^ d ^ Zu^un^, Mi^. Wif/iont ffo/iilca/ffm,va/iw received M'if/L interest ciyi^ (o /^ /itr ^^j2^ fu/dafknweor/ru>n'tffc/a/t/fioas/flet/,ca/^x'i^i!flffmpnt/i/fainsf . . iJ^t^tr'C^^ //x/i/ f/ny /cmi /i>rtfic oAmrsii/n wM /hsts/?/'siii/.andMamfys«>nmissu?n€/' __^^L£:^hiy''l_. ' peroJit /or cMc/mt a//i/jr/ea.rf,(f/u/m/At>u/ s/ayafejnHfiouMHlm/msi/wnanaaclaisimupffn^iwMyon/ra/e^^ orpeJWlM/■/^nvMr^y/wmh1ya/ldsa/conev/yexccutimAenvn,isais0AerrfyTxpnx^^/y^^r^m *uult>yv/r/MUH'aiiyfMin/>tMi/mvnoivm/^re.orwA/ckmayieAava/lerpd^<8^^ £^ /^^^^^^^^ f ya ^.^ A <^^.' i?^//t^c^..<^^4^y^<.^^ ^ <^ 7^ ^^ ^ ^. y^ AJ.,^^6 /^/6 "^ 0^^.^ ^_ 274 PARTIAL PAYMENTS 275 The above note had the following indorsements, showing pay- ments made with the consent of the payee. Example. What amount w^as necessary to pay the note and interest at maturity? Solution. Time from January 16, 1913, to March 10, 1913, 1 mo. 24 da. Interest on $1800.00 for 1 mo. 24 da. is $16.20. 1200.00 (first payment) -$16.20 (accrued interest) =$ 183.80, surplus to apply on principal. $ 1800.00 - % 183.80 = % 1616.20, unpaid principal. Time from March 10, 1913, to April 13, 1914, is 1 yr. 1 mo. 3 da. Interest on $ 1616.20 for 1 yr. 1 mo. 3 da. is % 105.86. The payment of % 75.00 does not cover the accrued interest, and the principal therefore remains undiminished. Time from April 13, 1914, to August 13, 1915, is 1 yr. 4 mo. Interest on $ 1616.20 for 1 yr. 4 mo. is % 129.30. $105.86 + $129.30 = $235.16, total accrued interest. $ 75.00 + $ 500.00 = $ 575.00, total payments. $575.00 — $235.16 = $339.84, surplus remaining to apply on principal. $1616.20 - $339.84 = $ 1276.36, unpaid principal. Time from August 13, 1915, to January 16, 1916, is 5 mo. 3 da. Interest on $ 1276.36 for 5 mo. 3 da. is $32.55. $1276.36 -f $ 32.55 = $1308.91, amount required to pay principal and accrued interest at maturity. The work may be arranged in tabular form, as shown by the following illustration : 276 PARTIAL PAYMENTS Partial Payments on a Note Computed by the United States Rule Accrued Interest Datk Time Amount Payment APPLY ON Principal Principal Yr. Mo. Da. Of Note, 1913-1-16 1st Payment, 1913-3-10 1 1 1 1 4 5 24 3 3 16 20 200 00 183 339 80 84 1800 1616 1276 1308 A.mount at matu 00 20 2d Payment, 1914 4 13 3d Payment, 1915-8-13 105 129 86 30 75 500 00 00 235 16 575 00 36 Maturity, 1916-1-16 32 55 91 due rity 234. The Merchants' Rule. The Merchants' Rule is generally used by banks and by business men to find the balance due when partial payments are made on interest-bearing notes in which the time is one year or less. It provides that : a. The principal shall draw interest from the date the loan is made until the date of the final settlement. b. Each payment shall draw interest from the date the pay- ment is made until the final settlement. Example. On a note of $500.00, dated July 8, 1914, payable in one year with interest at 6 %, the following payments were made : Sept. 15, 1914, $200.00; Jan. 8,1915, $150.00; May 8, 1915, $60.00. What amount was necessary to make final settlement on July 8,1915? Solution. Principal Int. on % 500.00 for 1 yr. at 6% Total First payment Int. on first payment from 9-15-14 to 7-8-15 Total Second payment Int. on second payment from 1-8-14 to 7-8-15 Total Third payment Int. on third payment from 5-8-14 to 7-8-15 Total Sum of payments and interest Balance due July 8, 1915 $500.00 30.00 $530.00 1200.00 9.78 $209.78 $150.00 4.50 154.50 $60.00 .60 60.60 424.88 $105.12 PARTIAL PAYMENTS 277 This work may be arranged in tabular form as shown in the following illustration : Tabular Form for Indicating Results of Partial Payments Computed by the Merchants' Rule Loan Partial Payments Dates Princi- pal Interest Amount Pay- ment Interest Amount of Pay- Time mo. da. Dollars ment and Interest Of note Maturity First payment Second payment Third payment 7-8-1914 7-8-1915 9-15-1914 1-8-1915 5-8-1915 500 00 30 00 530 530 00 00 200 150 60 Bal. 00 00 00 due 9 6 2 atfi 25 nal 9 4 settl' 78 50 60 m't 209 154 60 424 105 530 78 50 60 88 12. 00 Written Work The first two problems, being for long-time loans, should be computed by the United States Rule. Prepare a ruled form similar to the model and show your results thereon. In each problem, find the balance due at maturity. 1. Principal, 14000.00. Date of paper, November 16, 1916. Time, 4 yr. Rate, 6%. Payments : Jan. 20, 1917, $ 75.00 Sept. 26, 1917, 125.00 Apri] 5, 1918, 500.00 Oct. 21, 1918, 100.00 July 10, 1919, 250.00 Oct. 21, 1919, 1500.00 278 PARTIAL PAYMENTS 2. Principal, -11200.00. • Date of paper, October 29, 1917. Time, 2 yr. 6 mo. Rate, 6%. Payments : Jan. 16,1918, $ 60.00 Nov. 6, 1918, 25.00 March 12, 1919, 165.00 July 10, 1919, 15.00 Sept. 28, 1919, 150.00 Dec. 3, 1919, 275.00 The following problems, being for short-time loans, should be computed by the Merchants' Rule. Rule a form similar to the model. 3. Principal, 8600.00. Date of paper, September 15, 1917. Time, 1 yr. Rate, 6%. Payments : Oct. 20, 1918, $ 75.00 Nov. 11, 1918, 60.00 Feb. 16, 1919, 115.00 4. Principal, #1000.00. Date of paper, March 19, 1917, Time, 6 mo. Rate, 5%. Payments : April 21, i 65.00 May 27, 125.00 June 24, 180.00 Aug. 19, 200.00 CHAPTER XXVI CX)MPOUND INTEREST 235. Compound Interest. Compound interest is interest com- puted, at regular intervals, on the sum of the principal and any un- paid interest. In other words, as soon as interest becomes due and is unpaid, it begins to draw interest at the same rate as the princi- pal. Compound interest is generally paid on the deposits in savings banks and is used in calculating sinking funds. Interest may be compounded quarterly, semi-annually, annually, or at the end of any other period agreed upon. In some states the collection of compound interest is not permitted. Example. Find the amount and the compound interest of 11200 at 6% for two years, interest compounded semi-annually. Solution. | 1200.00 First principal 36. Interest for 6 months 1236. Principal at beginning of second 6-months period 37.08 Interest for second 6 months 1273.08 Principal at beginning of third period 38.19 Interest for third period 1311.27 Principal at beginning of fourth period 39.34 Interest for fourth period $ 1350.61 Amount at end of two years f 1350.61 Amount at end of two years 1200.0 Principal $ 150.61 Compound interest Written Work 1. Find the compound interest on i 500. 00 for 5 years at 6 %, interest compounded annually. 2. What is the amount and the compound interest on $7500.00 loaned for 3 years at 6%, interest compounded semi-annually? 3. Find the interest on $1200.00 loaned for 2 years at 5% compound interest, interest compounded quarterly. 279 280 COMPOUND INTEREST Compound interest is computed with much less work by the use of tables showing the accumulation of interest and principal when $1.00 is loaned at compound interest. 236. Compound Interest Table. Showing the amount of |1.00 compounded annually at various rates Yeaes 1% U% 2% 2i% 3% Si% 4% 4i% 5% 6% Years 1 0.010000 1.005000 1.020000 1.025000 1.030000 1.085000 1.040000 1.045000 1.050000 1.060000 1 2 1.020100 1.030225 1.040400 1.050625 1.060900 1.071225 1.081600 1.092025 1.102500 1.123600 2 3 1.030301 1.045678 1.061208 1.076891 1.092727 1.108718 1.124864 1.141166 1.157625 1.191016 8 4 1 ,040604 1.061364 1.082482 1.103818 1.125509 1.147528 1.169859 1.192519 1.215506 1.262477 4 5 1.051010 1.077284 1.104081 1.131408 1.159274 1.187686 1.216658 1.246182 1.276282 1.338226 5 6 1.061520 1.093443 1.126162 1.159693 1.194052 1.229255 1.265319 1.302260 1.340096 1.418519 6 7 1.072135 1.109845 1.148686 1.188686 1.229874 1.272279 1.815932 1.360862 1.407100 1.503630 7 8 1.082857 1.126493 1.171659 1.218403 1.266770 1.316809 1.868569 1.422101 1.477455 1.59384S 8 9 1.093685 1.143390 1.195093 1.248863 1.304778 1.862897 1.423312 1.486095 1.551328 1.689479 9 10 1.104622 1.160541 1.218994 1.2S00S5 1.843916 1.410599 1.480244 1.552969 1.628895 1.790848 10 11 1.115668 1.177949 1.248874 1.812087 1.384284 1.459970 1.539454 1622853 1.710839 1.898299 11 12 1.126825 1.195618 1.268242 1.344889 1.425761 1.511069 1.601032 1.6958S1 1.795856 2.012197 12 13 1.138093 1.213552 1.293607 1.378511 1.468584 1.563956 1.665074 1.772196 1.885649 2.132928 13 14 1.149474 1.231756 1.319479 1.412974 1.512590 1.618695 1.731676 1.851945 1.979932 2.260904 14 15 1.160969 1.250232 1.345868 1.448298 1.55T967 1.675849 1.800944 1.985282 2.078928 2.896558 15 16 1.172579 1.268986 1.372786 1.484506 1.604700 1.788986 1.872981 2.022870 2.182875 2.540352 16 17 1.184304 1.288020 1.400241 1.521618 1.C52848 1.794676 1.947901 2.118877 2.292018 2.692778 17 18 1.196148 1.807341 1.428246 1.559659 1.702488 1.8574S9 2.025817 2.208479 2.406619 2.854839 18 19 1.208109 1.826951 1.456811 1.598650 1.758506 1.922501 2.106849 2.307860 2.526950 3.025600 19 20 1.220190 1.846855 1.485947 1.688616 1.806111 1.989789 2.191128 2.411714 2.653298 3.207186 20 21 1.232392 1.867058 1.515666 1.679582 1.860295 2.059481 2.278768 2.520241 2.785968 3.399564 21 22 1.244716 1.887564 1.545980 1.721571 1.916103 2.131512 2.369919 2.633652 2.925261 3.603537 22 23 1.257168 1.408377 1.576899 1.764611 1.973587 2.206114 2 464716 2.752166 8.071524 3.819750 28 24 1.269735 1.429503 1.608437 1.808726 1.082794 2.283328 2.563304 2.876014 3.225100 4.048935 24 25 1.282432 1.450945 1.640606 1.853944 1.093778 2.363245 2.665886 3.005484 3.386355 4.291871 25 Example. Find the compound interest on $3562.80 for 4 years at 6 %, interest compounded annually. Solution. $ 1.00 compounded annually at 6 % for 4 years amounts to $ 1.262477, as shown by the table. 3562.80 X $1.262477 = $4497.95, amount of $3562.80 compounded annually for 4 years at 6 %. $4497.95 - $3562.80 = $935.15, compound interest. When interest is compounded semi-annually, take | the rate for twice the time. COMPOUND INTEREST 281 When interest is compounded quarterly, take ^ the rate for 4 times the time. Example. What is the compound interest on $ 5000.00 at 8 % for 3 years 6 months, interest compounded quarterly ? Solution. ^oiS% = 2%. 4 times 3 years 6 mo. = 14 years. The amount of $ 1.00 compounded at 2% for 14 years is 11.319479. 5000 X II. 319479 = 1 6597.40. $6597.40 - 15000.00 = 11597.40, compound interest. Written Work 1. Find the compound interest on !$ 2500. 00 for 5 years at 5%, interest compounded annually. 2. i 5000. 00 was invested at 4%, interest compounded semi- annually. To what sum did this investment amount in 7 years ? 3. What was the compound interest on a loan of f 3750.00, made June 1, 1909, and due December 1, 1914, at 6%, interest com- pounded quarterly ? 4. What sum must be invested at 5 % compound interest to amount, in 7 years, to $3249.84, if the interest is compounded semi-annually ? CHAPTER XXVII SAVINGS BANKS 237. Checking and Savings Accounts. Most banks receive de- posits under two classes of accounts, checking accounts and savings accounts. Money deposited in checking accounts can be drawn out by checks payable to the depositor or to any other party. These checks are payable on presentation at the bank. The cash on deposit usually does not bear interest. Money deposited in a savings account cannot be drawn out by a check payable to any person other than the depositor himself. The law usually provides that the bank may require notice of from 10 to 60 days before paying money from a savings account. Banks rarely take advantage of this privilege, however. The cash on deposit bears interest at some rate fixed by the bank. 8%, 3J%, and 4% are common rates. 238. Computing Interest on Savings Accounts. Interest is com- puted on the smallest balance which the depositor leaves in the bank during the entire time between fixed days. These fixed days are called interest days, and the time between the interest days is called the interest term. Some banks pay interest on dollars only, and ignore the cents. Interest which is not withdrawn by the depositor is added to his account, and draws interest the same as a deposit. Thus, savings banks really pay compound interest. Example. The interest days of the Snowden Savings Bank are January 1, April 1, July 1, and October 1. On each of these interest days, interest at the rate of 4% per annum is computed on the smallest quarterly balance. The account of W. M. Scott is shown on the following page. 282 SAVINGS BANKS 283 W. M. Scott Date Deposits Intekest Withdrawals Balance 1915 Feb. 7 120 00 120 00 April 20 300 00 420 00 April 30 100 00 320 00 July 1 1 20 321 20 July 15 50 00 371 20 Sept. 17 75 00 446 20 Oct. 1 3 21 449 41 Nov. 16 80 00 369 41 1916 Jan. 1 1 1 3 i 69 373 10 Explanation. The first interest term was from Jan. 1 to April 1, but since Mr. Scott made no deposit until Feb. 7, the smallest balance on deposit during the entire interest term was $ 0.00, and, therefore, no interest was added on April 1. The second interest term was from April 1 to July 1. The smallest balance on deposit during the entire term was $120.00 (the balance on April 1). Interest, $ 1.20. The third interest term was from July 1 to Oct. 1. Smallest balance, 1321.20. Interest, $3.21. The fourth interest term was from Oct. 1 to Jan. 1. Smallest balance, $369.41. Interest, $3.69. 239. Interest Terms and Dates of Adding Interest. Interest terms are not of uniform length among the various banks of the country. Some banks compute interest on monthly balances, some on quarterly balances, and some on semi-annual balances. Some banks add interest quarterly and some add it semi- annually. The rules applying to the interest computations of any bank may usually be found in the by-laws of the bank, printed in the depositor's pass book. Examples. 1. Suppose the Snowden Savings Bank computed interest on quarterly balances, but added interest semi-annually. W. M. Scott's account would appear as follows : 284 SAVINGS BANKS W. M. Scott Date Deposits Interest Withdrawals Balance 1915 Feb. 7 120 00 20 00 April 20 300 00 420 00 April 30 100 00 320 00 July 1 1 20 321 20 July 15 50 00 371 20 Sept. 17 75 00 446 20 Nov. 16 80 00 366 20 1916 Jan. 1 6 87 373 07 Explanation. Smallest Balance Quarterly Interest Semi-annual Dividend of Int First Quarter $ 0.00 10.00 Second Quarter 120.00 1.20 $1.20 Third Quarter 321.20 3.21 Fourth Quarter 366.20 3.66 6.87 2. Suppose the Snowden Savings Bank computed interest on the monthly balance and added interest quarterly. Scott's ac- count would appear as follows : Explanation. Month Monthly Balance 1 Month Interest i0Fl% Quarterly Dividend OF Interest Feb 1000 00 $0 00 March 120 120 00 40 40 $0 40 April 40 May 320 40 06 June 320 322 40 92 06 2 52 July ^ 07 Aug 372 92 24 Sept 372 451 92 47 24 3 55 Oct 50 Nov 371 47 23 Dec 371 47 23 3 96 SAVINGS BANKS • 285 In computing interest on savings accounts, cents in the principal are dropped. Fractions of cents in interest are dropped. Written Work 1. Check the computations in each of the illustrations above. 2. Prepare W. IVl. Scott's account on the supposition that the bank computes interest on monthly balances and adds interest semi-annually, Jan. 1 and July 1. 3. Prepare W. M. Scott's account on the supposition that the bank computes interest on semi-annual balances and adds interest semi-annually. Remember that interest is paid on the smallest balance on deposit during the entire interest term. 4. Which of the methods employed in this section is most profitable for the depositor? 5. Suppose you deposited i 30 in a savings bank and left it to draw compound interest for 5 years at 4%, interest compounded semi-annually. How much could you withdraw at the end of the fifth year? 6. Suppose you had loaned the 830 for 5 years at 4% simple interest. What would the interest have been for five years ? 7. Compare the simple and compound interest in Problems 5 and 6. 8. A man deposits f 1200 in a savings bank to be used to send his boy to college. The savings bank pays 4% interest, com- pounded semi-annually. The deposit was made on the boy's tenth birthday. What amount will he have to his credit on the boy's eighteenth birthday if no withdrawals and no other deposits are made? 9. Make accounts with D. O. Dorman ; one for each of the following methods of declaring interest. Rate 4%. a. Interest computed on monthly balances. Dividends added Jan. 1, April 1, July 1, and Oct. 1. h. Interest computed on quarterly balances. Interest days same as above. 286 SAVINGS BANKS c. Interest computed on quarterly balances. Dividends added Jan. 1 and July 1. Date Deposits Withdrawals 1915 Jan. 16 $500.00 Feb. 19 700.00 . Mar. 1 i 25.00 Mar. 8 60.00 June 10 125.00 July 19 60.00 Aug. 5 200.00 Oct. 19 • 145.00 Nov. 20 125.00 240. Postal Savings Banks. The United States Government has provided a savings bank system operated in conjunction with the postal service, whereby savings may be deposited at interest with the security of the United States Government. Deposits. Any person ten years of age or over may become a depositor. Sums less than 1 1.00 cannot be deposited. No person can deposit more than $100.00 in any one calendar month, nor have a balance at any time of more than $500.00, exclusive of interest. Depositors receive a postal savings certificate for the amount of each deposit. Interest is allowed on these certificates at the rate of two per cent for each full year that the money re- mains on deposit, beginning with the first day of the month following the one in which it was deposited. Withdrawals. Money may be withdrawn by surrendering to the officer where the deposit was made the savings certificates covering the desired amount. Bonds. Under certain conditions a depositor may surrender certificates in amounts of $ 20.00 or any multiple of $20.00, up to and including $ 500.00 and receive in return government bonds bearing interest at 2 J % per year. These postal savings bonds may be held in addition to the $ 500.00 deposit allowed to one depositor. SAVINGS BANKS ' 287 Written Work 1. How much interest would a man receive if he deposited 815.00 in a postal savings bank on March 1, 1915, and withdrew it three months later ? 2. How much interest would he receive if he withdrew the money on March 11, 1916 ? 3. A man made the following deposits in a postal savings bank: May 20, 1915 115.00 June 17, 1915 6.00 August 11, 1915 26.00 October 29, 1915 17.00 When would he be entitled to the full year's interest on each of his deposits, and how much interest would he receive all together ? CHAPTER XXVIII CONTRACT PURCHASES AND INSTALLMENT PAYMENTS Real estate and other forms of property are often purchased and sold on contracts. Such contracts usually specify that the pur- chaser shall make periodic payments of a stated sum in payment of accrued interest and principal. The contract may permit the purchaser to pay, if he desires, a larger sum than that specified by the contract. 241. Applying the Payment to reduce the Principal. Contracts vary widely in the provisions for reducing the principal. The following typical cases will illustrate : a. C borrows f 1000.00 from D on May 1, 1915 at 6 %, under a contract to pay i 25.00 on the first day of each month. Each payment of f 25.00 to be applied as follows : 1. To pay the interest on the unpaid principal for the preceding month ; 2. The balance of the payment to be applied immediately to the reduction of the principal. A record of the payments might be kept in the following manner : Date Payment Accrued Interest Balance of Pay- ment TO Apply ON Principal Principal May 1, 1915 $1000 00 June 1, 1915 $25 00 -15 00 $20 00 980 00 July 1, 1915 25 00 4 90 20 10 959 90 Aug. 1, 1915 25 00 4 80 20 20 939 70 b. On September 1, 1915, M sells a house to N for $6400.00. N pays cash $2500.00 and signs a contract agreeing to pay in- 288 CONTRACT PURCHASES 289 stallments of §35.00 monthly, with the privilege of paying larger amounts. Each payment is to be applied as follows : At the expiration of every quarter (three months) the total accrued interest at 6 % is to be deducted from the total payments, and the balance applied to the reduction of the principal. A record of the payments might be kept in the following manner : Date Payments Total Payments ACCKUED Interest Balance to Apply on Principal Principal Sept. 1, 1915 $3900 00 Oct. 1, 1915 $35 00 Nov. 2, 1915 45 00 Dec. 1, 1915 35 00 $115 00 $58 50 $.56 50 3843 50 Jan. 2, 1916 60 00 Feb. 1, 1916 35 00 March 1, 1916 40 00 135 00 57 65 77 35 3766 15 Written Work 1. Check the items in the above form. 2. On May 1, 1917, G. A. Sanders sold a house and lot to A. R. Grain; purchase price, 84850.00. Mr. Grain paid 12900.00 cash and gave the following note for the balance. $ 1950.00 Bartlett, Iowa, May 1, 1917. For Value Received, I promise to pay to the order of G. A. Sanders, the sum of Nineteen Hundred and Fifty Dollars, with interest thereon at the rate of six per cent per annum, principal and interest payable in monthly install- ments in the sum of twenty-five dollars or more, each, the first of which is due on June 1, 1917, and one on the first day of each and every month thereafter until said principal sum of Nineteen Hundred and Fifty Dollars and interest thereon are fully paid. Each and every of said installments is to be applied as follows: 1st. In payment of accrued interest on said sum of $1950.00 or on the un- paid portion thereof. 2d. In monthly reduction of said principal sum of $ 1950.00. A. R. Grain. )0 CONTRACT PURCHASES Payments were made as follows : June 2, 1917 125.00 January 2, 1918 $40.00 July 1, 1917 25.00 February 2, 1918 25.00 August 1, 1917 30.00 March 2, 1918 32.50 September 1, 1917 25.00 April 1, 1918 25.00 October 1, 1917 27.50 May 1, 1918 45.00 November 1, 1917 35.00 June 1, 1918 25.00 December 1, 1917 25.00 Notice that some payments are made on the second day of the month, due to the fact that the first day of the month was either a Sunday or a holiday. Prepare a statement similar to the illustration on page 288, showing a record of the payments made. 3. Assume that the contract between Mr. Sanders and Mr. Grain called for a monthly payment of 125.00 or more, and that the principal was to be decreased semi-annually by the balance of the payments remaining after paying all accrued interest. Pre- pare a statement similar to the illustration on page 289, showing a record of the payments made. 4. Which of the two propositions is better for the purchaser ? Explain, CHAPTER XXIX DISCOUNTING NOTES AND OTHER COMMERCIAL PAPER 242. Borrowing from a Bank. Banks prefer to have the bor- rower pay the interest in advance. The interest may be paid in cash, or the bank may subtract it from the face of the note, giv- ing the borrower the difference, which is called the proceeds. If you gave a bank the following note : $100,00 Chicago, III., March, 2, 1915. Ninety days after date, I promise to pay to the order of the Bowen National Bank One Hundred Dollars. Your Signature the bank would deduct ninety days' interest, il.50, and you would receive the proceeds, 198.50. Note. There is no promise to pay interest, because the interest is prepaid. Banks charge any rate they choose, within the limits set by the state law. In this text, when no rate is mentioned use 6 %. The above illustration shows the method of discounting a note. 243. Terms Used in Bank Discount. The following terms are frequently used, and you should become familiar with them : Maturity means the date on which the note is due. The value of the note is the amount due at maturity. If the note draws interest, the value is the sum of the principal and the interest. Otherwise, the value is the face of the note. The discount period is the exact number of days between the date of discounting the paper and its maturity. The bank discount is the simple interest on the value for the discount period. The difference between the value and the bank discount is called the proceeds. 291 292 DISCOUNTING NOTES Oral Work In the illustration on the previous page what is : The maturity? The discount period? The proceeds? The value ? The bank discount? 244. To find the bank discount and the proceeds. To compute the hank discount, compute the simj^le interest on the value of the note for the discount period. To find the proceeds, subtract the hanlc discount from the value of the note. Written Work How much would you receive from the bank if you discounted the following notes ? 1. A note for 1^500, without interest, due in 30 days, discounted at 6 %. 2. A note for $ 725, without interest, due in two months, dis- counted at 6 %. 3. A note for ^85.50, without interest, due in 90 days, dis- counted at 7 %. 4. The following blank shows the value of several notes and the periods for which they were discounted. Compute the bank discount at 6 %, and fiud the proceeds. Note Value Due In $87.00 $265.00 $962.50 $1000.00 $275.00 $765.00 $35.00 30 days Bank discount Proceeds .44 86.56 60 days Bank discount Proceeds 80 days Bank discount f^roceeds 90 days Bank discount Proceeds 120 days Bank discount Proceeds DISCOUNTING NOTES 293 245. Discounting the Paper of Other Persons. If you have a note signed by some person of good financial standing, you can borrow money on it by discounting it in the same way that you would discount a note made by yourself. Suppose John Doe had given you the following note : $ 500.00 Chicago, III., January 1&, 1915. Ninety days after date I promise to pay to the order of Your Name, Five Hundred Dollars.- John Doe. By the following indorsement, Pay to the order of The First National Bank (Your Name) you transfer the note to the bank. Moreover you promise to pay the bank |500 on April 16, in case Doe fails to do so. The bank will loan you i 500 minus the discount. When you discounted your own note (in the exercise just given), you did so on the same day that the note was made. The discount period and the time of the note were therefore the same. But you may keep the notes of other people some time before discounting them. The bank will charge you interest from the day you discount the note until it is due. Thus, if you did not discount the above note until March 6, the bank would charge you interest for the number of days from March 6 to April 16, the date of maturity. How many days in this discount period ? What would be the discount period if you discounted the note January 23 ? February 16 ? March 20 ? 246. To find the discount period. Find the maturity of the note. Find the exact number of days between the date of discount and the date of maturity, 247. To find the maturity. Notes due a certain number of months after date fall due on the same day of the month as the day on which they were made, with the following exceptions : Notes made on the 31st, maturing after a specified number of 294 DISCOUNTING NOTES months, falling due in a month having only 30 days, mature on the 30th. Notes made on the 28th, 29th, 30th, or 31st, maturing after a specified number of months, falling due in February, mature on the last day of February. Examples. Note Made Dttb in Maturity Jan. 16, 1915 2 months March 16, 1915 July 31, 1915 2 months September 30, 1915 Dec. 31, 1915 2 months February 29, 1916 Notes due a certain number of days after date, mature after the exact number of days has elapsed. Examples. Note Made Due in Maturity 1915 a. Feb. 16 30 days March 18 Since February has only 28 days, the 30 days of the note will be divided as follows : 12 February days (after the 16th) 18 March days h. March 18 30 days April 17 March has 31 days; 13 left after the 18th ; the remain- ing 17 of the 30 days must be in April. c, April 17 30 days May 17 April has 30 days; 13 left after the 17th ; the remaining 17 of the 30 days will be in May. From these examples, the following should be clear. To find the maturity. Change the days to months ; (30 days = 1 month}. Assume that the note will mature on the same day of some follow- ing month. Correct this result hy subtracting 1 day for each month of 31 days through which the note runs ; and hy adding 2 days if the note rmis through February. (^In case of leap year^ add 1 day.} DISCOUNTING NOTES 295 The following table provides a convenient method for indicating the months for which corrections are to be made. Month ' Number ( )F Month Days COKREOTION January 1 13 31 _ ^ February 2 14 28 + 2 (or + 1) March 3 15 31 — 1 April 4 16 30 May 5 17 31 — 1 June 6 18 30 July 7 19 31 — 1 August 8 20 31 — 1 September 9 21 30 October 10 22 31 _ 1 November 11 23 30 December 12 24 31 — 1 Examples. 1. Find the maturity of a note dated May 16, 1915, due in 4 months. Solution. May is the fifth month. Add 4 months. The note will be due in the ninth month, which by the table is September. Maturity, September 16. 2. Find the maturity of a note of the same date, due in 120 days. Solution. Call 120 days 4 months. May is the fifth month. The note is due in the ninth month, shown by the table to be September. Call the maturity September 16. Correct as follows: Note runs through May Subtract 1 day Note runs through July Subtract 1 day Note runs through August Subtract 1 day Total 3 days Therefore the maturity is September 13. 3. Find the maturity of a note dated December 19, 1914, due in 150 days. Solution. Call 150 days 5 months. December is the twelfth month. The note is due in the seventeenth months which, by the table, is May. Call the maturity May 19, 1915. 296 Correct as follows : DISCOUNTING NOTES December — 1 January — 1 February + 2 March — 1 April (has 30 da.) Note does not run through May. Total - 1 Maturity, May 18, 1915. 4. Find the maturity of a note dated June 16, 1915, due in 70 days. Solution. Call 70 days 2 months, 10 days. June 16 plus two months is August 16; plus 10 days is August 26. To correct : For June For July - 1 Total - 1 Maturity, August 25, 1915. Written Work Enter the maturity of each note in the proper column: Note Dated Sept. 23, 1915 Oct. 9, 1915 Mayl, 1915 July 20, 1915 Dec. 15, 1915 Feb. 9, 1915 Due in 1 Month Due in 80 Days Due in 2 Months Due in 60 Days Due in 150 Days Due in 45 Days 248. To find the discount period. Compute the actual number of days between the date of discount and the date of maturity. Illustration. A note, dated July 17, due in 4 months, was dis- counted on August 5. What was the discount period ? Solution. Four months from July 17 is November 17, the date of maturity. The discount period, therefore, extends from August 5, the date of dis- count, to November 17, the date of maturity. DISCOUNTING NOTES 297 To find the number of days between August 5 and November 17 : 31 total number of days in August 5 number of August days expired before discounting 26 number of August days in the discount period 30 number of September days in the discount period 31 number of October days in the discount period 17 number of November days in the discount period 104 total number of days in the discount period Oral Work After studying the illustration, state a method for finding the number of days in the discount period. Written Work 1. On a form ruled like the following, enter the date of ma- turity on the upper line, and the discount period on the lower line. The notes dated February 12 were discounted April 8. The notes dated February 17 were discounted March 2. The notes dated March 23 were discounted April 29. The notes dated March 17 were discounted April 15. The notes dated March 30 were discounted May 20. Dates Notes WERE Made Time 60 Days 75 Days 100 Days 120 Days 6 Months Feb. 12, 1915 Feb. 17, 1915 Mar. 23, 1915 Mar. 17, 1915 Mar. 30, 1915 2. Complete a table ruled like the following model. Enter the date of maturity on the first line, the discount period on the 298 DISCOUNTING NOTES second line, the discount on the third line, the proceeds on the fourth line, as illustrated by the first problem in the table. Date of Papkr AND Face Time, 90 Days Time, 3 Months Time, 120 Days Time, 6 MjOnths Discounted April 13 Discounted Ai>ril 11 Discounted April 28 Discounted May 20 Jan. 16, 1915 1300 April 16 3 days 1.15 $299.85 Jan. 30, 1915 1285 Feb. 19, 1915 $126 249. Discounting Interest-bearing Notes. If you had in your possession the following note and wished to discount it, you would first add 90 days' interest (11.50) to the face of the note to deter- mine its value at maturity. This note is really Roe's promise to pay you $101.50 at maturity, and the bank will give you as much for it as for a note for $101.50 without interest. '^ r f /oo~ -^'^^W^ ^^ ^ ^gg^ii'^^ii^ *^V^^^-vr7^v?-; Ua.--yt.£^:.^Z./i^ J^/'y./>?-Y^^-'/yy ( '^^^^yt^^.^^t^y^^. ) ■_y^(^^x^^^^^^^/^^^^^<^y^ K.J-^^c^-^^^^y^r^:^^^.^.^^^ ^ 2)x^//a yyouaU y/ /" .t^yi^^ ^^7^^^^^, -^c^^^^^^'-n.i'^iyt^d^ ^ ^/ o. 9^^^^ ^^- 9^ '='«>««»»=**°**«««'«»««»«''*«'««*»'»«*^^ DISCOUNTING NOTES 299 When discounting interest-bearing paper, compute the interest for the full time the note is to run, and add this interest to the face, to determine the value at maturity. Find the discount on this value. Subtract the discount from the value to determine the proceeds. Written Work Complete a table ruled like the following model, entering the facts as illustrated in the first problem. All notes discounted at 6 <5^. Time, 90 Days Time, 4 Months Time, 6 Months Without Int. With Int. 6% Without Int. With Int. 6 % Without Int. With Int. 5% Principal, $500.00 Date of Paper, June 3, 1915 Date of Discount Aug. 21, 1915 Maturity Interest Value Dis. Period Bank Dis. Proceeds Sept. 1 $500.00 11 days $ .92 $ 499.08 Sept. 1 $ 7.50 $507.50 11 days $ .93 $506.57 Principal, $1250.00 Date of Paper, Aug. 6, 1915 Date of Discount Sept. 18, 1915 Maturity Interest Value Dis. Period Bank Dis. Proceeds Principal, $47.96 Date of Paper, July 16, 1915 Date of Discount Aug. 27, 1915 Maturity Interest Value Dis. Period Bank Dis. Proceeds Principal, $55.00 Date of Paper, Aug. 14, 1915 Date of Discount Oct. 5, 1915 Maturity Interest Value Dis. Period Bank Dis. Proceeds 300 DISCOUNTING NOTES 250. Discounting Acceptances. Time drafts were discussed in Chapter XIX. An accepted draft is a written promise of the acceptor to pay money at a definite date, and accepted drafts may be discounted, just as notes may be discounted. In case the person who has accepted the draft does not pay it when due, the person who discounted it will be required to pay it. The following draft drawn by you on John Doe and accepted by him is just as truly his promise to pay $,500.00 at a given date, as a promissory note signed by him would be. - <^oo~ jS;,^^^^ ^(l^^^^yr^^. ^ ,^ ^^J^SL. C^^icyt^/. .^/<:t^/^^ t^g^^ g^^^ r^:J.^..^^..^. ^-^ .AP ^.^ ^^ This draft could be discounted in exactly the same manner as a note dated January 6, payable 30 days after date. If the draft were drawn payable 30 days after sight, instead of after date, the bank discount would be different because the date of maturity would be different. i:^^3i£sS-::^6iiifc2i2^fe2i2^1_^^^^ ^ v^^ C/yO' [Lr^.t^ ^2t»^ DISCOUNTING NOTES 301 Written Work 1. What is the date of maturity of the draft on page 300 pay- able 30 days after date? 2. What is the date of maturity of the draft on page 300 pay- able 30 days after sight? 3. What is the discount period of each draft if discounted on Jan. 14? 4. Find the bank discount and the proceeds of each draft. Review Write the notes and drafts called for in the following. Show all acceptances and indorsements. On October 3, you received from B. A. Anderson, of Batavia, New York, a note dated October 1, due in two months, for $135.00, without interest. On August 28, you sold to N. M. Davis, of Toledo, Ohio, an in- voice of goods amounting to $84.00; terms 1/10; N/30. This invoice was due September 27, but Mr. Davis was unable to pay it. He agreed, however, to accept a thirty-day draft for the amount. You drew the draft on September 30, payable thirty days after date, and sent it to him for acceptance. He accepted it and re- turned it to you. On October 5, you sold a bill of goods amounting to $68.00 to J. D. Robinson, of Burlington, Iowa. Terms, 30 day draft less 1 %. On October 5, you drew a draft on him, payable 30 days after sight ; he accepted the draft on October 7. On July 10, you received from J. F. Cook of Lime Springs, Iowa, a note made by him on July 8, in your favor, for $500.00, due six months after date, with interest at 6 %. On June 4, you received a note for $600.00 from A. B. Hicks of Chicago. The note was drawn on April 16, by D. F. Fairchild of Omaha, Nebraska, in favor of Hicks, payable nine months after date, without interest, and was transferred to you by full indorsement. On October 15, you took these notes and drafts to the Dairy State Bank to discount. The bank's discount rate was 6%. 302 DISCOUNTING NOTES Finding that the proceeds would not be sufficient to meet your needs, you gave the bank your own note, dated October 15, due in 20 days, for 1250.00, without interest. 1. Find the proceeds of each of the papers discounted. Your balance at the bank before discounting this paper was $167.25. You deposited the proceeds of the discounted paper. What was your balance after discounting the paper? 2. On October 25, the bank wished to increase its deposit with its correspondent bank at Chicago. It therefore rediscounted the notes and drafts received from you. How much did the bank receive for the paper, when discounted on October 25 at 6 % ? 3. Marshall owed Daniels $485.90; on September 23 he gave Daniels the following note, properly indorsed. 1450.00 Brainerd, Iowa, September 3, 1915. Sixty days after date, I promise to pay to the order of J. F. Marshall, Four Hundred and Fifty Dollars. Value received Without interest. F. S. Crosby. How much did Marshall owe Daniels after transferring the note? BUSINESS EXPENSES CHAPTER XXX WAGES AND PAY ROLLS There are several wage systems in use, each of which is designed to encourage employees to produce as much as possible. Several of the most common systems will be discussed in this chapter. 251. The Day or Hour Rate. This system is the one generally used, because it is the simplest. When the day or hour rate is used, the employee's wage depends upon the time he has labored. Work done overtime or on holidays is usually paid for at one and one half times the regular rate. In many factories time clocks are installed. As each employee begins work, he registers the time on his card ; when he stops work, he again registers the time. At the end of the week, each employee's card shows his actual hours of labor. A pay roll is prepared showing the total number of hours each employee has worked, his hourly rate, and his total wage. Written Work Supply the missing facts in the following pay roll. No Name Hours worked per day Time Overrime Total Wa Wafet M T w T F S Hr». Rate Amouni Hr.. Amount Advanced Due . y ,sCt.<,(t^^?>h42j!g^ (7 f <7 ., a <"■? ,^n />5 (-o ^ /'.O /~S' /.n a. 1-7 I-? /• f fT 'f i7 I'i'f- Pf /J /•? • ■5- S /f) /'r ■?"? / "y t*} f •? ? /^ ,? (7 ft a r7 ? Oq ? ? 7 JT O (7 /|0 '0 // n 9 ■'■■ ? 9 ? .ju s^s:3>C> y3>^.¥6 u-6^/Ay rj^AUXTHOL TZMAM J^S.8^ J>Ys:vy 3ys.£/y ¥^Z.SS Devise a form which will show the above data and enter the following : Each salesman's commission on goods sold in each depart- ment. The total commissions paid to each salesman. The total commissions paid for each department. The total commissions paid to all salesmen. The total sales in each department. The total sales of each salesman. The total sales in all departments. 255. Pay Roll Slips. Laborers are sometimes paid by check, and sometimes by the envelope system. When the latter method is used, each employee receives an envelope containing the exact amount of his wages. A coin sheet is prepared from the pay roll, showing the change needed for each envelope. A pay roll No. Name Bi !s $.50 $-25 $.10 $.05 $.01 Wages S 10.00 $5.00 S2.00 $1.00 / Z2 /.-/ z / / / ^ -? .9/ ^7 3 / / / / O- ?; <::^^yA.^.^.yi^^^. Z6 :p. / / / / ^ /X \A>^^j>. (^k,.^,^^ .. ,., . / ^ / / ,^ ^y^^^'^^JA'^^ .. if. / / / / / ^ f ^ /s ' /•s- / / / / / / -T /"' . ^^7 So /& _^J L=^= -^^^ ^ -^-^ r ,. -5 /o Coin Sheet 310 WAGES AND PAY ROLLS slip, designating the number and denomination of the bills and coins desired, is then filled out and sent to the bank. When the THE FIRST NATIONAL BANK CURRENCY FOR PAY ROLL DOLLARS CENTS $50 Bills. 20 /£i /Ac O la ¥- 2io OO 5 ^ /o oo 2 ^ ^ OO 1 ^3 / so Halves. v3 7^ Quarters, 'y JO Dimes. f v3 / /v5- Nickels. /O /o Pennies. /^7 ZO TOTAL Pay Roll Slip currency is delivered a check is made out to the bank for the amount of the pay roll. Written Work Rule a coin sheet and enter the number of coins of each denomi- nation necessary to pay each of the employees in the pay roll prepared in the differential wage rate problem on page 307. Make out a pay roll slip on the First National Bank of your city, to obtain the money to pay these employees. CHAPTER XXXI POSTAGE, FREIGHT, AND EXPRESS RATES Postage 256. The Rates for Domestic Postage. Domestic mail matter includes all matter deposited in the mails for delivery to points in the United States or its possessions, including Porto Rico, Hawaii, the Philippine Islands, Guam, and the Canal Zone ; with certain exceptions, it includes matter sent to Canada, Cuba, Mexico, and the Republic of Panama. The domestic rate applies also to letters, but not to other articles, addressed to Great Britain, Ireland, Newfoundland, and Germany. CLASSES OF DOMESTIC MAIL First Class : Written matter : Letters and all mail which is sealed. Rate : 2 cents for each ounce or fraction thereof. Post cards and postal cards, 1 cent each. Second Class : Unsealed. Newspapers and periodicals. Rates : When mailed by the publisher, 1 cent per pound. When mailed by others than the pub- lisher or a news agent, 1 cent for each four ounces or fraction thereof, on each separately addressed copy. Third Class : Circulars, newspapers, and printed matter (except books) not admitted to the second class. Rates : 1 cent for each two ounces or fraction thereof. The limit of weight of third-class matter is four pounds. Fourth Class : Parcel post : All matter not embraced in the first, second, or third classes, and not likely to injure the employees of the postal service, or the mails 311 312 POSTAGE, FREIGHT, AND EXPRESS RATES This includes merchandise, farm and tactory products, seeds, books, etc. Rates : Parcels weighing four ounces or less, except books, seeds, plants, etc., 1 cent for each ounce oi fraction of an ounce, regardless of the distance. Parcels weighing eight ounces or less containing books, seeds, cuttings, roots, etc., 1 cent for each two ounces or fraction thereof. Parcels weighing more than eight ounces contain- ing books, seeds, plants, etc., parcels of miscella- neous printed matter weighing more than four pounds, and all other parcels of fourth-class mat- ter weighing more than four ounces are subject to pound rates, a fraction of a pound being con- sidered a full pound. The pound rates vary with the distance the parcel is to be carried. 257. Units of Area and Zones. For the purpose of determining the various pound rates, the United States is divided into " units of area," each unit being thirty miles square. Each unit is the center of a series of zones : First Zone : Territory within a radius of 50 miles. Second Zone : Territory within a radius of 150 miles and beyond 1st zone. Third Zone : Territory within a radius of 300 miles and beyond 2d zone. Fourth Zone : Territory within a radius of 600 miles and beyond 3d zone. Fifth Zone : Territory within a radius of 1000 miles and beyond 4th zone. Sixth Zone : Territory within a radius of 1400 miles and beyond the 5th zone. Seventh Zone : Territory within a radius of 1800 miles and beyond the 6th zone. Eighth Zone : All territory beyond the 7th zone. 258. Size and Weight of Parcels. No package can be sent by parcel post, if its length plus its girth is more than seventy-two POSTAGE, FREIGHT, AND EXPRESS RATES 313 inches. For delivery in the first and second zones, parcels may weigh not more than fifty pounds ; for delivery in other zones, they may weigh not more than twenty pounds. 259. Parcel Post Rates. The rates of postage on parcels exceed- ing 4 ounces in weight are as shown on the opposite page. The local rate applies to parcels to be delivered from the same office at which they are mailed. The delivery may be made at the office, by city carrier, or by rural free delivery. Books. Books weighing 4 ounces or less are mailed at the third-class rate of 1 cent for each 2 ounces or fraction thereof. Those weighing more than 4 ounces are mailed under the regular zone rates. 260. Special Regulations. When two classes of mail matter are mailed in the same package, the higher rate is charged on the entire package. For example, inclosing a letter in a parcel of merchandise subjects the whole parcel to the letter rate. As a general rule the postage on all mail must be prepaid in stamps affixed to the package. Publishers, however, do not always affix stamps to their publications ; and the postage on third-class matter, mailed in quantities of not less than 2000 identical pieces, may be paid in money. Postage stamps are issued in the following denominations : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 20, 30, and 50 cent, and 1, 2, and 5 dollars. Special Delivery. By affixing a " special delivery " stamp (cost, 10 cents), or ten cents' worth of ordinary stamps, in addition to the regular postage, and writing the words " Special Delivery," prompt delivery by special messenger is obtained. Registry. The registry system provides greater security for valuable mail matter. The registry fee is ten cents. If regis- tered mail is lost, the sender is indemnified up to $ 50 for first- class, and up to $ 25 for third-class domestic mail. Insurance of Parcels. Mail sent by parcel post may be insured against loss upon the payment of a fee of 5 cents for value not exceeding $ 25, or 10 cents for value not exceeding $ 50, in addi- tion to the postage. It may not be registered. 314 POSTAGE, FREIGHT, AND EXPRESS RATES 1 5 1 (N -^ O 00 O (M-*?OQOO (N "^ CO 00 O (M -^ «0 00 O O r-.' r-^ ,-1 ,-H r-J ,-; rH T-H !N (N (N* C. o o X o § l-i 5 t»i <1 1^^ % i«i g«^ P5 ^ S fc, a: ir. 1 ir. 1 > 5 h h > P ^ 1st $20 $980 2d 19 60 960 40 3d 19 208 941 192 4th 18 824 922 368 5th 18 447 903 921 6th 18 078 885 843 7th 17 717 868 126 Use the table just prepared in solving the following problems. 10. Machinery in a factory cost $7460.00, and depreciation was computed at 7 % on decreased annual values. What was the depreciation during the fourth year, and the inventory value at the end of the fourth year ? 11. Cost of equipment, 15600.00 ; depreciation computed at 3 % on decreased annual values. What was the depreciation during the third year, and the inventory value at the end of the third year ? 12. Cost of machinery $23,746.00; depreciation computed at 12| % on decreasing annual values. What was the amount of the depreciation during the sixth year, and the reduced value at the end of that year? The depreciation during the sixth year was what per cent of the original cost of the machinery ? CHAPTER XXXIII ADVERTISING During the last fifty years the annual cost of advertising in this country has increased to more than seven hundred million dollars. The advertising methods employed are numerous. The principal mediums are newspapers, magazines, street car signs, posters, electric signs, circulars, booklets, and novelties. 278. Newspapers. Newspaper space is sold by the page, inch, and agate line. The word "agate" refers to the size of the type. This is a line of agate type. An inch contains nine lines of agate type when a lead is placed between each line; or 12 lines when set solid. The price varies with the circulation of the newspaper ; 3 cents per inch per thousand subscribers is considered a fair basis on which a news- paper may determine its rates. On this basis, a newspaper with a circulation of 5000 would charge 15 cents per inch for its space. The larger newspapers generally compute their rates on the basis of 7 cents per line per thousand subscribers, but there are many exceptions to this. Rate Card of a Daily Newspa PER Display Eates per Agate Line Daily Sunday Run of paper, 5 lines or more Next to reading matter $.40 .50 .45 $.50 .60 .55 Specified paere Discounts for Yearly Contracts Lines Per Cent Insertions 2,500 or more lines 5,000 or more lines 10,000 or more lines 10 25 28 26 52 312 327 328 ADVERTISING 279. Magazines. The rate charged by magazines for advertis- ing space also depends upon the circulation, a fair basis being considered J cent per line, or •$ 1.00 per page, per thousand sub- scribers. Higher rates are charged for the desirable positions, such as cover page, and for printing in colors. Specimen Rate Card of the - Magazine Katks per Issue One page $100.00 Half page 50.00 Quarter page 27.00 Eighth page 15.00 Less than } page, per agate line .75 Inside cover page 150.00 Back cover, 3 colors 350.00 Three per cent discount for cash. Forms close on the 10th day of the month preceding date of issue. One well-known magazine with a circulation of one million charges $4000 per page, and there are several magazines which charge $250 per page. 280. Street Car Signs. Space is provided above the windows of most street cars for printed signs. These signs differ in size, but the standard size is 11 in. x 21 in. Some cards of double length are used ; these are 11 in. x 42 in. The ordinary rate for street car advertising space is 50 cents per month per car for a half run, which means six months in all the cars, or one year in one half the cars. It is 45 cents a car per month when all cars are used for a full year. Exceptions to this rate apply in New York, Chicago, and other large cities. The cards are furnished at the expense of the advertiser. 281. Posters. Posters are printed in various sizes, but the standard unit is a sheet 28 in. x 42 in. The billboards are usually about 10 feet high, in order to accommodate 4- sheet posters. The charge made for rent of boards and posting signs depends upon the size of the city and the desirability of the location. The rates range from 4 cents to 30 cents a sheet per month. A dis- count of 5 % is usually given on a contract for three months' service, and 10 % on a contract for six months' service. The cost ADVERTISING 329 of printing the posters ranges from 1 J cents to 4 cents per sheet depending on the quality and quantity. 282. The Advertising Agency. In many of the larger cities there are advertising agencies which assist advertisers in preparing copy, in directing advertising campaigns, and in selecting the best medium for advertising a particular article. On the theory that the agency creates new business, publishers usually allow agencies a commission of from 10 % to 15% of the gross cost of all advertising placed with them for publication. 283. Checking Results. Large advertisers make special efforts to determine the mediums which bring the greatest number of in- quiries, and which result in the most sales and the largest amount of profit. For this purpose, the advertisements in the various news- papers and magazines are " keyed " ; for example, the address may be differentl}^ stated in each medium, or different booklets may be offered, so that when the replies are received in the office, it will be possible to determine the medium which attracted the reader. Each periodical is credited with the replies received from its readers. Further records are kept to determine the value of the goods sold to the readers of the periodical, and the profit result- ing therefrom. Written Work Refer to the newspaper rate card on page 327 to obtair facts for Problems 1, 2, and 3. 1. On the basis of nine agate lines to the inch, what is the cost of a four-inch, single-column advertisement? The advertisement appears next to reading matter. 2. What is the cost of a double-column, 40-line display adver- tisement, printed by request on the financial page? How much would the same advertisement cost if printed on a specified page of the Sunday paper? Can you account for the increased cost? 3. A clothing store contracted for 10,000 lines to be printed in the course of a year. 8000 lines were printed in the daily editions, '" run of paper." 1200 lines were printed in the daily editions on specified pages, and the balance appeared in the Sunday editions next to the reading matter. What was the total cost ? 330 ADVERTISING 4. A breakfast food manufacturer ran the following amount of advertising in the magazine whose rate card is printed on page 328. January 1-page July • Inside cover page J'ebruary Ipage August Inside cover page March i page September Back cover April 12 agate lines October 1 page May 1 page November 1 page June Inside cover page December ipage What was the cost for the year • if he paid cash ? 5. The advertiser in Problem 4 placed his copy through an agency which received from the publishers 121 % of the gross cost as its commission. How much commission did the agency receive ? How much did the publishers receive? 6. An insurance company advertised in the street cars of a city in which one of its offices was located. There were 850 cars, and the insurance company contracted for a " full run " at the rate of 45 cents per month per car. What was the cost (not including the cost of printing) ? If the cards were changed every two months, and if 400 extras were printed to allow for "torns" and "dirties," how many were required for the year? What was the cost of the cards at ^15 per thousand? What was the total cost of this company's street car advertising ? 7. A manufacturer advertised his product with posters. Each poster was 112'' x 126'^ How many sheets 28'' x 42" to each poster? He signed a six months' contract for 250 posters at 16 cents per sheet per month, posters to be changed only when worn out, and received the customary 10 % discount. What was the cost of the service ? He purchased 15 % more posters than were actually required for the boards, estimating that this number would be necessary to allow for damaged sheets. What was his printing bill at 2J cents per sheet? What was the total cost of the six months' advertising? 8. Complete the following table : ADVERTISING 331 10 xsoo OMisixHaAay ONixonaaa aax^y xijohj xaj^ €©= saivg Koaj xiiosti CD CO tH CO CO r-( sa-ivs dO xsoQ oKisixaaAav S a-iog 8aoo£) m aaivA CO 10 CO t^ -^ 05 t^ GO CO (M CO (M CD CM (M I— t T— I I— ( €©= aivg aad xsoq aiog eanaaji ao XNLao aaj g eaivg ao aaaren]^ 8 S S8 S S § S aaa xsoo s €©= sanaaa ao aaawnN CO t- 00 05 t^ "^ CM lO CO CO CO '—I CO OHisixaaAay ao xsoQ 0000^00 »0 CO CO t^ CO CO -^ (M rH 6©^ aovdg CO 3^ bO "3? bJO be ;^ bo 5 Ch J3 Ph Ph be & 9; 5 2 Literary Guide . . Readers' Monthly . Inland Monitor Firelight .... Romance and Story Youth and Age . . Farming Age . . r-^H 03 O o be a, ^ o o be o CO -^ d p I" p. .2 p. O ^M ■u f^ f-i O « I— ^ CO cS ri 02 O O be P a (D o) «*-' C« S +3 Q. W '^ '^ 00© o ^ 43 .2 <^ ^ £2 ID 5 fr! +^ ^ «W O r^ O ^ ® P +3 tp3 (D O -(J o c« ^ ^ P QQ fl Si P poo O Pi ^ •=« ^ CO oQ ^ en "-• ^ CO 4J > O ^ O '^ 332 ADVERTISING Which columns do you think give the best evidence as to the value of each magazine as an advertising medium for this product ? Which is the better evidence of the value of an advertising medium, the cost per reply or the cost per sale ? List these magazines in the order of their value as advertising mediums for this particular advertiser (on the basis of per cent of net profit). CHAPTER XXXIV PROPERTY INSURANCE Property is in danger of destruction from many causes ; insur- ance companies have been organized to assume the risks of' destruction, thus relieving the owners from anxiety and loss. Any person having a financial interest in a property may insure himself against its loss or destruction by paying an insurance company a certain per cent of the value of the property insured. The person who purchases insurance is called the Insured. The company which assumes the risk is called the Underwriter. The contract between the insured and the underwriter is called a Policy. 284. The Value of Insurance. a. In case of loss the insured receives a certain sum, called an indemnity, which wholly or partially repays his loss. h. Even though the property is not destroyed, the insured has the security which the insurance gives. c. Some wholesale houses are unwilling to sell goods on credit to persons whose property is inadequately insured. 285. Risks for which Insurance is Written. Insurance companies are organized to furnish protection against numerous kinds of risks. Some of the most common classes of insurance are : Fire. Lightning and Tornado. Marine, oil vessels and cargoes at sea. Live stock. Transportation. Burglary. Plate Glass. Boiler Explosion. Automobile. Crop. 333 334 PROPERTY INSURANCE The principles underlying all types of property insurance are the same, and for the purposes of this text fire insurance only will be explained. It will be understood that other forms of in- surance may be written, settled, or canceled in a similar manner. 286. Process of Insuring. When a person wishes to secure a policy insuring his property, he should first ascertain the value of the property. To do so, it may be necessary to take an inventory, applying to the goods a price at which they would sell in the market at the time of taking the inventory. After the valuation has been determined, the next thing to de- cide is the amount of insurance it is desirable to carry. If the property is insured at its total valuation, the owner will bear no loss in case of fire. But since, in most fires, a portion of the prop- erty is saved, it is customary to insure only a fraction of the total valuation. Thus, if a stock of goods worth -110,000.00 is in- sured at 1^ of its value, in case of fire the insurance company will pay all loss up to 17500.00. If goods to the value of $2500.00 or more are carried from the building and saved, the merchant will not suffer any loss. If only 11000.00 worth of goods are saved, the merchant will lose $1500.00. It is a matter of choice how much risk the insured wishes to take. If he wishes to be free from all risk, he should insure his property at its full valuation. Insurance companies, how- ever, are rarely willing to insure property at its full value. Business men usually insure from J to -| of the valuation of their property. In some rural communities where the fire protection is poor, insurance companies sometimes refuse to insure more than -I of the valuation of property. On the other hand, in cities where the fire protection is good and the probability of total loss is comparatively slight, people are not inclined to insure a large fraction of the valuation. To counteract this tendency, the in- surance companies frequently offer a lower rate, or price per hundred dollars of insurance carried, to those who insure 80 % or more of the valuation than they offer to persons insuring less tlian 80%. PROPERTY INSURANCE 335 287. Tne Cost of Insurance. Insurance companies charge a certain number of cents or dollars for insuring each $100.00 worth of property. Thus, if the insurance rate were 60 cents per hun- dred dollars of insurance carried, and you insured a building worth 15000.00 at its full value, the insurance cost would be com- puted as follows : f .60 the rate per $ 100 insurance 50 the number of hundred dollars of insurance purchased $30.00 the premium, or cost of the insurance per year 288. To find the premium : Multiply the valuation of the property hy the fraction of the value insured. Point off two places in this product^ to determine the number of hundred dollars of insurance purchased. Multiply hy the rate per $100. Example. What is the premium for insuring, at 80% of its value, a building worth $10,000.00, if the rate is 90 cents per year ? Solution. $ 10,000.00 value of the property ^ fraction of property to be insured $8,000.00 insured value $ .90 rate per hundred 80 number of hn;mdred dollars of insurance carried $72.00 premium 289. Insurance Rates. The insurance rate per hundred dollars per year varies from $.30 on brick dwellings in cities, where the fire protection is good, to $ 7 or more on very dangerous risks, such as garages storing gasoline, and buildings located in districts where the fire protection is poor. Thus it is seen that the rate depends upon the hazard, or the danger of the property burning. This hazard is determined by four things, which are always taken into account in fixing the rate on different pieces of property. They are: a. The Construction of the building. If it is built of wood, a higher rate is charged than if it is built of brick, or other slow- burning material. If it has many stories, so that a fire starting 336 PROPERTY INSURANCE near the roof will be difficult to extinguish, a higher rate will be charged. h. Its Occupancy. If the building is occupied by some hazardous business, such as a woodworking mill in which wood shavings accumulate, or a clothes-cleaning establishment containing dan- gerous chemicals, a higher rate will be charged than if the business caused no particular hazard. c. Its Exposure. By " exposure " is meant : first, the distance from other buildings from which it might take fire ; and second, any hazard which might arise from its being in the neighborhood of a dangerous building. d. Its Protection. The rate will be lower if the building is close to a fire hydrant, in a city with an efficient fire department, or if the building is equipped with automatic sprinklers which are opened by the heat from a fire. If a night watchman is engaged, this also may reduce the rate. The rate depends also upon the length of time for which the in- surance is purchased. 290. Typical Rates. The following table will illustrate the rates which apply on different classes of property. On business houses and factories the rate is fixed after an inspection of the property made by a representative of the insurance company. The insurance companies of a state frequently join in organizing an " inspection bureau " which fixes the rates. The rates on city property will be lower than those which apply generally throughout the country, because of the more adequate fire protection of a large city. A City Insurance Tariff DWELLINGS One Teak, PER $ 100 Brick, stone, tile, cement-block, or concrete dwellings and contents . % 0.30 Single frame dwellings and contents, detached not less than 50 feet in all directions 50 Single frame dwellings and contents, detached not less than 25 feet in all directions 60 Single frame dwellings and contents, detached 50 feet on one side . . .60 PROPERTY INSURANCE 337 One Year, PER $100 All other frame dwellings and contents, not less than 10.75 Brick-veneered or tile-veneered dwellings and contents 40 Dwellings plastered outside, with tile or other noncombustible roof, and contents 40 Dwellings plastered outside* with shingle or other combustible roof, rate same as frame dwellings. Dwellings in part brick and frame rate as frame, subject to survey and rating by the board. Streets, without reference to their width, to be considered as cutting off charge for exposure. BRICK BUILDINGS AND CONTENTS, OCCUPIED FOR APARTMENT HOUSES OR FLATS One Tear, PER $100 Three stories in height $0.40 Four stories in height and 50 feet or less wide 50 Five stories in height and 50 feet or less wide 60 Six stories or more in height and 50 feet or less wide 75 BRICK BUILDINGS (OTHER THAN APARTMENT HOUSES, CHURCHES, SCHOOLS, FLATS AND WOODWORKING RISKS) IN PROCESS OF CONSTRUCTION One Year, PER $ 100 Two stories or less in height $0.40 Three stories in height .50 Four stories in height 60 Five stories in height 75 Over five stories in height, add 25 cents for each story. SCHOOLHOUSES One Year, PER $ 100 Brick or stone, with metal, slate, or composition roof, and contents . $0.60 Brick or stone, with shingle roof, and contents 75 Frame, and contents 1.00 CHURCHES One Year PER $ 100 Brick or stone, and contents $0.75 Frame, and contents 1.00 338 PROPERTY INSURANCE TERM RATES When policies are written for several years, the following will apply : 2 years, 1| annual rates. 3 years, 2 annual rates. 4 years, 2^ annual rates. 5 years, 3 annual rates. • FARM PROPERTY One Thbbe Fivk Year, Yeaes, Years, PKR $ 100 PER $ 100 PER $ 100 Dwellings, barns, outbuildings, and contents, when written under same policy $0.50 $1.00 $1.50 When farm barns and contents are written with- out the dwellings 75 1.50 2.25 Written Work Compute the premiums on the following fire insurance policies. The proper rates will be found by a study of the preceding tariffs. One-year Policies — City Property 1. Single frame building, value $4000. No buildings nearer than 60 feet. Insured at 80 % of its valuation. 2. Single frame dwelling, value $5400. House on north, 70 feet away; store on south, 25 feet away. Insured at full value. 3. Brick dwelling, value $6800. Insured at 75% of its value. Nearest building, 50 feet. 4. Dwelling, plastered outside; shingle roof. Value, $4200. Insured for $3600. No building nearer than 35 feet. 5. Five-story apartment house, 48 feet wide. Value, $36,000. Insured at | of value. 6. Four-story brick store in process of construction. Value, $3900: Insured at 80 % of its valuation. Term Policies — City Property 7. Three-year policy on brick schoolhouse, with tile roof. Value $40,000. Insured at full value. 8. Five-year policy on frame church. Value, $7500. Insured at full value. PROPERTY INSURANCE 339 Policies on Household Goods — City 9. Three-year policy of f 1000 on household goods in frame dwelling. Building on north, 10 feet ; building on south, 60 feet. 10. One-year policy of f 500 on household goods in brick- veneered building. Farm Policies 11. One-year policy of ^8500, covering dwelling and barns. 12. Five-year policy of $3000 on barn and silo. 291. Insurance Agent's Commission. Local agents of the fire insurance companies are located in almost every city and town. They act as the representatives of the companies, soliciting the business, and collecting the premiums. For this service they receive a certain per cent of the premiums, usually varying from 15 % on mercantile risks to 25 % on dwellings. To find the agent's commission. Example. Suppose that a store building valued at $ 6000 were in- sured for J of its value, the rate being 70 cents per hundred. What would be the agent's commission if he received 15% of the premium ? Solution. | of^ 6000 = ^ 4500, the insured value. 45 X $ .70 = $31.50, the premium. 15% of $31,50 = $4.73, the agent's commission. Written Work In each of the following problems find The premium ; The agent's commission ; The amount of the premium received by the insurance company. 1. A one-year policy of $3000 on a store building. Rate, 90 cents. Agent's commission, 20%. 2. A three-year policy on a dwelling valued at $6500, insured at 80 % of its valuation. Rate, 65 cents. Three-year policy for 2 annual rates. Agent's commission, 18%. 3. A one-year policy of $800 on household goods. Rate, 50 cents. Agent's commission, 15%. 340 PROPERTY INSURANCE 292. Settlement of Losses. When a fire occurs, causing a small loss, settlement may be made by the local agent. When the loss is large, a special adjuster is sent by the company to make the settlement. The adjuster first determines with the owner the actual cash value of the property immediately preceding the fire. This may be done by finding the cost of the property when new, and sub- tracting a certain amount for depreciation ; that is, the decrease in value due to use, age, change of style, or any other cause. This cash value is called the sound value. The adjuster next determines the value of goods which were saved from the fire. In determining this value he deducts any loss due to damage by the fire, or by water used in extinguishing the fire. The property saved is called salvage. It is evident that : Sound Value — Salvage = Loss. The companies pay this actual loss up to the value of the insurance carried. Examples. 1. Valuation of property by insured when taking the policy 110,000.00 Insured for 80 % of its value ; Insured value . . 8,000.00 Sound value agreed upon by adjuster and insured after allowing $500 for depreciation .... 9,500.00 Salvage 3,000.00 Actual loss 116,500.00 Since the insured carried $8000 insurance, the loss would be paid in full. 2. Valuation of property by insured when taking policy $8,000.00 Insured for J of its value; Insured value . . . 6,000.00 Sound value, after deducting 10 % for depreciation 7,200.00 Salvage 500.00 Actual loss $6,700.00 PROPERTY INSURANCE 341- Since the insured carried only 86000 insurance, the company is liable for only $6000 of the loss; the insured bearing the remain- ing 1700 loss. In adjusting losses, the insurance companies reserve the right to: a. Settle the loss as shown above ; or b. Pay the sound value of the property, taking possession of all the salvage; or c. Replace the property by other property of like kind and quality. Written Work 1. An apartment building worth -145,000 was insured at 80 % of its valuation. A fire occurred resulting in a total loss. If the sound value was considered to be the same as the original valuation, how much insurance did the owner of the property re- ceive, and what was his loss ? 2. A dwelling valued at $ 3500.00 was insured at its full valua- tion. A fire resulted in a partial loss, the salvage being estimated at 11250.00. If the sound value of the property was 13325.00, how much insurance did the owner of the property receive ? 3. If the property in Problem 2 had been insured for $1500.00, how much insurance would have been paid ? 4. A policy of $1500.00 was written on a man's household goods. When adjustment of the loss was made, the following facts were determined : Value of household goods immediately preceding the fire, $1855.00; salvage, $575.00. How much money did the insured receive as a settlement ? 5. If the salvage in Problem 4 had been $215.00, how much would the insured have received ? 6. A building worth $5000.00 was insured under a five-year policy at its full value. Four years after taking the policy, the house was completely destroyed by fire. In making adjustment of the loss, it was agreed that the sound value was 5 % less than the insured value. How much did the owner of the house receive in settlement ? •342 PROPERTY INSURANCE 7. If the salvage in Problem 6 had been $1350.00, how much insurance would the insured have received ? 8. Cost of building, $ 6000 ; insured for 80 % of its value under five-year policy secured by the payment of three annual rates of 75 cents. Burned at end of third year. Sound value determined by deducting 4% annual depreciation. Salvage, $1200. Find premium and loss, if any, to owner. 293. Canceling Policies. Both the insurance company and the insured have the right to cancel an insurance policy at any time. When the policy is canceled by the insurance company^ the portion of the premium to be repaid to the insured is determined pro rata. The exact fraction of the time of the policy which has not ex- pired is determined and this fraction of the premium is returned to the insured. Example. On Juiy 7, 1917, the owner of a building insured his property for one year. The premium was $24.00. On September 17, the policy was canceled by the insurance company. What rebate did the insured receive for the unexpired term ? Solution. Time from September 17, 1917, to July 7, 1918, 293 days, unex- pired term of policy. Ill of $24.00 = % 19.27, amount of ptemium returned. The table on page 267 will be of assistance in finding the un- expired term of a policy. Example. An insurance policy for one year was purchased on July 9, and was canceled by the company on the 17th of the following December. How many days in the unexpired term of this policy ? What fraction of the premium will be refunded ? Solution. The number of days between December 17 and July 17 is shown by the table to be 212. Subtracting 8, we have 204, the number of days from December 17 to July 9. Iff of the premium will be refunded. When the policy is canceled by the insured^ the amount of premium returned is determined by the "short rate." The short rate is an arbitrary per cent fixed by the insurance companies, and is shown by a table, a portion of which is shown on page 343. PROPERTY INSURANCE 34B Per Cents of the Annual Premiums to be Charged or Retained for Periods less than One Year. Arranged by Days from One to Three Hundred and Sixty Days Days Per Cent Days Peb Cent Days Peb Cent Days Peb Cent 66 34 32 71 36 30 76 37 50 81 38 85 67 34 97 72 36 58 77 37 90 82 39 13 68 35 46 73 36 79 78 38 20 83 39 34 69 35 79 74 36 93 79 38 40 84 39 48 70 35 95 75 37 00 80 38 50 85 39 55 Table for Cancellation of Term Risks Three- Year Policies For 3 mo. or less 20 per cent of term Over 3 and not exceeding 6 mo 30 per cent of term Over 6 and not exceeding 9 mo 40 per cent of term Over 9 and not exceeding 12 mo 50 per cent of term Over 12 and not exceeding 15 mo 60 per cent of term Over 15 and not exceeding 18 mo 70 per cent of term Over 18 and not exceeding 21 mo 75 per cent of term Over 21 and not exceeding 24 mo 80 per cent of term Over 24 and not exceeding 27 mo 85 per cent of term Over 27 and not exceeding 30 mo 90 per cent of term Over 30 and not exceeding 33 mo 95 per cent of term Over 33 mo 100 per cent of term premium premium premium premium premium premium premium premium premium premium premium premium Example. 1. On October 28, 1917, a one-year policy for 12500.00 was written on a dwelling. Premium, 112.50. On January 15, 1918, the policy was canceled at the request of the insured. What rebate did the insured receive ? Solution. Time from October 28, 1917, to January 15, 1918, 79 days. The table shows that 38.40% of the premium is to be retained when the policy has been in force 79 days. 38.40% of $12.50 = 14.80. $12.50 - $4.80 = $7.70, amount of premium returned. 344 PROPERTt INSURANCE 2. On August 12, 1914, a three-year policy was written at a premium cost of #78.00. On February 11, 1915, it was canceled at the request of the policyholder. What was the amount of the premium rebate? Solution. Time from August 12, 1914, to February 11, 1915, 5 months 29 days. The table states that when a three-year policy has been in force 3 months and not exceeding 6 months, 30 per cent of the premium shall be retained. 30 % of 1 78.00 = ^ 23.40, amount of premium retained. $78.00 - 123.40 = $54.60, premium returned. Written Work Find the premium rebates on the following canceled policies: 1. One-year policy of $2400.00. Premium, 116.00. Policy written May 19, 1917 ; canceled by the company on July 29, 1917. 2. Same facts as Problem 1, except that the policy is canceled at the request of the policyholder. 3. Three-year policy, dated July 23, 1917. Face of policy, $ 3600.00. Rate, 65 cents, three-year policy being written for term rates. Policy canceled at the request of the policyholder on October 7, 1918. CHAPTER XXXV TAXATION 294. Purpose of Taxation. The national government requires money to support the army and navy, to pay the salaries of gov- ernment employees, to pay pensions, and to finance other activities carried on by the nation. During a recent year, Congress appro- priated $ 1,098,678,788 for the annual budget. The state governments require money for the expense of their officers, and to support their various institutions, schools, universi- ties, asylums, and penitentiaries. The counties require money for the building of bridges, the trial of criminal cases, the salaries of officers, the relief of the poor, etc. Cities must pay for police and fire protection, care, of streets, etc. School districts contribute to the support of the public schools. The money required for all these expenses is raised by taxes, licenses, fees, assessments, and fines. 295. A tax is a sum of money levied by the proper officers of a government to defray government expenses. The funds of the national government are raised largely in three ways: Customs Duties on Imports ; Internal Revenue ; ' Income Tax. The funds of the state and local governments are raised largely, by direct taxes on real estate and personal property. State and Local Taxes 296. Taxable Property. The amount of property tax paid by any individual to state and local governments depends upon the value of the property which he owns and the tax rate. 345 346 TAXATION Real estate consists of land and buildings. Personal property consists of movable property, such as mer- chandise, furniture, machinery, live stock, cash, notes, stocks, bonds, and mortgages. 297. Determining the Assessed Value of Property. The value of each person's taxable property is determined by the assessor. The assessed value is usually a fractional part of the real value. For example, in a certain state, property is assessed at ^ of its real value. Jones owns a farm which the assessor considers to have a real value of $30,000. He therefore assesses it at ilO,000. Although the law gives the assessor the power to determine the taxable value of property, property owners usually have the privilege of appearing before a Board of Equalization to prove a claim that their property has been assessed at too high a valuation. The Board of Equalization judges between the values fixed on property by the assessor and by the owner. 298. The Tax Rate. The tax rate may be expressed in several ways, the most common of which are : *A per cent ; A certain number of mills on each dollar of assessed valuation ; A certain number of dollars or cents on each hundred dollars of assessed valuation. The following tax rates are equivalent: 1.6%; 16 mills (on the dollar) ; 11.60 (on each hundred dollars). 299. To find the amount of tax. To find the amount of tax to be paid by any property owner : Multiply the assessed value of the property hy the tax rate. (a) When the rate is stated as a per cent. Example, Bennet's property is assessed at 1 3000 ; the tax rate is 1.6 %. Solution. $ 3000 assessed valuation .016 tax rate $48.00 tax TAXATION 347 (J) When the rate is stated as a certain number of mills on the dollar. Example. Taylor's property is assessed at t3800. The rate is 24 mills. Solution. $ 3800 assessed valuation .024 tax rate in mills $91.20 tax (c) When the rate is stated as a certain number of dollars on each hundred dollars of assessed value. Example. Finch's property is assessed at f 5470. The tax rate is '11.95. Solution. $ 1.95 the rate per hundred dollars 54.70 the number of hundreds of dollars assessed value $106.67 the tax Oral Work 1. State each of the following tax rates in two other ways : 3.6% 27 mills ^12.83 2. A certain state assesses property at f of its real value. What is the assessed value of a house worth f 5000 ? Of a factory worth $15,000 ? Of a building worth |4000 ? 3. Dickinson has a house assessed at f2000. The rate is 2.5%. What is his tax? 4. Barnes has a store building assessed at $ 3000 and a house assessed at •! 2000. The tax rate is 30 mills. What is his tax ? 5. If property is assessed at ^ of its real value, what is the assessed value of a city lot worth $ 1200 ? How much tax will the owner pay if the tax rate is 22 mills ? 6. Property valued at f 6000 is assessed at ^ oi its value and taxed at a rate of $ 2.50. What tax does the owner pay ? 7. Three men living in different cities were comparing their tax rates. A's rate was $ 3.56 ; B's rate was 28 mills ; C's rate was 3.14%. Which had the largest rate? How much tax should each pay on an assessed value of f 2000 ? 348 TAXATION 8. Bailey owns property worth $ 15,000 and is taxed $ 4.50 per hundred dollars on ^ of the real value. Osborne owns property worth $ 15,000 and is taxed 32 mills on -J the real value. Which pays the larger tax ? How much does each pay ? 9. Powell pays 3 % on ^ of the real value of his property. What per cent of the value of his property does he pay annually as taxes ? 10. A loaned money at 6 % and took a mortgage. Since a mortgage is personal property, it is taxable. The mortgage was taxed at a rate of f 4 on ^ the real value. What per cent of the value of the mortgage did A pay annually as taxes ? his per cent of net income on the loan ? What was Written Work 1. Complete the following table : liEAL Value of Property Fraction of Value Assessed Assessed Value Rate Tax $16,250 i $5.42 7,920 i 3.18% 22,000 i $2.89 960 i 64 mills 4,000 i 2.92% 2. Hill rents his house for 130.00 per month. The house cost him 13850.00. What is the per cent of net profit on his invest- ment, after paying the following annual expense ? Insurance, $15.40. Repairs, $60.00. Taxes : Property assessed at ^ its value and taxed at 16.23 per hundred dollars. 300. To determine the tax rate. Each of the taxing govern- ments (state, county, township, city, school district, etc.) pre- pares a budget or estimate of the money needed for the following vear. TAXATION 349 The assessed value of the property available for taxes is found from the assessors' lists. The amount of funds needed, divided by the assessed value of the property, gives the rate which must be levied in order to obtain the required amount. The rates for the state, county, city, school district, etc., are added to form a single rate. The following illustration shows the method of determining a tax rate. State Tax State budget $ 3,600,000 Assessed value of the property in the state $1,000,000,000 $ 36,000 ^ 1 1,000,000,000 = .36 % state rate County Tax County budget $30,000 Assessed value of the property in the county $4,000,000 $ 30,000 ^ 14,000,000 = .75 % county rate City Tax City budget . • $12,000 Assessed value of property in the city . $ 1,000,000 $12,000 -4- $ 1,000,000 = 1.20% city rate School Tax School district budget $24,000 Assessed value of the property in school district $1,000,000 $24,000 H- $ 1,000,000 = '2A0 % school tax rate 4.71 % total tax rate Example. Mr. Owen has a building worth 115,000.00, which is assessed at J of its real value. What is the tax on the build- ing at the above rate ? Solution. Assessed value, $ 5,000.00. Rate, 4.71 %. .0471 X $5,000.00 = $235.50, tax. Oral Work Explain why the tax rate in your city may be different from the rate in a neighboring city. 350 TAXATION Written Work 1. Find the tax rate (approximate). State budget, 12,850,000. Assessed value of property in the state, 11,450,000,000. State rate? County budget, $ 33,000. Assessed value of property in county, $5,600,000. County rate ? City budget, f 14,800. Assessed value of property in city, 11,345,000. City rate ? School district budget, $ 32,500. Assessed value of property in school district, f 1,345,000. School tax rate ? Total rate ? 2. The following is the tax rate in the town of M. State tax $ .QO County tax 1.25 Township tax .26 City tax 2.18 School district tax 2.86 $7.15 In this town, property is assessed at ^ of its real value. Snyder owns the following property : Rkal Values Residence 16,500.00 Store 4,950.00 Office building 13,000.00 What is his total tax ? 3. How much of this tax goes to the state, and how much to each of the other taxing units ? 4. What per cent of his tax goes to each of the taxing units ? 5. The assessed value of Miller's real estate is $13,395.00. What is his total tax ? 6. How much school tax does Miller pay '^ CHAPTER XXXVI THE INCOME TAX 301. Basis of the Tax. The income tax bill, which became a law on October 3, 1913, and which was amended Sept. 8, 1916, places a tax on all net incomes in excess of $3000.00 a year in the case of single persons, whether adults or minors, and in excess of $4000.00 per year in the case of the head of a family. The normal tax is based on the excess only. The tax is levied on American citizens living in this country and abroad, on aliens liv- ing in the United States, on corporations, joint-stock companies or associations, and insurance companies. Exemptions are not allowed except in the case of individual citizens. 302. Gross Income. Gross income consists of salaries, wages, interest, rent, and all profits or income arising or accruing from whatsoever source, with the exception of interest on the bonds of the United States government and its political subdivisions. Property acquired by gift or bequest, and the proceeds of life insurance policies paid on the death of the insured, are not con- sidered as income. 303. Net Income. Only the net income is taxed. The net income for the purpose of the tax is found by deducting from the gross income all necessary expense actually paid in carry- ing on the business (but not personal, living, or household expenses) ; interest paid on indebtedness ; taxes ; fire losses not covered by insurance or otherwise, loss from bad debts, if actually charged off; a reasonable depreciation on the value of property. 304. The Normal Tax. The rate of the normal tax is 2 % of the net income above the amount exempted. 351 352 THE INCOME TAX Example. A married man living with his wife has a net income of S7000. How much income tax is he required to pay? Solution. $7000 Net income 4000 Exemption $3000 Taxable income .02 Normal rate $ 60 Income tax 305. The Additional or Super Tax. In addition to the normal rate of 2 % levied on incomes in excess of the exemption, an addi- tional tax is assessed on large incomes. The following table gives the additional rates charged on the portions of net income which exceed specified amounts. On the amount by which the total net income (not deducting the $3000 or $4000 exemption applying to the normal tax). exceeds $ 20,000 but does not exceed $ exceeds 40,000 but does not exceed exceeds 60,000 but does not exceed exceeds 80,000 but does not exceed exceeds 100,000 but does not exceed exceeds 150,000 but does not exceed exceeds 200,000 but does not exceed exceeds 250,000 but does not exceed exceeds 300,000 but does not exceed exceeds 500,000 but does not exceed exceeds 1,000,000 but does not exceed exceeds 1,500,000 but does not exceed exceeds 2,000,000 Example. Dudley, an unmarried man, has a net income of 1125,000 per year. What is his income tax? Solution. $125,000 Total net income 3,000 Exemption $122,000 Basis of normal tax 29^0 of $122,000 $2440 Normal tax 1% of $ 20,000 (excess between $20,000 and $40,000) 200 Additional tax l^fo of $ 20,000 (excess between $40,000 and $60,000) 400 Additional tax 3% of $ 20,000 (excess between $60,000 and $80,000) 600 Additional tax 4^0 of $ 20,000 (excess between $80,000 and $100,000) 800 Additional tax 59ij of $ 25,000 (excess of total net income over $100,000) 1250 Additional tax $5690 Total tax 306. Collection at the Source. The law provides that the tax on incomes derived from interest, rent, salaries, wages, and other S 40,000 1% 60,000 2^0 80,000 3% 100,000 4^0 150,000 5% 200,000 6-^0 250,000 7fo 300,000 8% 500,000 9% 1,000,000 109^0 1,500,000 \\oJo 2,000,000 12itrr. ;. Vi>Aal....C,^J,y^.^t'!i/s,ir. on ..QA{i/...'kT. , Invoice No. .?::/^.. e out this line for direct i PACKAGES AND CONTENTS. ;K ^9^/fc M f.(ifarM, .-?'nooo ^-^^^«^ O^^..^/:.^^^^^^. /rinnn ^'^^^^^uc^ Jy-^i^««P*5' Vi4^^ f/ ^^. ^ /onn ^.^.JA/^^^^^yJ^ 7'^r,t^:;^^zr-'3bu^t. ^ CORPORATIONS, STOCKS, AND BONDS 383 323. Terms Used. The Capital Stock of a corporation is the amount of capital authorized by the charter. Shares. The capital stock is divided into shares of equal size, having a nominal or face value, usually of i 100. 00. Shares may be of any denomination within the limits fixed by law. When the stock has been subscribed (and, in some states, paid in) a meeting of the stockholders is held at which meeting a board of directors is elected to manage the business. At this meeting each share owned by a stockholder entitles him to one vote. (How many votes should Austin have?) By this method of voting it is possible for a few stockholders own- ing a majority of the shares to control the business. 324. Stock Certificates. Each stockholder receives a certificate, signed by the officers of the corporation, stating the number of shares for which he has subscribed and paid. Capital Stock $100,000.00 1000 Shares $100.00 Each The Eclipse Carriage Company STOCK CERTIFICATE NO. _^£: Stjia (HertififB that IS the owner oiS NUMBER OF SHARES c^rU. shares of the Capital Stock of Qllff &litiar Qlama^r (Sontfiany. fully paid and non-assessable, transferable? only on the books of the Corporation by the holder hereof in person or by Attorney upon surrender of this Certificate properly endorsed Jn Sitttfaa Vifrrrof. the said Corponmon has caused this Certificate to be signed by its duly authonzed ) c„i ( officers, and ration, at- o\ yt^''tc r AD. iq /<^ be sealed with the Seal of the Corpo- C^C^. this / day M-^/--^-.(^.yr^.,_ '■"'^r^. 384 CORPORATIONS, STOCKS, AND BONDS Oral Work Refer to the stock certificate, and answer the following questions : 1. What is the total capital stock of the corporation? 2. Into how many shares is the capital stock divided? 3. What is the par (face) value of each share ? 4. How many shares does Robbins own ? To how many votes is he entitled? 5. What is the par value of his stock? 325. Dividends. The profits of the corporation which are divided among the stockholders are called Dividends. The board of directors has the authority to determine the amount of dividends which shall be declared out of the profits. 326. Surplus. The undivided profits of a corporation are held as surplus. Examples. 1. Let us suppose that the Eclipse Carriage Com- pany's profits at the end of one year amounted to »$6800. What per cent of dividends could the directors declare ? Solution. ^ 6800 (Profits) -- 1 100,000 (Capital Stock) = 6.8 %. Therefore, the largest dividend which the directors could declare is 6.8 %. If such a dividend were declared, each stockholder would receive 6.8 % of the par value of his stock. Austin, owning 500 shares, with a par value of f 50,000, would receive a divi- dend of 6.8 % of the par value of | 50,000, or $3400. 2. Let US suppose that the directors vote to declare a 5 % divi- dend. How much of the profits would be divided among the stockholders, and how much would remain as surplus ? Solution. 5 (fo of % 100,000 = $ 5000, Total Dividend. $6800 (Profits) -$5000 (Dividends) =$1800, Surplus. 327. Par Value and Market Value of Stock. The par value or nominal value of stock is its face value, shown by the stock cer- tificate. The market value of a share is the amount for which it can be CORPORATIONS, STOCKS, AND BONDS 385 sold. The market value depends upon several factors, the fol- lowing being the most important : a. The value of the property owned by the corporation. When the Eclipse Carriage Company was organized, each stock- holder paid for his stock in cash, and for each share of stock there was ilOO in the treasury. Each share, therefore, was worth f 100. But let us assume that a surplus of i 1600 has been created. Since there are one thousand shares, this surplus adds f 1.60 to the property represented by each share. h. The dividends paid by the corporation. Let us suppose that 9 % dividends are declared each year. $ 9 is 6 % income on 8 150, and Jones might be willing to pay 'f 150 for a share of this stock. If only 4 % dividends were paid, Jones would probably not be willing to pay $ 100 for a share because he would not receive 6 % on his investment. When stock sells for more than its par value, it is said to be above par, or at a premium. Stock selling for i 105 per share is quoted at 105. When stock sells for less than its par value, it is said to be below par, or at a discount. Stock selling for f 95 is quoted at 95. 328. Assessments. When money is required to cover losses, or to extend the business, in some companies the stockholders may vote to levy an assessment. The assessment is a per cent of the par value of the stock, and is paid by the stockholders to the treas- urer of the corporation. Shares of stock may be non-assessable. Written Work 1. The stock of a corporation has all been subscribed and is owned as follows : A, 150 shares; B, 220 shares; C, 80 shares; D, 50 shares. Par value per share, f 100. What is the capital stock of the corporation ? 2. How much will a dividend of 8 % yield each stockholder ? 3. If the annual profits are 1 4500, what per cent dividend can be declared ? 386 CORPORATIONS, STOCKS, AND BONDS 4. If a 5 % dividend is declared from the profits of $ 4500, how much will remain as surplus ? 5. If a 2| % assessment is levied, how much will each stock- holder pay to the corporation ? 329. Kinds of Stock. There are two principal classes of stock, common and preferred. Common Stock entitles its owner to a proportionate share of the net profits of the corporation when dividends are declared by the directors. The rate of dividend is not fixed, but depends upon the success of the business. Preferred Stock entitles its owner to a fixed per cent of dividend provided the profits are sufficient to pay this dividend. Thus, 5 % preferred stock entitles the owner to a 5 % dividend before any dividends are declared on the common stock. Cumulative Preferred Stock. Preferred stock may be cumulative or non-cumulative. If the stock is cumulative, a dividend which is unpaid one year becomes a claim against the corporation, to be paid out of future profit. Participating Preferred Stock. In some states unless the pre- ferred stock is expressly declared to be non-participating, the preferred stock participates equally with the common stock in any dividends after both common and preferred stock have re- ceived an equal dividend. That is, after 6 % preferred stock has received its 6 % dividend and the common stock has also received 6 %, remaining dividends must be shared equally. Example. The P^clipse Carriage Company desires to build and equip a new factory at a cost of #25,000. A meeting of the stock- holders is held, and it is decided to issue 5 % cumulative non- participating preferred stock, in order to obtain the required funds. Two hundred and fifty shares, with a par value of $ 100 dach, are issued. At the end of the year, a profit of $ 9750 is shown. How may this profit be divided among the holders of the common and pre- ferred stock ? CORPORATIONS, STOCKS, AND BONDS 387 Solution. 5 % of ^ 25,000 (Preferred Stock) = $ 1250, dividend on preferred «tock. $ 9750 — $ 1250 = $ 8500, remaining for dividends on common stock. An 8^ % dividend may be declared on the common stock. If an 8| % dividend is declared, no surplus will remain. Written Work if an 8| % dividend is declared on the common stoek : 1. How many dollars are paid as dividend on each share ? 2. How many dollars are paid as dividend on each share of 5 % preferred stock ? The profits of the second year are only $500, and the directors are able to pay only a 2 % dividend on the preferred stock. No dividends are declared on the common stock. 3. How much does Clark, who owns one share of preferred stock, receive? 4. Comstock owns five shares of preferred stock. How much does he receive ? 5. What is the total unpaid dividend on the preferred stock ? The third year a profit of $12,000 is made. Settlement among the shareholders is made as follows : $ 12,000 Profits 750 Last year's unpaid dividends on preferred stock $ 11,250 Balance 1,250 Dividends on preferred stock for current year $10,000 Available for dividends on common stock, and surplus Clark, the owner of one share of preferred stock, now receives : 3 (fo unpaid dividends of previous year, $3.00 5 % dividends of current year, 5.00 $8.00 Dividends up to 10 % may be declared on the common stock. From this illustration you should understand: a. The claim of the owners of cumulative preferred stock for un- paid dividends in case sufficient profits are made in future years. h. The fact that preferred stock is usually an investment, but common stock is more of a speculation. 388 CORPORATIONS, STOCKS, AND BONDS c. In a business of proved success, where the preferred stock is non-participating, the common stock may be a better investment than the preferred stock. 330. Buying Stocks. Stocks are bought and sold at market value which may be the same as par value, but which is usually either more or less than par. The quotation is the statement of market vali:ffe. Example. Mr. Ross purchased 10 shares of the Eclipse Carriage Company's stock from F. L. Robbins at 115. What was the cost of each share ? What was the total cost of the stock purchased ? Solution. $ 115 market value per share 10 number of shares purchased .|1150 cost of ten shares When this sale of stock is made, Robbins surrenders his stock certificate of fifty shares to the secretary of the corporation, who issues a new certificate to Robbins for forty shares, and a certificate to Ross for ten shares. 331. Dealing in Stock through a Broker. Stock is usually bought and sold through a stock broker. Brokers charge a certain per cent of the par value of the stock which they buy and sell for customers. \ of one per cent of the par value is a common charge for such services when stock is sold in large blocks. Examples. 1. What is the cost of 100 shares of stock quoted at 112J, purchased through a broker ? Brokerage \ %. Solution. 112^^ or $112.50 market price per share i or .12|- brokerage added to cost 112|or$112.62i cost including brokerage 100 X $112,621 = $11,262.50, cost to purchaser. 2. What is received by the seller of 100 shares of stock quoted at 11 2|, sold through a broker ? Brokerage \ %. Solution. 112-|^ or $112.50 price per share ^ or .12^ brokerage deducted 112f or $112.37^ returns per share after deducting brokerage 100 X $112,374- = $11,237.50, returns from sale of 100 shares. . CORPORATIONS, STOCKS, AND BONDS 389 332. Profits from Stocks. Stocks are usually purchased with the hope of making a profit in the following ways : a. Holding tlie stock and receiving dividends ; or h. Selling the stock when the market price advances. Income from Dividends. The per cent of income from dividends depends upon two things : a. The price paid for the stock. h. The dividends, which are always expressed in terms of a per cent of the par value. Example. The par value of the common stock of the Butler Dairy Company is $100.00. A dividend of 8% is declared. What per cent of income does the holder of stock receive if the stock cost him 119 J, plus brokerage ? Solution. 1100.00 par value of stock .08 rate of dividend $ 8.00 dividend per share $119|^ market value when purchased \ brokerage fl20 cost per share 18.00 (dividend) -=- $120 = 6|% income on investment. Profit or Loss from Buying and Selling Stock. Example. Perry buys 200 shares of stock at 107^, and sells at 108 1, buying and selling through a broker. What profit does he make? Solution. % 107^ market value when purchased \ brokerage added f 107^ total cost per share ^ 108f market value when sold \ brokerage deducted $ 108|- received for each share ^ 108|^ received per share $ 107^ cost per share % 1\ profit per share $1.25 profit per share 200 number of shares $250.00 profit on 200 shares 390 CORPORATIONS, STOCKS, AND BONDS Written Work 1. What would have been the total loss if Perry had sold at 106|-? 2. What would have been the total loss if he had sold at 107-^ ? 3. 7 % preferred stock is purchased at 110, without brokerage. What per cent income does the purchaser receive on his investment ? 4. What is the cost of 7 shares of stock, par value 100, pur- chased through a broker at 109|? Brokerage | %. 5. 6 J % dividends are declared on this stock. What per cent income does the purchaser receive on his investment ? The following is a partial list of the quotations of a day's sales by brokers on the New York Stock Exchange. Current quota- tions can be found in the daily newspapers. Sales Description Open High Low Close 1,200 Am. Smelting pfd. 1041 105 102 103i 2,300 Am. Sugar common 108| 108f 107 108J 400 Am. Sugar pfd. 113| 113f 1121 11 2i 1,600 Central Leather pfd. 96| 971 96| 97i 2'?,900 C. M. & St. P. common 105i 106| 104 106i 400 C. M. & St. P. pfd. 14H 141^ 140 141 6. What is received for 400 shares of Am. Smelting pfd. sold through a broker at the opening price in the table ? Brokerage \1o. 7. What is the cost of 400 shares of this stock if purchased through a broker ? Brokerage \ % . Note. Other problems may be given by the teacher, either from the above table or from the quotations of sales of stock printed in the daily newspapers. Written Review Martin, Owen, and Rathbun wish to organize a corporation. They circulate a subscription list, on which they receive subscrip- tions for the entire authorized capital stock, as follows : CORPORATIONS, STOCKS, AND BONDS 391 g)ub0crtption Mat The Roadbed Grader Company We, the undersigned, hereby subscribe for the number of shares and the amount of the Capital Stock of the Roadbed Grader Company, set opposite our names, agree- ing to pay calls upon the said stock as they shall be made by the directors of company. Number of Shares ^ ^^/j- .^^ o^^^^..^^,^.^je^^ ^£^> Jc ^A- (fr^M^u^€^ Qit£.^L:^xU3^t£i^^.^l^&tt^.^AsA£^ /S^OOO I H: . Clcoeyi^ '^ O^.^/..^^^,^. ^^ <^J^^^^ J).^.:^jn^AJnj^j ^^t^>z^v:y '^CAL ^.^y^^^ ^ ^, Tf^U.^^..^ 3.00 ^.^^^--^=<:^^.2<^ 1. What is the capital stock of the company ? 2. Into how many shares is the capital stock divided ? 3. What is the par value of each share of stock ? 4. How many votes does each stockholder have in the meetings of the stockholders ? 5. Which two of the stockholdei's have votes enough (combined) to control the management of the corporation ? 6. The Roadbed Grader Company is duly organized, and a call is made on each of the subscribers for one half of his subscription, payable on September 1. Martin, Owen, and Sanders pay the call on September 1. How much is received by the treasurer of the company on that date? 7. Rathbun pays his " call " on September 6, and is charged 6 % interest on the % 5500 for the 5 days during which the call remained unpaid. How much does Rathbun pay, including call and interest ? 8. Wilbur pays his call on September 10, including interest on the delinquent payment. Mr. Wilbur sends a check to the treasurer for % . 392 CORPORATIONS, STOCKS, AND BONDS 9. Call is made for one quarter of the subscriptions, payable on September 20. The subscribers pay as follows : Martin, September 20 ; Owen, September 20 ; Sanders, September 22 ; Wilbur, September 25 ; Rathbun, September 27. - How much does each subscriber pay, including interest? 10. Final call for subscriptions is made payable on October 1, at which time each of the subscribers pays the balance of his subscription. How much does each subscriber pay ? 11. The net profits the first year were $4075. How much is the income tax ? 12. How much profit remains for dividends and surplus? 13. A 6% dividend is declared on the stock. The total dividend amounted to % . 14. What was the amount of the surplus ? 15. What was the amount of dividend received by each stockholder? 16. Considering {a) the dividends, and (5) the surplus, if you owned a share of the stock of the, Roadbed Grader Co., would you be willing to sell it at par ? 17. The net profits for the second year were $4690. After paying the income tax, how much remains ? 18. What is the largest per cent of dividend which the direc- tors can declare out of the second year's profits and accumulated surplus ? 19. What amount of dividend would each stockholder receive ? 20. After the payment of the dividend indicated in question 18, how much surplus remains ? 21. Rathbun sells 7 shares of his stock to S. F. Cromer at 114|, without brokerage. How much does Rathbun receive ? 22. The Roadbed Grader Company issues $15,000.00 of 6 % non-participating stock, which it sells at 103. How much does the company receive for the stock ? CORPORATIONS, STOCKS, AND BONDS 393 23. The stock is issued in $ 100 shares and is sold to the fol- lowing persons : F. R. Gridley, 45 shares, G. C. Moore, 105 shares. How much does each pay for his stock ? 24. The net earnings for the third year were $6280.00, which were distributed as follows : 2 % income tax on net earnings. Dividends on preferred stock, $ . The directors declare $ 4000.00 dividends on the common stock. What is the per cent of dividend on the common stock ? 25. What is the amount of surplus remaining from this year's profits ? What is the total surplus accumulated to date ? 26. What per cent of income do the holders of the preferred stock, who purchased it at 103, without brokerage, receive on their investment ? 27. F. R. Taylor and J. E. Price engaged in partnership. Taylor invested 8 6000.00 and Price invested $9000.00. The business was conducted as a partnership for several years, when it was decided to reorganize as a corporation. A statement of resources and liabilities showed that the net capital of the partner- ship was $28,619.50. The corporation was organized with a capital stock of $25,000.00. The capitalization was how much larger than the actual net resources of the firm ? 28. The stock was divided between Taylor and Price in pro- portion to their original investment. If the stock was issued in $ 100 shares, how many shares did each partner receive ? 29. Burns, Randall, and Anderson were partners. Burns in- vested $ 8000, Randall $ 9000, and Anderson $ 18,000. They de- cided to organize as a corporation with a capital stock of $ 50,000. $ 45,000 of the stock was distributed among the partners in pro- portion to their original investments. How many $ 100 shares did each receive ? 30. The remaining stock is sold to Chapman at 98|-. How much did Chapman pay for his stock ? 394 CORPORATIONS, STOCKS, AND BONDS 31. The profits for the first year, after paying the income tax, were $ 4500. What dividend could be declared on the stock ? 32. A corporation is organized with §100,000 of common stock and $ 50,000 of participating 5 % preferred stock. Dividends of $13,500 are declared. What is the total amount of dividends paid on the common stock ? on the preferred stock ? What rate of dividend does the holder of a share of preferred stock receive "^ What rate of dividend does the holder of a share of common stock receive ? 333. Bonds. When an individual borrows money, he usually gives a promissory note. When a corporation borrows money in large amounts, it usually issues bonds. Bonds are the promissory notes of a corporation. They are usually issued in denominations of $1000.00, although there are bonds of smaller amounts. There is an increasing tendency to issue bonds in denominations of $500.00 or 1100.00, so that they may be sold to small investors. Bonds are issued by : Business Corporations, called Industrial Bonds U. S. Government called Government Bonds State Governments called State Bonds Cities called Municipal Bonds Counties called Municipal Bonds School Districts called Municipal Bonds Security of Bonds. A first-mortgage bond is secured by a mortgage on the property of the corporation. If the bond is not paid, the property of the corporation may be sold to pay the bond- holders. Second-mortgage and third -mortgage bonds are also secured by mortgage on the property, but the bondholders are paid, if the mortgages are foreclosed, in the numerical order of the mortgages. Maturity of Bonds. A bond states the time at which the principal is payable. Some bonds state that the corporation re- CORPORATIONS, STOCKS, AND BONDS 395 serves the right to redeem the bond at any time after a specified date, either at par or at some specified rate above par. Interest. Bonds bear interest payable annually, semi-annually, or quarterly, as specified. The method of collecting the interest depends upon whether the bond is a, A Registered Bond, or h. A Coupon Bond. When a person owns a registered bond, his name is recorded on the books of the corporation. When the interest is due, a check is sent to the bondholder in payment. A coupon bond is one to which small coupons are attached, there being one coupon for each interest payment. For example : a bond maturing in ten years with interest payable quarterly would have forty coupons. On the date when each interest pay- ment is due, the coupon bearing that date is clipped from the bond and delivered to a bank to collect, or it may be collected directly from the treasurer of the corporation. Value of Bonds. Bonds, unlike common stock, pay a fixed income. The market value of a bond may be above or below par, depending in general upon the security and the rate of interest. Bonds are usually known by the name of the issuing corporation or government, the nature of the security, the rate of interest, and the date of maturity. Thus first-mortgage bonds issued by the Eclipse Carriage Company, bearing 5% interest and payable in 1925, would be called Eclipse Carriage Company, 1st Mortgage 5 % Bonds, 1925. 334. Buying and Selling Bonds. When a bond is sold, the buyer usually pays not only the market value of the bond, but also the interest which has accrued since the last interest day. Example. Murdock owned an Eclipse Carriage Company 5% bond which he wished to sell. The par value of the bond was i 1000.00, and it was quoted at 95. Henderson bought the bond on April 1, at its market value plus accrued interest. Interest is payable semi-annually, June 1 and December 1. How much did Murdock receive ? 396 CORPORATIONS, STOCKS, AND BONDS Solution. Since the bond was sold at 95, the owner received 95 % of its par value. 95 ^^ ^^ ^ lOOO.OO = $ 950.00. Interest at 5 % has accrued on the bond from December 1 to April 1, four months. Interest on $ 1000 for 4 months at 5 % = $ 16.67, accrued interest. $950.00 market value of bond 16.67 accrued interest $966.67 selling price Many banks and trust companies buy an entire series of bonds from corporations and sell them to investors. Prices are quoted by these bond houses in the following ways : Price, Par and Accrued Interest ; Price, at the Market and Accrued Interest. 335. Dealing in Bonds through a Broker. When bonds are pur- chased or sold through a broker, brokerage is charged in the same manner as when stocks are transferred. -^ % of the par value of the bonds is the customary brokerage for large transfers. Written Work 1. S. & J. 6% coupon bonds are quoted at 104 and accrued interest. Interest payable June 1 and December 1. What is the cost of a i500 S. & J. bond purchased on August 15 at the market and accrued interest ? No brokerage. 2. In delivering the coupon for collection on December 1, the owner files a certificate claiming exemption under the income tax law. What is the amount of interest which he receives ? 3. What would the bond have cost if purchased through a broker? Brokerage |^%. 4. A bond house quotes Murdock Apartment 5| % bonds of 81000.00 at par and accrued interest. Interest due March 26 and September 26. What is the cost of a bond purchased May 12 ? October 19 ? 5. Laclede Gas Light Company's $1000 5% bonds were quoted by the Harris Trust and Savings Bank at 101^ and interest. Semi-annual interest payable April 1 and October 1. What is the cost of a bond purchased June 15 ? CORPORATIONS, STOCKS, AND BONDS 397 6. Wilmington Power Company's 5% bonds are quoted at 97J and interest. Interest payable semi-annually January 1 and July 1. The Wilmington Power Company reserves the right to redeem the bonds on January 1, 1919, or on any interest day thereafter at 105 and interest. What is the cost of a 1 1000 bond purchased October 15, 1917, at the quoted price ? If the bond is redeemed on July 1, 1920, what gain is made by the increase in the redemption price over the purchase price ? The following is a partial list of a day's transfers of bonds through Chicago Brokers. Brokerage ^%. No. Sold Par Value Description Open High Low Close 1 67 16 214 ^1000.00 1000.00 1000.00 1000.00 Armour 4^'s Chicago City Ry. 5's Com. Edison 5's Peo. Gas 5's 92 lOOf lOlf 99^ 92 loii lOlf 99| 92 100^ lOlf 99i 92 lOOi lOlf 99| 7. What was the cost of 5 Chicago City Ry. 11000 bonds, purchased at the opening price in the table ? 8. What did the seller receive for these bonds? How much was the brokerage on the sale ? 9. What was the gain or loss from purchasing 60 Peo. Gas $ 1000 bonds at the opening price and selling them at the closing price ? Brokerage J % on purchase and -| % on sale. TABULATIONS TO PROMOTE EFFICIENT MANAGEMENT CHAPTER XLII BUYING EXPENSES; SELLING EXPENSES; NET PROFIT 336. Expenses and Profits. In Chapter XXIII the principles of gross earnings were discussed. You have now studied many of the expenses incurred in conducting a business, and are ready to consider the problems which arise in computing net profit. Net Profit is the difference between the gross earnings of an enterprise and the total expense of conducting it. Expenses are divided into two classes : Buying Expenses. Selling Expenses. 337. Buying Expenses include all the costs of buying goods, such as freight and drayage, customs duties on goods imported, commissions of purchasing agents, insurance, and the cost of keeping goods in warehouses and placing them on the shelves of the salesroom. Buying expenses are added to the original pur- chase price of goods to determine the total cost. Thus : Prime Cost of Merchandise is the original or purchase price ; Total Cost of Merchandise is the prime cost plus the buying expenses. Example. A retail furniture store purchases goods during the year, amounting to $36,450.00. This is the prime cost. The freight, drayage, rent of warehouse, labor of warehouse employees, and other costs of placing the goods in the salesroom are $2187.00. What is the total cost of the merchandise purchased? Solution. $36,450.00 Prime cost 2,187.00 Buying expenses $38,637.00 Total cost 338. Marking Cost of Goods. When the cost price is marked on goods, some merchants add a certain per cent to the prime cost to cover the buying expenses. The records of previous years are used as a basis to determine the per cent to be added. 398 BUYING EXPENSES 399 In the illustration on page 398, the prime cost is $36,450.00, and the buying expenses 12187.00, or 6% of the prime cost. The furniture dealer might say, "Next year's buying expenses will probably be about the same as they were this year, and I will therefore add 6 % to the prime cost to cover them." A safer method, however, is to base the computation on the average expenses of several years. Yeae Prime Cost Bttting Expenses 1916 835,275.00 $1840.13 1917 41,391.00 2069.55 1918 62,387.00 3618.45 1139,053.00 $7528.13 $7528.13 - $139,053.00 = 5.41+%. For convenience, 5.4% probably would be adopted as the per cent of buying expenses. Illustration. An article cost $ 8. At what price is it marked to cover buying expenses ? Solution. 1 8 Prime cost ■055 Per cent of buying expenses $ .44 Buying expenses $ 8.00 Prime cost .44 Buying expenses $8.44 Total marked cost Written Work The prime cost of a merchant's purchases and the buying ex- penses for several years are given below. Find the per cent of buy- ing expenses for each year and the average for the entire interval. Yeab Purchases Buying Expenses 1. 1914 $ 9,426.90 $ 643.92 1915 12,318.26 812.29 1916 14,126.29 830.12 1917 11,341.72 690.19 1918 14,985.29 752.29 2. 1916 39,286.26 2326.80 1917 47,562.83 3146.29 1918 59,286.28 4210.08 400 BUYING EXPENSES 3. The prime cost of merchandise in a certain store is increased 8% to include buying expenses; the selling price is determined by adding 9% to the total cost. Mark the total cost (using "blacksmith" as the key and "g" as a repeater) and the selling price (in figures), of articles, the prime cost of which was as follows : Stock No. Prime Cost A 326 $2.19 A 394 6.25 F 246 ' .90 A 385 2.78 4. The manager of one of the departments in a large store adds 6 % to the prime cost to cover the buying expenses. He re- ceives quotations of prices from manufacturers who offer different discounts. He prepares a table showing the total cost after de- ducting the discount offered and adding the 6 % buying expenses. The following is a similar table which you will complete : .00 .25 .50 .75 1 Less 2% Plus 6% Less 5% Plus 6% + C% -2% + c% -5% + 6% -2% -5% + 6% + 6% -2% + 0% -5% + 6% -7% + 6% 1 2 3 4 5 6 7 8 9 10 1.0388 1.007 .9858 .2597 .25175 .24645 5. By referring to the table, find the total cost, including buy- ing expenses, of an article quoted at 12.25 less 5% ; $3 less 2%. Refer to the table, and find 6. Which is the better price, and how much better: 81.75 each, less 2 %, or $2 each, less 7 % ? How much will be saved by purchasing one gross at the cheaper quotation ? SELLING EXPENSES 401 339. Selling Expenses. After the goods have been placed on sale, all further costs, such as rent of store, salaries of clerks, ad- vertising, heat and light, delivery, store supplies, insurance and taxes, depreciation and shrinkage, bad debts, and general ex- penses, are considered as selling expenses. • 340. Finding the per cent of selling expenses. The per cent of selling expenses is a matter of valuable information to a mer- chant. It is determined by the formula : Selling Expenses -h Gross Sales = % of Selling Expenses. Example. A merchant's gross sales during one year are f 124,265 ; the selling expenses for the same year are $29,078.01. The selling expenses are what per cent of the gross sales ? Solution. $ 29,078.01 h- $ 124,26.5.00 = 23.4 ^o. 341. Increase of Selling Expenses. During recent years, as shown by the graph reprinted from System^ a Magazine of Business^ selling expenses, such as advertising, delivery, etc., have greatly increased. 27 24 21 18 15 12 9 6 3 n ■~" — n — n ~~" y' ,y ^ ^ -■' .'' ,, ^' -' ___^ .-- ^ ^ ^ '' ^ jy .-- — ' cr ^ ^ ia ^ 1^ xy -^ /^ ^ ^ — ' ,-- ■^ ^r ■^ >-• . . — 7^ ^^ -C ^ — Department Store (Annual Sales $17,000,000 in 1912) Dry Goods Store ( ,. „ $150,000 .. .. ) Small Store ( m .. $25,000" •• ) o __ ^■^ """■ '^~~ "~~ — — — — — — ~~~' 18 90 1895 1900 1905 1910 19U | 402 SELLING EXPENSES Oral Work Trace the rise in the per cent of selling expenses in each busi- ness, stating what per cent the selling expenses in each business are of the gross sales in each year. Written Work The following statistics are reprinted from System^ and show the result of an investigation made by that magazine to determine average or standard per cents of selling expenses in various busi- nesses. Find what per cent each item of expense is of the total sales. Find what per cent the total selling expenses are of the sales. Dky Goods Stoke General Store Gross Sales, $ 50,000.00 Gross Sales, $ 50,000.00 Shoe Stokb Gross Sales, $ 25,000.00 Rent Salaries Advertising Heat and light Delivery Supplies Insurance and taxes . . . General expense .... Depreciation and shrinkage Bad debts $1,550.00 4,800.00 750.00 200.00 450.00 200.00 . 550.00 2,200.00 700.00 150.00 .$1,154.85 4,067.09 351.48 251.04 954.01 150.63 200.84 150.63 301.27 150.63 I 778.13 2,786.21 376.51 225.91 75.30 100.40 301.21 1,029.14 150.61 25.10 Vehicle Store Gross Sales, $57,000.00 Hardware Store Furniture Stork Gross Sales, $ 46,000.00 Gross Sales, $ 100,000.00 Rent Salaries Advertising Heat and light ; . . . . Delivery Supplies Insurance and taxes . . . General expense .... Depreciation and shrinkage Bad debts $1,094.63 5,818.81 633.73 345.67 518.51 230.45 460.90 230.45 403.28 115.22 $ 1,305.61 5,042.35 405.20 226.10 270.13 180.08 495.23 360.17 225.10 180.08 3,507.36 8,317.60 2,906.15 801.70 1,102.33 501.06 1,402.97 1,803.82 1,904.03 1,202.54 SELLING EXPENSES 403 Rent Salaries Advertising Heat and light Delivery Supplies . , Insurance and taxes . . . General expense .... Depreciation and shrinkage Bad debts Clothing Stoke Gross Sales, $ 60,000.00 1,322.24 5,469.29 2,043.47 180.31 360.61 120.20 661.12 1,681.84 721.22 240.41 Dbxjo Stoke Gross Sales, $ 20,000.00 I 924.66 2,191.01 522.64 160.81 80.40 60.30 281.40 482.42 100.50 40.20 Jewelry Store Gross Sales, $ 80,000.00 $ 1,080.40 3,361.23 1,050.38 180.07 30.01 270.10 540.20 630.23 360.13 90.03 Save your results for use in the problems which follow. 342. Efficient Management to Determine Economies and "Leaks." When a merchant has a reliable standard with which to com- pare the various per cents of selling expenses in his business, he is able to determine the items of expense which are too large. Written Work A dry goods store has gross sales during one year amounting to i 40,000.00. The expenses are as follows : 165.00 180.00 155.00 120.00 42.00 Rent $1200.00 Salaries 3240.00 Advertising 250.00 Heat and light 225.00 Delivery 1135.00 Supplies Insurance and taxes General expense Depreciation and shrinkage Bad debts 1. Each item of expense is what per cent of the gross sales ? 2. Th9 total selling expenses are what per cent of the sales ? 3. Accepting the per cents found in the dry goods store prob- lem on page 402 as a standard, determine which expenses are larger than the standard, and which are smaller. 4. Complete the following table : 404 NET PROFIT ^ 1 o 1 II ^ — 1 E- t 1 11 » p« ^ § CU lO i-( CO iC CO t^ O ^ »o Oi r^ r^ g o: o O xo rH (M O 00 rH o Tji Ttl ,-1 (^ o (M Ci o o Oi 1-* o 00 H h i-c O CO r^ CO CO U3 CO (>l ■^ lO <£> ■^ CO o CO CO lO '^ iO 'Tt* r^ CO O ,—1 Ol "^ CO CO lO 00 1-^ Oi -^ w c^ 4 CO CN < «3 'M -* r- <-> -^ TiH -^ lO fN ■^ (jq ,—1 ?D 00 05 (>1 r— t^ CO CO ■^ 1— (^ CO 1—1 I— 1 rH i-i cq I— 1 rl rH cq m= . oo^^ o (N rH Oi CO CO 05 1-1 t- Oi t^ CO T-l w „ t^ l>> CO o t^ rH CO •^ r-l Tj^ T-l TJH t- Tjl r^ ,_l ^ t- T-^ CO CO (N r- 1^ « T-l (M --H ■* CO t- rH CO T-l. CO T-l CO o oa CO CO t^ (M CO TtH Ci (N CO (N Tfl (N -§ t- iC »o uo o CO t- f>) ■^ Oi Oi CO ,-( (M (N CN (M (M (N ■• (M •Tf W t- 1-^ ■^ ^ (M ^ « O rH CO CO o t^ lO y-{ CO O 00 lO -•! -1 -5 O fi H w 02 no -. f ^ ^ C/J ■♦J O) crt >>, r^ e ,£2 £ f>> CC ^ CO 2 GO o Ph (D ^, J^ ■t-3 O) 'A bn ■•.■3 2 e bn Ts -d n hf) > ^3 G TS > 'O >^ T3 > pQ >> 'd 'O rQ ;>> 1 Tl rO ^ TS ^ a 02 «Ti ^Q- ^5 = Dress Goods Date 5/2/17 jg Cleek's Number Gross Sales Returned Goods Net Sales Checks 4501 287 96 113 02 314 39 128 03 136 32 4 92 84 04 315 26 12 25 115 05 503 16 121 06 263 50 1 25 103 07 98 30 2 80 67 08 193 50 123 09 215 67 3 96 89 10 309 50 15 75 131 11 235 80 26 15 98 12 96 15 35 13 103 28 5 60 65 14 128 95 82 15 202 75 3 10 96 16 127 30 60 Total 363. Salesman's Cumulative Tabulation. This blank is used to record the sales of a traveling salesman who sells the goods of several departments. Each month his sales are entered by depart- ments in the proper column. After the January and February sales are entered, the amounts for the two months are cumulated ; that is, added. As each month's sales are entered they are cumulated with the preceding total. Thus, at any time during the year, this blank shows the following facts : The salesman's sales per month in each department ; His total sales to date in each department ; His total sales each month in all departments ; His total sales in all departments. Written Work Prepare a cumulative sales report for Salesman No. 32. Find the total sales per month. Cumulate the sales as indicated on the form on page 440. 440 TABULATIONS FOR THE SALES MANAGER t m o w Jz; 6 g a C/2 1 1 '5 ?? CO ^ ?? fe ?^^ ^ CO CO fe s g§ CO 00 CO 1—1 1-1 to CO 1—1 CO CO CO 1-1 o t^ 1-1 1—1 i-O OS ^ CO OS ?o 00 CO ?? s n 00 00 >o OS 00 CO (M (M O i 05 CO 1—1 CO 1—1 8 CM CO 1-1 1—1 OS 1—1 1—1 CO . CO lO fe 1 s 1—1 CO 1-1 g 1—1 OS O g CO 1—1 1 1-1 CO 1—1 i l:^ CO CO CI lO o 1-1 a CD ^ § S ^ ^1 g co CO §? § J^^ CO O CO 05 CO CO 1— ( CO 1— 1 1-1 o CO CO CO CO OS OS 00 tH o o CO 1—1 CO 1-1 t- CO to Ttl 00 a ea* ^ CO OJ CO Oi b- ''^H CO OS CO s§ ^ u 1—1 OS (M 00 CO CO s i CO (M 1— ( 1—1 CO CO i 1—1 CO CO 00 OS CO §? 1-1 CO CM 1—1 CO OS ^ ^ CI (M CO OS § o § g ^ g v^ OS CO ^ ^ CO g fe SJ^ QO CO 1-1 O t- ^ 1-H ^ t^ 1—1 i ^ t CO CO P M > > 1— i >— 1 l-H ^ '^ s > > TABULATIONS FOR THE SALES MANAGER 441 364. Monthly Percentage Comparison of Salesmen. Sales mana- gers consider it very important to have comparisons of their different salesmen. They wish to know not only the amount of the sales made by each, but also what fractional part of the total sales was sold by each. The most convenient way to state these fractions is by percentage. Written Work Prepare a form similar to the one indicated in the following illustration : Monthly Comparison of Salesmen Salesman's No. First Week Second Week Third Week fottrtii Week Fifth Week Total Per Cent I $320.70 $230.49 $563.40 $834.70 $123.70 II 470.65 870.43 933.60 274.80 85.70 III 376.80 543.70 625.80 735.43 137.89 IV 339.40 763.35 347.84 347.96 99.89 V 276.80 563.90 743.90 876.90 470.96 VI 723.96 439.65 375.63 648.93 275.93 VII 374.99 687.93 684.96 532.89 99.64 VIII 268.37 536.96 648.97 374.88 63.96 IX 469.89 746.93 387.93 479.69 364.84 X 479.89 489.89 683.89 874.96 216.80 XI 376.86 375.94 632.61 276.93 - 39.96 XII 546.64 789.94 346.49 832.24 162.27 XIII 345.49 328.84 769.94 962.63 137.90 XIV 476.63 374.84 265.89 649.84 202.03 XV 763.47 239.84 646.63 389 84 62.99 Totals Enter the sales in the proper columns. Find the total sales made each week by all salesmen. These totals should be entered at the foot of the columns. Find the total sales made by each salesman during the month. This will require horizontal addition, and the totals should appear in the " Total " column at the right. Find the grand total sales for the month. (As a means of checking your work, find the grand total in two ways: (a) by 442 TABULATIONS FOR THE SALES MANAGER adding the totals at the foot of the blank, and (6) by comparing this result with the total of the " Total " column at the right. Find what per cent of the grand total sales was made by each salesman. Enter these per cents in the column at the right. 365. Comparisons with Previous Year. Business men are inter- ested in the growth of their sales, profits, etc., and make frequent use of comparative tables which bring out clearly the increase or decrease in the business. In addition to recording each salesman's sales by weeks, months, and cumulatively, and in addition to comparing the records of different salesmen to deter- mine their comparative efficiency as shown by their per cent of sales, the office often prepares a record of each salesman's sales for the current year as compared with his sales of the preceding year, to show the amount of increase or decrease, and also the per cent of increase or decrease. Written Work Enter the following information on a properly ruled form. Find the yearly totals, the increase or decrease in dollars, and also in per cents. Finding the Per Cent of Increase or Decrease. First express the increase or decrease over the previous year as a fraction^ using as the numerator the increase or decrease^ and as the denominator^ the previous years sales. Change this common fraction to a per cent. Example. What is the per cent of increase in a business that yields, respectively, $3000 and 83600 in two successive years? Solution. This year's sales for January $3600 Last year's sales for January 3000 Increase 600 Fraction showing increase over last year ^ ^ 3000 Changed to per cent = 20 %. From this tabulation the sales manager can determine the sales- men whose efficiency is increasing, and can reward them by in- creased salary. TABULATIONS FOR THE SALES MANAGER 443 Chart Showing Increase or Decrease of Sales Name Month Sales Last Year Sales This Yeab Inckease Per Cent Increase Decrease Per Cent Decrease January .... $346 29 $427 95 February . 457 75 515 86 March 385 86 395 57 April . . 416'87 402 75 May . . 29584 312 75 June . . 212 67 235 84 July . . 416 47 493 75 August . 328 57 319 56 September 425 65 483 75 October . 513 86 603 52 November 627 94 673 49 December 743 85 623 57 Total . 366. Salesman's Record of Comparative Sales and Profits by Departments. The following form is somewhat similar to the form on page 441. This form, however, compares the profits of one year with the profits of the preceding year. This traveling salesman sells goods in ten departments. The profits from his sales are computed by the profit clerk, and his total profits by departments are entered on the record. Written Work Prepare a record of comparative sales and profits for the sales of E. H. Barlow. Find the total sales and the total profits for each year. The profits were what per cent of the sales in each depart- ment ? After the per cent of profit in each department for the two years has been determined, the increase or decrease in the per cent of profit can be found by subtraction. Enter increases in black ink, and decreases in red ink. 444 TABULATIONS FOR THE SALES MANAGER Salesman's Record of Comparative Sales by Departments Salesman's Name — E. H. Barlow Dbpt. 1917 1918 Per Cent Decrkase Increasb Sales Profits Per Cent Sales Profits Per Cent I II III IV V VI VII VIII IX X $12162.40 3147.90 14127.65 3287.96 5372.47 6392.49 15271.34 896.29 1247.89 13467.47 $ 1456.80 629.60 1732.86 362.80 437.89 326.80 1376.45 46.86 97.62 1263.43 $13162.90 3319.80 15216.90 3347.80 5629.90 5146.79 15423.66 1989.60 1462.96 14362.62 $ 1562.80 640.90 1927.90 367.90 469.90 294.90 1389.90 66.80 103.60 1346.90 Total 367. Daily Classification of Sales by Departments. The tabula- tion described in this section shows the daily sales in each depart- ment, the total daily sales in the entire store, and the total sales of each department for the week. Weekly Classification of Sales by Departments Dept. Monday I'UESDAV Wednes- day TlIURSDA\ Friday Saturday- Total I II III IV V VI VII VIII IX X > Total Per Cent TABULATIONS FOR THE SALES MANAGER 445 The per cent column at the bottom shows what per cent of the week's total sales was made each day. The per cent column at the right shows what per cent of the week's total sales was made in each department. Written Work Prepare a form similar to the illustration. Enter the following facts on the form. Dept. Monday Tuesday Wednesday Thursday Friday Saturday I 11213.85 $1194.83 $ 949.37 $1384.39 $1029.47 $1593.48 II 1023.75 1094.82 1127.49 1284.29 974.92 1326.83 III 1125.94 1183.27 1248.48 1494.84 827.84 1426.46 IV 923.85 1184.37 1395.47 1029.84 831.15 1285.31 V 2539.75 1823.57 1531.84 1925.29 2041.73 2848.57 VI 1925.85 1482.16 1632.83 1451.61 1348.41 2154.38 VII 1594.85 1238.57 1285 94 923.74 1128.48 1328.94 VIII 1923.84 1528.49 1228.47 1395.47 1463.94 1927.47 IX 2594.48 2049.47 1829.46 1739.84 1832.47 2885.81 X 1523.82 1449.82 1327.46 1554.53 1232.84 1723.49 Find the total sales for each day. Find the total sales for the week in each department. Find the total sales made by the store during the week. On the bottom line, show what per cent of the week's sales was made each day. In the column at the right, show what per cent of the week's sales was made in each department. Plot a curve on graphically ruled paper, showing the total sales made in the store each day of the week. From this form and the graph, the sales manager can determine which days had the lowest sales and he will probably offer extra bargains on those days in order to attract more customers. He will also be able to locate the departments with the smallest per cent of sales, and will take measures to increase the trade in those departments. 446 TABULATIONS FOR THE SALES MANAGER 368. Yearly Sales by Months in All Departments. The form illustrated in this exercise shows the total sales per month in each department of a store. It furnishes the basis for various compari- sons ; for illustration, the gross sales by departments can be com- pared either by months or for the entire year. A graph could easily be prepared from this table, showing the variation of monthly sales in each department. Written Work Prepare a table from the following information. Find the annual sales in each department ; find the total sales each month for the entire store. Dept. I Dept. II Dept. Ill Dept. IV Dept. V Total January . 11238.95 $3728.94 15238.64 $2927.46 $6223.58 February . 1136.95 3927.47 5329.47 2842.14 6128.47 March . . 1145.98 4023.45 5183.92 2812.51 5923.74 April . . 1032.84 3925.36 5023.94 2642.23 5414.42 May . 947.83 3723.75 4823.46 2523.95 5324.94 June . 923.45 3582.45 4213.27 2348.41 5942.38 July . 1123.76 3327.74 3928.48 2493.48 5283.85 August . 946.73 3527.94 3215.13 2493.15 5328.47 Septembei 982.67 3628.94 3921.14 2532.57 • 5623.95 October 1095.85 3825.93 4428.48 2724.71 5923.42 Novembei ' 1123.86 3927.85 4913.73 3124.93 6113.81 Decerabei • 1357.94 4129.54 5492.14 3295.58 6395.73 Plot a curve on graphically ruled paper, showing the variations in monthly sales in Department I. 369. Sales and Returned Goods by Departments. The form illustrated on page 447 shows the annual sales in each depart- ment, the goods returned by customers to each department, the net sales, and the per cent of sales returned to each department. Written Work Prepare a form similar to the model. TABULATIONS FOR THE SALES MANAGER 447 Enter the following facts : Dept. I, Sales, f 27,493.75; Returns, 8823.85. Dept. II, Sales, 154,294.74; Returns, $924.74. Dept. Ill, Sales, $82,583.84; Returns, $1239.36. Dept. IV, Sales, $107,239.75; Returns, $1257.34. Dept. V, Sales, $85,294.63; Returns, $923.75. Dept. VI, Sales, $112,437.85; Returns, $723.74. Dept. VII, Sales, $82,374.50 ; Returns, $1328.85. Dept. Sales Eetttkned Goods Net Sale Per Cent of Sales Returned Total . . . Find the net sales for each department, the per cent of sales returned to each department, the total sales for the year, the total amount of goods returned to all departments during the year, the net sales for the year, and the per cent of sales returned to the store during the year. Show by a curve plotted on graphically ruled paper, the per cent of sales returned to each department. 370. Sales Classified by Days and Departments. The form on page 448 shows the daily sales for one week in twenty-five selling sections. (Each department may be subdivided into several sell- ing sections ; for example, the men's clothing department into sections for suits, overcoats, hats, etc.) Written Work Prepare a classification of sales by days and by departments. Enter the amounts in the proper column ; find the total sales for each day, and for each section. Also find the grand total sales. Be sure that this grand total checks all additions. 448 TABULATIONS FOR THE SALES MANAGER Sales Classified by Days and by Departments Dept. Monday Tuesday Wednesday TUUKSDAY Friday Saturday Total 1 $423.60 $187.47 $279.19 $789.01 $203.94 $101.97 2 543.54 632.65 443.22 339.75 365.93 234.56 3 100.10 999.99 203.82 901.09 584.85 475.86 4 594.32 567.98 213.45 191.12 218.12 345.09 5 555.33 224.60 • 100.00 201.35 857.02 905.43 6 504.60 543.52 421.05 164.30 305.34 465.89 7 102.93 621.19 178.92 630.95 304.89 985.64 8 567.23 324.54 858.87 664.88 234.98 876.32 9 908.23 765.54 510.25 654.21 894.32 564.32 10 809.32 432.66 141.15 234.65 124.56 784.32 11 239.08 111.03 400.00 191.31 123.45 621.31 12 178.92 543.98 753.60 555.33 135.62 152.02 13 164.30 324.98 827.26 578.98 113.56 105.15 14 594.32 234.65 252.42 421.05 211.31 202.01 15 339.75 432.66 323.23 213.45 135.62 615.20 16 911.26 234.56 789.02 512.12 218.21 201.51 17 345.67 890.23 456.78 518.29 14L19 520.20 18 902.34 567.89 589.13 234.13 720.95 111.11 19 979.15 860.17 762.95 729.84 789.01 33.33 20 519.79 790.11 825.85 678.11 101.97 754.46 21 200.20 996.57 908.23 456.34 656.54 644.57 22 987.87 100.98 819.38 517.83 671.78 135.76 23 112.34 567.67 450.78 189.58 150.85 200.43 24 109.32 528.49 246.18 ISO.81 917.99 774.82 25 933.47 467.83 239.08 652 29 493.86 496.73 Total 371. Daily Sales Compared with Sales of Corresponding Day of Preceding Year. One of the most common methods of noting the growth of a business is to compare the sales of each day with the sales of the corresponding day of the preceding year. It is as- sumed that trade conditions will be about the same, year after year, at the same time of the year. By comparing the sales of the first Monday in October, 1917, with the sales of the first Monday in October, 1916, a basis of comparison is furnished to show increase or decrease in business. It is customary to enter on the blank the TABULATIONS FOR THE SALES MANAGER 449 weather conditions for the two days, since the weather would affect the volume of sales. Written Work Prepare a blank similar to the model. Enter the following facts on the form. Daily Sales Report by Selling Sections Aug. 2, 1917 Section No. This Year Last Year Increase Per Cent Decrease Per Cent 1 $619.20 $603.60 2 85.70 90.21 3 214.00 196.80 4 716.26 654.30 5 426.80 397.80 6 562.70 571.32 7 627.80 503.60 8 462.80 403.40 9 1037.90 862.40 10 729.60 642.80 . 11 327.96 417.84 12 526.94 327.64 13 827.83 941.62 14 987.60 864.95 15 479.90 532.60 16 362.85 325.90 17 762.35 629 89 - 18 236.80 329.40 19 246.89 639.90 20 427.86 547.77 21 572.96 563.84 22 294.84 289.77 23 276.89 286.89 24 347.80 329.99 25 532.87 531.39 26 274.79 239.80 Total Find the increase or decrease, and the per cent of increase or decrease, in the sales for each selling section, and for the entire department. 450 TABULATIONS FOR THE SALES MANAGER 372. Form Showing the Per Cent of the Stock on Hand at the Be- ginning of the Month Sold during the Month. The following form shows what per cent of the stock on hand at the beginning of the month is turned during the month. An inventory is taken at the beginning of the month, the sales of the month are recorded, and the per cent of the inventory sold is computed. Example. The inventory at the beginning of January showed 540 suits on hand. During the month 360 suits were sold. What per cent of the stock was sold ? Solution. f|§, the fraction of the stock sold. 360 -^ 540 = 66f %. Written Work Prepare a blank similar to the model. Enter the following data. 1916 1917 Month Stock Sales Per Cent OF Stock Sold Stock Sales Per Cent OK Stock Sold Per Cent Increase Per Cent Decrease Jan. $1864 $1631 87.5 $2163 $1731 80.0 7.5 Feb. 1632 1437 1973 1562 March 1689 1307 1865 1437 April 1432 787 1437 986 May 1063 836 1237 884 June 1773 824 1147 835 July 1089 829 1312 846 Aug. 1002 786 1562 897 Sept. 1347 965 1575 979 Oct. 1689 1087 1734 1137 Nov. 1947 1476 2074 1562 Dec. 2137 1694 2263 1734 Total Complete the form by showing what per cent of the stock on hand at the beginning of the month was sold during the month ; also show the per cent of increase or. decrease the second year. TABULATIONS FOR THE SALES MANAGER 451 373. Department Record of Sales, Profits, etc. The following table shows one of the more elaborate forms of store records. Written Work Rule a form similar to the illustration. Use the following data and complete the blank. Your ability to prepare this exer- cise without further explanation will be a good test of your efficiency. Prorate the salaries, commissions, and other expenses, according to sales. Department Sales, Gross Profits, Returned Goods, Net Profits, Per Cent of Net Profits, and Comparison with Last Year Dept. Sales Gross Profits ■5 1 p4 Prorated Shake of Salesman's Salary ani> Expenses 1 i! ill H < 1 $ 3465.80 1 832.46 $134.60 $27.30 7 2 2247.95 629.22 94.97 21.13 12 3 1276.96 169.94 4 4 974.44 202.41 15 5 326.87 164.69 21 6 16,374.39 2,234.62 99.84 11.20 10 1 22,365.24 4,162.94 232.62 49.20 14 8 16,264.64 3,148.88 194.39 41.29 10 9 22,239.39 8,366.86 265.24 42.30 12 10 1,646.62 624.30 42.00 19.00 14 11 9,347.27 1,689.90 164.69 16.24 8 12 6,362.94 2,144.64 196.62 62.21 18 13 976.46 202.03 12.13 2.63 14 14 3,274.74 968.66 47.31 11.21 12- 15 9,639.99 1,244.19 111.12 12.16 10 16 12,244.84 2,646.29 199.96 35.19 13 n 8,348.98 1,294.68 96.25 12.12 11 18 16,264.42 3,000.99 47.73 10.09 13 19 18,297.78 2,346.98 169.89 18.94 12 20 1,362.63 423.37 21.31 7.96 11 Salesman's total salary and commissions . .$2,461.00 Salesman's total expenses 1,992.00 MISCELLANEOUS CHAPTER XLVII CONSIGNMENTS AND COMMISSIONS Grain, live stock, and many other articles of produce and manu- facture are usually marketed through commission merchants or brokers. 374. Illustration and Explanation of Terms. Mr. Williams, who lives in a small town in Minnesota, sends a car of grain to Owen and Bartlett, commission merchants of Chicago. Owen and Bartlett are engaged to sell the grain, pay all charges, deduct their commission, and remit the proceeds to Williams. Williams is called the principal ; Owen and Bartlett, the agents. Williams calls the grain a shipment ; Owen and Bartlett call it a consignment. The statement of the transaction furnished to Williams is called an account sales. When a commission mer- chant is engaged to buy produce, the statement of the transaction furnished to his principal is called an account purchase. 375. Selling Consignments of Grain. The city produce ex- changes provide a ready market for grain at all times. The com- mission merchants and brokers are members of these exchanges, and act as the agents of farmers and elevator companies in the sale of the grain. The farmer or elevator owner consigns his cars of grain to his broker, who sells the grain, has it unloaded at the elevator designated by the purchaser, receives cash in payment, and accounts to his shipper for the full amount received, minus his commission and the charges which he has paid. Commission is the charge made by the broker for handling the sale. The following are Chicago rates : ^ cent per bushel on corn and oats. 1 cent per bushel on wheat, rye, and barley. 452 COJSFSIGNMENTS AND COMMISSIONS 453 Inspection. A nominal fee (usually 35 cents) is charged by the state grain inspection bureau for determining the grade or quality of the grain. Weighing. A fee is charged by the board of trade weighing bureau for determining the number of pounds of grain in the car. SALES BY OWtiN ik BAK 1 Lt 1 I COMMISSION MERCHANTS AND RECEIVERS CHICAGO DATE OF SALE CAR NO KtND OF GRAIN LBS. PRICE TERMS „.„., 1 <:Z^,^ A^ SH-JiL/^ ^2:^i^j!^'5^M^ /ii.i?s / ^ So r/( 9 (7So 2.0 ^V Pro. No CHARGES Freight. i-5' '/'X 3-7 7*^ Extra Charges, '^S(2e'^^^^c.c-tyt ^7 ^Q. Net proceeds to your credit, ao^ 6S E.&O E 4^ /^ Soo GO CHICAGO, C^/^f/(^ '9' a K.Cet.-un^ t^ /:^2. (is BiU Book, Fc Iw ' ow EN a BART _ET By b An Account Sales Drafts. The consignor frequently draws a demand draft on his broker in part payment. The draft does not usually exceed 80% of the estimated value of the grain. The shipper deposits the draft, with bill of lading attached, with his local bank. The local 454 CONSIGNMENTS AND COMMISSIONS bank sends the draft to its correspondent bank in the city where the broker is located. The city bank presents the draft to the broker, receives payment, and turns over the bill of lading. When the broker renders an account sales of the grain, he deducts the amount of the draft, plus interest at the ruling rate from the date the draft was paid until the date on which he received the money from the sale of the grain. 376. Buying Grain. Brokers buy grain as the agent of millers, refiners, and other manufacturers using grain as a raw material. Purchases are made both for immediate and for future delivery. In the produce exchanges there is a quotation on grain purchased for immediate delivery, and also on contracts calling for the delivery Purchased By OWEN & BARTLETT COMMISSION MERCHANTS AND RECEIVERS CHICAGO For Account of ^yf^^JJi'yi'^^ (yjy-t^y ^-J^^j^C^Jto) 9u^ ^o ,J^ -4- :i ^^f-i^'>iy /^ ^^^^ SyJa ^ Sold / o Thousand Bus. @ S / '^i- ^ /S.S ^ ^ <; ^ /^^o -^—-^ E. & O. E. OWEl «4 & BARTLETT p, t 456 CONSIGNMENTS AND COMMISSIONS Table of Grain Weights per Bushel Corn 56 pounds Wheat 60 pounds Oats 32 pounds Barley 48 pounds Written Work 1. What is the value of 71,980 pounds of corn at 62 cents per bushel ? 2. What is the value of 89,720 pounds of wheat at $ 1.42 per bushel? 3. What is the value of 54,350 pounds of oats at 52 cents per bushel ? 4. What is the value of 67,320 pounds of barley at 81 cents per bushel ? 5. If a farmer sells the elevator company in his town 514 bushels and 28 pounds of corn at 62| cents per bushel, how much does the farmer receive ? 6. If an elevator company buys 514 bu. 28 lb. of corn at 58|- cents, 312 bu. 14 lb. of corn at 58J cents, 410 bu. 14 lb. of corn at 59 cents, what does the grain cost the elevator company ? 7. If the elevator company sells this grain through a Chicago broker for 65|- cents, and pays 61 cents per hundred pounds, freight, J cent per bushel commission, 25 cents for weighing, 35 cents for inspection, how much profit does the elevator company realize on the trans- action ? CONSIGNMENTS AND COMMISSIONS 457 8. The Sedan Elevator Company shipped you, as its broker, 1145 bushels and 40 pounds of wheat, which you sold at 11.40. Charges were as follows : Commission, 1 cent per bushel ; Freight, 8|^ cents per hundred pounds ; Weighing, 30 cents ; Inspection, 35 cents. The elevator company drew a draft for $;700, which you paid Ieiii(.'iits uv.sl, iiumiUt uf totuU, etc< 00 ,30- .00 ,30- ,00- .30— .00 .30 .00 .30— .00 .30- .00- .30— .00- .30- .00 — ^a^Mjt, yy\ijU^ -^ ct{Lf..^^{^ (S««-A,<- o-^ CS^>-»>^>^L^<^c<^ ^ 00 ««WORKMAN 6^. 7te.<^ TOTAL HOURS /2. /i^ (3^ryv.'^^a Xd % ^ ^ ^ 2^ srri ^ ^^ f^^ AA^ io ■~~° ■^^ Io u~ — -H — ■ - — //t — " jx — — — If - /o a«? IO xc a. ^ s/ A a ii't -v^ 9 li fi "f /■A (.•A -"^ ?it "^ i^l^ 4 3-f .^If rf i/ 10'" 1 ^ .1 4 ^S 6 7 8 9 20 2Z 30 3 1 •To^o/ 38£ Atth man The belo\^ Co Ho e ho cc /■ : st Ul F en UI )St of ^S d s I ir wc ^6 of an )er lai )rl^ 25. a d 1 il ■ed 00 th m( ho 101 ab Id e 3n1 rs< Lir or ur -2 bh 3l] n pe ] in 50 5t or lOl ia3 r Bo ro ?: [) = of ot irs T ye arc tal = i M he c be ar 3S, \r, [ai an f 2, ^5, 1 I Dei b ou 1 $i 50( la .al •io e nd m [0( m ). be )or d( de 1 ).0 ).0 ).0 r a )f tei ^y QOi Qd tir ^m t] 3t B ne in be pe [or , t ed r r r se he fr ne na L tc or th n ab( )ta Q 1 od ho )r li :he i ur pe m J I 111] r Ho mbei ecor Lstral ur ds bee FARM RECORDS 473 Cost of a horse hour is determined in a similar way. Total value of 2 horses, $600.00 Int. on $ 600.00 at 5 %, $ 30.00 Feed and expense, 550.00 Total cost per year, 1 580.00 Total number of horse labor hours, 6500. $ 580.00 -^ 6500 = 8.9 cents, labor cost per horse hour. After the labor cost records have been made, the profit or loss from the crop may be determined by the preparation of a table similar to the following : Account with a Crop of Corn in Field B (36.48 Acres) on an Iowa Farm, ]910i Date Total Per Acre Per bushel Items op Statement Man hours* Horse hours * Cost Man hours * Horse hours 2 Cost Plowing, fall of 1909 (14- inch gang) . , . . Disking Harrowing Planting (with planter) Harrowing (after plant- ing) Cultivating (tirst time) . Cultivating (second time) Cultivating (third time) Cultivating (fourth time) Picking seed corn . . . Husking (from standing stalks) Mar. 25 to Apr. 2 Apr. 7 to 29 Apr. 29 to May 4 Apr. 30 to May 5 Mav 10 to 14 May 27 to 30 June 3 to 6 June 14 to 18 June 23 to July 5 Sept. 27 to Oct. 7 Nov. 2 to 22 90i 30§ 58 545 51-1 57 59 305J 342 361 51 61 72i 116 109 103 114 $46.48 49.28 8.56 10.25 11.86 19.49 18.31 17.31 19.15 7.44 102.65 2.34 2.47 .70 .84 .92 1.59 1.49 1.41 1.56 1.62 8.38 9.38 9.89 1.40 1.67 1.99 3.18 2.99 2.82 3.12 $1,279 1.351 .235 .281 .325 .534 .502 .474 .625 .204 2.814 611 16.75 Total labor cost , . Manure charge . . Seed, 5i bushels, at $5 General expense . . Equipment . . . Taxes Interest (rent) . . 851 1,940J 310.98 124.91 27.50 18.24 23.27 25.53 255.35 23.32 53.19 8.524 3.424 .754 .500 .638 .700 7.000 Total cost . . 78.5.78 91.54 Summary : Income 3 .... Cost 1,127.36 785.78 30.90 21.54 $0,512 .357 Profit 331.58 9.36 .155 1 Previous crop : Timothy for seed, 1909. 2 Rates per hour : Man hours, 12.6 cents ; horse hours. 10.5 cents, » Yield : 2200 bushels of grain, at 50 cents (average, 60.3 bushels per acre), $ 1100 ; stalks, $ 27.86 ; total, $ 1127.36. 474 FARM RECORDS The labor records show the number of horse hours and man hours spent on each crop* After determining the hourly rate, it is necessary to multiply as follows : The number of man hours by the rate per man hour ; the num- ber of horse hours by the rate per horse hour ; to determine the total labor cost of each. The costs and returns of each crop may then be summarized, and the gain computed, as illustrated in the following table : Corn Crop on South 40 Item 40 Acres Pee Acre Seed $ 24.00 70.00 28.30 450.00 40.00 109.01 228.60 .60 Fertilizer 1.75 Taxes .7075 Interest 11.25 Expense 1.00 Man labor, 991 hours at 11 cents . . Horse labor, 2286 hours at 10 cents 2.725 5.715 Total cost 949.91 23.7475 Yield, 2552 bu. corn at 1.48 .... Stalks, 75^ per acre . $1224.96 30.00 1254.96 949.91 a Total returns 31.374 23.7475 Gain 305.05 7.6265 The illustrations in this section are reprinted by permission from Farmers' Bulletin 511, U. S. Department of Agriculture. Written Work 1. Find the labor cost to be charged against the corn crop, in the production of which 136 man hours and 312 horse hours of labor were expended. The total number of hours of man labor for the year was 4825, and the annual cost was $868.50; total number of hours of horse labor, 4312 ; total cost of horse labor for the year, 1388.08. 2. Use the following facts to prepare a table similar to the model above : FARM RECORDS 475 Corn Crop on 20 Acres Yield : 10 bushels of seed corn worth |3.50 per bushel. Corn crop harvested, 67 bushels per acre, worth 54 cents per bushel. Stalks were estimated at a value of 60 cents per acre. Costs : 3^ bushels of seed at i4.50 per bushel. Fertilizer, $ 38.00. Taxes : The farm was worth $ 175.00 per acre, and was taxed on ^ the real value at a rate of $1.65. The farm contained 160 acres, and the taxes were prorated among the various fields in proportion to their acreage. Interest : 4 % on the value of the land. Expense: #31.25. Labor : 560 man hours at 19 cents. 1348 horse hours at 9 cents. APPENDIX DENOMINATE NUMBERS SURVEYORS' LONG MEASURE 7.92 inches = 1 link (Ik.) 25 links = 1 rod 4 rods, or 100 links = 1 chain (ch.) 80 chains = 1 mile SURVEYORS' SQUARE MEASURE 625 square links = 1 square rod 10 square rods = 1 square chain 16 square chains = 1 acre 640 acres = 1 square mile 36 square miles = 1 township The following units of measure are used by sailors : 6 feet = 1 fathom (Used for measuring depths 3,1 sea.) 120 fathoms = 1 cable length (Used for measuring depths at sea.) About 1.15 statute miles = 1 knot, or 1 nautical mile, or 6080.27 ft. CIRCULAR OR ANGULAR MEASURE 60 seconds (60") = 1 minute (') 60 minutes = 1 degree (1°) 90 degrees = 1 right angle 360 degrees = 1 circumference TROY WEIGHT 24 grains (gr.) = 1 pennyweight (pwt. ordwt.) 20 pennyweights = 1 ounce (oz.) 12 ounces = 1 pound (lb.) 477 478 APPENDIX APOTHECARIES' WEIGHT 20 grains (gr.) = 1 scruple (sc. or 3) 3 scruples = 1 dram (dr. or 3 ) 8 drams = 1 ounce (oz. or 3 ) 12 ounces = 1 pound (lb.) Apothecaries' weight is used by physicians and druggists. Troy weight is used in the measurement of precious metals. COMPARISON OF TROY AND AVOIRDUPOIS WEIGHTS 1 pound Troy • = 5760 grains 1 pound avoirdupois = 7000 grains 1 ounce Troy = 437^ grains 1 ounce avoirdupois = 480 grains The term carat has two meanings : In weighing precious stones, a carat usually means 3.2 Troy grains. In expressing the purity of gold, 24 carats means pure gold ; 18 carats means Jf pure gold, and ^^ alloy. PAPER MEASURE 24 sheets = 1 quire (qr.) 20 quires = 1 ream (rm.) Although a ream contains 480 sheets, 500 sheets are usually sold as a ream. STANDARD UNITS OF WEIGHT 1 barrel flour weighs 196 pounds 1 barrel salt weighs 280 pounds 1 barrel pork or beef weighs 200 pounds 1 keg of nails weighs 100 pounds STANDARD BUSHELS IN MANY STATES 1 bushel shelled corn weighs 56 pounds 1 bushel ear corn weighs 70 pounds 1 bushel wheat weighs 60 pounds 1 bushel barley weighs 48 pounds 1 bushel rye weighs 56 pounds 1 bushel oats weighs 32 pounds TABLE OF ABBREVIATIONS USED IN BUSINESS (The singular form is commonly used for both the singular and plural.) A. . . . acre ans. . . . answer acct.ora/c. account Apr. . . April agt. . . agent Aug. . . August amt. . . amount av. . . . average APPENDIX 479 TABLE OF ABBREVIATIONS USED IN BUSINESS — (con^nz^d) . bag; bags ea. . . . each . balance e.g. . . for example )rl. barrel e.o.e. . . errors and omissions ex- . bundle cepted . basket etc.. . . and so forth . bale ex. . . . example; express . bill of lading exch. . . exchange . bought exp. . . expense . bushel f. . . . franc . box far. . . . farthing . one hundred Feb. . . February . cord ; card fir. . . . firkins . centigram f.o.b. . . free on board . chain; chest frt. . . . freight . charge ft. . . . foot . carriage and insurance free gal. . . . gallon . check gi- • . . gill . centimeter gr. • . . grain . commercial gro. . . . gross . care of ^'^'g^ '0. . great gross . company ; county guar. . . guaranty; guarantee . collect on delivery hf. . . . half . collection hf. cl it. . half chest . commission hhd. . . hogshead . consignment hr. . . hour . creditor; credit; crate i.e. . . that is . case in. '. . . inch; inches . cask ins. . . insurance . cent; centime inst. . . instant; the present month . cubic foot int. . . . interest . cubic inch I.;h IV. . invoice . cubic yard inv't . . inventory . hundredweight Jan. . . January . pence kg. . .keg • day km. . . kilometer . December 1. . . link . department lb. . . pound . draft l.p. . . list price . discount ltd. . . limited . ditto (the same) M . . . one thousand . dozen; dozens m. . . . mill; meter . debit; debtor; doctor Mar. . . March . East mdse . . . merchandise 480 APPENDIX TABLE OF ABBREVIATIONS USED IN BUSINESS— (continmd) Messrs. . Messieurs i Gentlemen ; rec't . . receipt Sirs rm. . . . ream mi. . . . mile Rm.(orM.) Reich smark; Mark min. . minute s. . shilling; shillings mo. . . . month S. . . . south ; sales mortg. . . mortgage sec. . . second Mr. . . . Mister sec'y . secretary Mrs. . . Mistress Sept. . September N. . . North set. . . . settlement no. . . number ship. . . shipment Nov. . November shipt. . shipped Oct. . October sig. . . . signed; signature O.K. . all correct sq. ch. . . square chain oz. . . ounce sq. ft. . square foot p. . • page sq. mi. . square mile pay't . payment sq.rd. . square rod pc. . . . piece sq. yd. . square yard pd. . . . paid stk. . stock per . . by ; by the sund. . sundries per cent . per centum ; by the hun- . T. . . . ton dred tb. . . . tub pfd. . . preferred Tp. ; Twp. township; townships pk. . . peck; pecks tr.; trans. . transfer pkg. . . . package treas. . . treasurer; treasury pp. . . pages ult. . . last month pr. . . pair via . . . by way of prox. . - . the following month viz. . . namely; to wit pt. . . . pint vol. . . volume pwt. . . . pennyweight wk. . . week qr. . . . quire wt. . . weight; weigh qt. . . . quart yd. . . yard rd. . . . rod yr. . . year rec'd . . . received TABLE OF SYMBOLS a/c . I iccount c/o . care of a/s account sales ^ . . cent + . . addition V . . check mark ; correct ( ) . aggregation ° . . degree & . . and -f- . . division and so on $ . . dollar; dollars @ . . 5 it ; each ; to = . . € jqual; equals APPENDIX TABLE OF SYMBOLS - — (continued) foot; feet; minutes o/d . on demand fourths (written as exponents, fo , per cent thus, 31 = 31) £ . . pounds sterling greater than : . ratio hundred •.• . . since inch; inches; seconds — . . subtraction less than .-. . . therefore multiplication M . thousand if written before figures, means number; if written after figures, means pounds 481 INDEX Abbreviations, 94, 478. Acceptance, 300. Accounts, 245. cash, 245. personal, 245. receivable and payable, 247. Account sales, 452. Accuracy, 2, 12, 17, 26, 40. Accurate interest, 269. Acre, 94. Acute angle, 112. Adding machine, 47. Addition, 2. checking, 12. column, 4. dictation, 8. grouping, 5. horizontal, 8. of common fractions, 61, 69. of decimals, 74. of denominate numbers, 99. standards in, 8. Ad Valorem, 357, 359. Advertising, 327, 329. Agent, 307, 339. Aliquot parts, 85. division by, 86. multiplication by, 85. Altitude, 114. Amount, 257. Angle, 112. Apothecaries' Weight, 477. Appendix, 476. Approximate results, 80. Arc, 114. Are, 106. Area, 114. of circle, 117. of cylinder, 132. of parallelogram, 115. of rectangle, 114. of sphere, 133. of triangle, 115. Assessed value, 346. Assessments, 385. Assessor, 346. Average, 48. per cent of, 172. Avoirdupois weight, 95, 477. Bank, discount, 291. savings, 282. Bank drafts, 217. Bankers' bills, 236. Bankruptcy, 378. Base, 114. Base for percentage, 154, 162. Bill of exchange, 236. Bills, collecting, 225. Blank form, ruling, 9. Blank indorsements, 209. Board foot, 135. Board measure, 135. Bonds, 394. Broker, 388. Bushel, 133, 477. Business terms, 478. Buying and seUing, 176. Buying expenses, 256, 398. Buying stock, 388. Canceling policies, 342. Cancellation, 56. Carpeting, 129. Cash book, 464. Cash discount, 183. Casting out nines, 12, 26. Certificate of stock, 383. Certified check, 216. Change, 206. Check, 207, 241. Checkbook, 210. Checking results, 12, 17, 26, 40, 329. Cu-cle, 113. Circle graph, 144. 483 484 INDEX Circular measure, 476. Circumference, 116. Classifications, 317, 320. Clearing house, 212. Collecting biUs, 225. Column addition, 6. Commercial bills, 237. Commercial discount, 183. Commercial drafts, 227. Commission, 307, 452. Common denominator, 61. Common divisor, 57. Common fraction, 59, 79. Common stock, 386. Complement, 20. Compound interest, 279. Compound interest table, 280. Computing machines, 47. Consignments, 452. Contract purchases, 288. Cord, 132. Corporations, 354, 381. Cost book, 416. Costs, factory, 421. Courtis standards, 8. Credit, letters of, 241. Credit memorandum, 177. Cubic measure, 95. Customs duties, 357. CyUnder, 132. Day rate, 303. Decimals, 73. addition of, 74. division of, 77. multiplication of, 76. reading of, 73. reduction of, 79. subtraction of, 75. writing of, 73. Decrease, per cent of, 168. Denominate numbers, 94, 476. addition of, 99. division of, 101. multiplication of, 101. reduction of, 97, 98. subtraction of, 100. Denominator, 59, 61. Departments, profitable, 411. Deposit, 207. Deposit slip, 207. Depositors' ledger, 211. Depreciation, 323. Diagonal, 113. Diameter, 114. Dictation, 8. Differential rate, 305. Discount, 183, 291. bank, 291. cash, 183. fluctuation, 191. period, 293, 296. quantity, 190. series, 189, 192. trade, 186. Discounting paper, 291. Dividends, 384, 461. Divisibility, tests of, 55. Division, 39. aliquot parts, 86, 91. checking, 40. long, 40. of decimals, 77. of denominate numbers, 101. Division of fractions, 66. Divisor, 57. Documentary bill, 238. Domestic mail, 311. Dozen, 96. Drafts, 217, 227. commercial, 227. Drawee, 208. Drawer, 208, 227. Drawings, 137. Drawing to scale, 138. Drill table, 2, 16, 24, 43. Dry measure, 95. Duties, ad valorem, 357, 359. specific, 357, 359. Efficient management, 403. Eleven, multiplication by, 32. Endorsement {see Indorsement). English money, 96. Equilateral, 113. Exchange, 215, 235, 239, 240. Expenses, buying, 256. selling, 398. Express money order, 222. Express rates, 320. INDEX 485 Factoring, 56. Factors and multiples, 55. Factory costs, 421. Farm lands, 119, 122. Farm records, 464. Fathom, 476. Fees, 221. Finding the percentage, 155. Firm, 368. Floor plan, 137. Fluctuation discounts, 191. Foot, abbreviation for, 94. Foreign coins, 96, 97, 233, 234. Foreign exchange, 235. Foreign postage, 315. Fractions, 59. addition of, 61, 69. decimal, 73. division, 66. improper, 59, 60. lowest terms, 59. multipHcation of, 65. proper, 59. reduction of, 59, 60, 79. subtraction of, 63, 70. terms, 59. Franc, 97. Freight rates, 316. French money, 97. Fundamental processes, 2. German money, 97. Gothic pitch, 128. Gram, 103. Graphic representations, 137. Graphs, kinds of, 137. Greatest common divisor, 57. Grocery orders, 179. Gross, 96. Gross sales, 407. Gross trading profit, 255. Grouping, in addition, 5. Hand, 94. Horizontal addition, 8. Hour rate, 303. Hypotenuse, 113, 125. Improper fractions, 59, 60. Inch, abbreviation for, 94. Income tax, 351. Increase, per cent of, 166. Indorsement, 208, 209. Insolvency, 362, 378. Installment payments, 288. Insurance, 333. fire, 333. life, 458. of parcels, 313. Interchanging principal and 262. Interest, 257. accurate, 269. compound, 279. on savings accounts, 283. periodic, 272. simple, 257. six per cent, 258. tables, 280. terms, 257. Inventory, 249, 252. Invoice, 176. Isosceles, 113. Joint and several note, 258. Judgment note, 258. Key, 201, 204. Knot, 94, 476. Land measure, 94. Lapses, 462. Least common multiple, 57. Letters of credit, 241. Liabilities, 362. Life insurance, 458. Linear measure, 94. Link, 476. List price, 183. Liter, 103. Long division, 40. Long measure, 94. Long ton, 95. Losses, settlement of, 340. Lowest terms, 59. Machine rate method, 430. Magazine, 328. Mark, 97. Marking cost, 398. Marking goods, 201. time, 486 INDEX Maturity, 291, 294, 394. of drafts, 230. of negotiable paper, 291, 294. Maximum, per cent of, 171. Measures, 94. apothecaries', 478. avoirdupois, 95. capacity, 95. comparison of, 109. cord, 96. counting, 96. cubic, 95. dry, 95. linear, 94. liquid, 95. long, 94. money, 96. square, 94. time, 96. troy, 476, 477. weight, 95. Merchants' rule, 276. Meter, 103. Metric system, 103. Mixed numbers, 59, 60, 63, 64, 71. Money, 96, 233. English, 96. French, 97. German, 97. United States, 96. Money order, 221, 235. express, 222. post office, 221. telegraph, 223. Multiple, 57. Multiplicand, 89. Multiplication, 24. by aliquot parts, 85, 88. checking, 26. common fractions, 65. decimals, 76. denominate numbers, 101. short methods, 29. Multiplier, 89. Net profit, 255, 398. Newspapers, 327. Nines, casting out, 12, 26. Normal tax, 351. Notes, 257. discounting, 291. payable, 363. receivable, 363. Numbers, denominate, 94. prime, 55. Numerator, 59. Obtuse angle, 112. Order, 221. express, 222. postal, 221, 235.; telegraph, 223. Overhead expenses, 411, 421. Painting, 129. Papering, 129. Paper measure, 477. Parallelogram, 113. Parcel post, 312. Partial payments, 274. Partnership, 368. Party drafts, 227. Payee, 227. Paying for goods, 206. Pay roll slips, 309. Pence, 96. Per cent, of average, 172. of decrease, 168. of increase, 167. of maximum, 171. Percentage, 152. to find base, 162. to find percentage, 155. to find rate, 158. Perch, 95. Perimeter, 113. Period, of discount, 291, 293, 296. Periodic interest, 272. Periodic inventory, 249. Perpendicular, 112. Perpetual inventory, 252. Personal accounts, 245. Personal property, 346. Piecework, 304. Pitch of roof, 128. Plastering, 129. Policy, 333, 342, 458. Postage, domestic, 311. foreign, 315. INDEX 487 Postal money order, 235. Postal savings banks, 286. Preferred stock, 386. Prefixes, metric system, 103, 104. Premium, 335, 385. Price, list, 183. Prime factor, 55. Prime number, 55. Principal, 257, 271, 307. Prism, 130. Proceeds of note, 291. Profitable departments, 411. Profit, gross trading, 255. Profit, net, 255. Promissory note, 257. Proper fraction, 59. Property insurance, 333. Property tax, 345. Proprietorship, individual, 362. Prorating expenses, 411, 425. Purchases book, 196. Quadrilateral, 113. Qualified indorsement, 209. Quantity discounts, 190. Quotation, rates of exchange, 240. Quotient, 41. Radius, 114. Rate, 154, 158. Rate, day or hour, 303. Rate, differential, 305. Rate of discount, 183. Rate of exchange, 239. Rate of interest, 271. Rates, express, 320. Rates, freight, 316. Rates of insurance, 335, 459. Rates, parcel post, 314. postage, 221. Rate, tax, 346. Reading of decimals, 73. Records, farm, 464. Rectangle, 113. Rectilinear figures, 112. Reduction, 59, 60, 62, 97, 98. Registry, 313. Repeater, 201. Resources, statement of, 362. Right angle, 112, 125. Right triangle, 125. Roofing, 127. Sales book, 197. Sales manager, 439. Sales, recording, 438. Sales, sheet, 438. Salvage, 340. Savings accounts, 282. Savings banks, 282, 286. Scale, determining, 141. drawing to, 138. Scalene, 113. SeUing, 176. SeUing expenses, 398. Series, discount, 189, 192. Sharing profits, 371. Shilling, 96. Short division, 39. Short methods, 29, 69, 85. Sight draft, 227. Simple interest, 257. Six per cent method, 258. Sixty day method, 258. SoHds, 130. Specific, 357, 359. Speed tests, 2, 16, 24, 43. Square, 94, 113. Square measure, 94. Square root, 122. Standard bushels, 477. State taxes, 345. Statistics, how to enter, 9. Stock record, 252. Stocks, 381, 386. Subtraction, 16. checking, 17. complement method, 19. of common fractions, 63, 70. of decimals, 75. of denominate numbers, 100. Subtrahend, 17. Surface, 112. Surface measure, 94. Surplus, 384. Surveyors' measure, 476. Symbols in business, 479, 480. Tables, abbreviations in business, 478. aliquot parts, 88. 488 INDEX Tables, apothecaries' weight, 478. avoirdupois weight, 95. compound interest, 280. counting, 96. cubic measure, 95. English money, 96. express, 321. French money, 97. German money, 97. interest, 280. linear measure, 94, liquid measure, 95. parcel post, 314. symbols, 480. troy weight, 476, 477. Tariff, freight, 318. Tax, income, 351. Taxation, 345, 348. Telegraph money orders, 223. Term of discount, 183. Terms of fractions, 59. Terms of percentage, 154. Tests of divisibility, 55. Time, 96. draft, 227. Trade discount, 186. Trade profit, 255. Travelers' checks, 241. Triangle, 113. Troy weight, 476, 477. Turnovers, 408. Two party draft, 227. Underwriter, 333. United States money, 96. United States rule, 274. Unit fractions, 69. Units of measure, 94. Value, of foreign coins, 96, 97. Value, of note, 291. Vertex, 112. Volume, 95. of cylinder, 132. of prism, 131. of sphere, 133. Weight, 476, 477. apothecaries', 477. avoirdupois, 95. comparison of, 109. miscellaneous, 477. troy, 476, 477. Withdrawals, 207. Wood measure, 96. Writing decimals, 73. Zones, parcel post, 312. ^'B 3091 f 402220 UNIVERSITY OF CALIFORNIA UBRARY