EMERSON’S SECOND PART. 
 
 THE 
 
 NORTH AMERICAN 
 
 PARITHMETIC. 
 
 PART SECOND, 
 
 UNITING 
 
 ORAL AND WRITTEN EXERCISES. 
 
 HUNDRED 
 
 3 
 *O8 60008 
 
 - HALLOWELL, 
 GLAZIER, MASTERS, & CO. 
 
 See 
 
The person charging this material is re- 
 sponsible for its return to the library from 
 which it was withdrawn on or before the 
 Latest Date stamped below. 
 
 Theft, mutilation, and underlining of books 
 are reasons for disciplinary action and may 
 result in dismissal from the University. 
 
 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN 
 
 L161— 0-1096 
 
PREFACE. 
 
 Tus book is intended for the use of scholars who have 
 been taught in ‘Part First,’ or by some other means 
 have learned to add, subtract, and multiply numbers as 
 high as 10, mentally. 
 
 The whole Course of, Exercises, of which this is the Sec- 
 ond Part, has been divided into three parts, more for the 
 _ sake of economy and convenience, than on account of any 
 natural division of the subject. The work is not intended 
 to be a record of the science,—such as might, befit the pages 
 of an encyclopedia,—but, a system of mduction, through 
 which the scholar may be led to the discovery of arithmet- 
 ical truth, and the proper application of arithmetical ope- 
 rations. Rules, and the technical language necessary to 
 their composition, are avoided in the early part of the 
 course—they are not introduced until the learner is sup- 
 posed prepared, by intellectual improvement trom previous 
 Jessons, to meet them understandingly. 
 
 In the arrangement of the exercises in this volume, I 
 
 have been governed by the natural order of the science; 
 _ delieving, that any deviation fom thst order, witn-o-view 
 ‘of rendering the work more immediately practical, would 
 render it in reality less practical, as it would necessarily lead 
 the scholar into a habit of performing operations, without 
 comprehending the principles which justify them. The 
 first six chapters consist of oral exercises, and the last six 
 of correspondent written exercises, The work may there- 
 fore be viewed as two entire systems of arithmetic— Oral 
 and Written. ) 
 
 Although Part Second does not complete the series of 
 books, entitled ‘The North American Arithmetic,’ still it 
 
 contains the essential principles, and the common applica- 
 tion of the science. Scholars, therefore, who shall be 
 properly conducted through this volume, will have acquir- 
 ed a knowledge of Arithmetic, adequate to all the pur- 
 poses of common business. Part Third is designed for 
 those, whose continuance at school shall afford oppor- 
 tunity for prosecuting a more extended course of study. 
 
a 
 
 we ; ~— 
 
 ’ ) % 
 y) " ps 
 4 (- PREFAGE. e. 
 
 The mode of teaching arithmetic, and the text-books, 
 used for the purpose, in a great portion of our country, 
 are radically defective. Much of arithmetic is practised 
 at school, but little is learned. The scholar is put to 
 ciphering without adequate mental preparation, and is re- 
 ferred to the direction of rules, whose phraseology and 
 principles are to a learner equally obscure. By a tedious 
 course of practice, perhaps he acquires a certain mechan- 
 ical dexterity in performing operations; but no sooner does 
 he enter upon the business of life, than he abandons the 
 rules of his book, and, in his own way, learns so much of 
 arithmetic as his occupation requires. 
 
 “Whether the following treatise is calculated to afford 
 any remedy for the defects I have alluded to, others will 
 decide. I shall spare myself the task of a prefatory detail 
 of what ‘‘the author conceives” to be its advantages, and 
 will only add, that the design and execution of the work, 
 have cost me much time and labor. 
 
 ae ate : ae I’, Emerson. 
 
 Boston, January, 1832. 
 
 NOTE TO TEACHERS. 
 
 It will be most advantageous for young scholars, to go through with all the 
 Oral Arithmetic before they enter upon the Written Arithmetic. Older scholars, 
 however, after performing the exercises in the first chapter of Oral Arithmetic, 
 may. pass immediately to the exercises in the first chapter of Written Arithme- 
 tic; and after concluding this chapter, mov tole mm tha two second chapters 
 
 i PMs Stn teh achall Cage ta ; 
 in the same order; and thus proceed through the book. : 
 
 Much time has been wasted in some of our schools, by the practice of teach- 
 ing individually, instead of teaching ia classes. If this practice has been 
 owing in any degree to the arrangement of text-books, it is hoped the present 
 arrangement will afford aremedy. There can he no more objection to a distinct 
 classification of a school for the purpose of teaching arithmetic, than there is to 
 a like classification for the purpose of teaching orthography: and the advanta- 
 ges of class-instruction in the former branch, are as great as those in the latter. 
 
 The examples contained in the first six chapters, do not require the use of the 
 slate. The answers, with the process of obtaining them, and the reasons which 
 justify the process, are to be given orally. For example, the following question 
 may be supposed to give rise to the subjoined exercise. 
 
 Example. A trader purchased 9 barrels of flour, at 7 dollars a barrel, and 
 sold the whole for 68 dollars. What did he gain in the trade? Pupil. ¢ He 
 gained five dollars.’ Z'eacher. ‘How do youperceiveit? Pupil. ‘If one 
 barrel cost seven dollars, nine barrels must have cost nine times seven dollars, 
 which is sixty-three dollars. He must have gained the difference between 
 sixty-three dollars and sixty-eight dollars. 63 from 68 leaves 5. : 
 
 Learners should not be confined to any form of expression in solutions— 
 their reasoning should be their own. By a little practice, they will acquire 
 an astonishing acuteness of apprehension, and facility of expression. 
 
4 SNS 
 
 7 we 
 Eau 2, 4) yy LY APT 
 
 is 
 
 j G , 
 7, OF AD 
 
 ORAL ARITHMETIC. 
 
 CHAPTER I. 
 NUMERATION. 
 
 SEcTION l. 
 
 WHEN we have a large number of articles to count, such 
 as quills, nuts, cents, &c., we may, if we please, count 
 them by tens. Let us suppose we have a quantity of 
 cents before us, and proceed to count them as follows. 
 
 We first count out ten cents, and lay them in a pile. 
 We then count out ten more, and lay them in another pile; 
 then ten more for another pile; and thus we continue to 
 count out ten at a time, until we have counted ten piles. 
 We put these ten piles together, and they make a large 
 pile containing One Hundred cents. 
 
 Again we count outsten cents at a time, until we have 
 counted ten small piles, as before. We put these togeth- 
 er, and they make a large pile containing one hundred, 
 like the hundred we first “opuntéd: We have now count- 
 
 . ed two hundred cents, and they le in two large piles. 
 
 Having learned what is meant by two hundreds, we pro- 
 ceed to count out one hundred cents more; and after pla- 
 cing them by the side of the two hundreds, the three piles 
 
 semake three hundreds. Four lar ge piles will be four hun- 
 
 dreds; five piles will be five hundreds; six piles will be six 
 hundreds; seven piles will be seven hundreds; eight piles 
 will be eight hundreds; nine piles will be nine hundreds; 
 and when we have counted out ten of these piles, we put 
 the whole together. They make a pile still larger, and 
 the number of cents contained in it is One Thousand. - 
 
 A* 
 
f™} wht bus A eae ee 
 “ig ORAL ARITHMETIC. CHAP. L. 
 
 Examine the arrangement of dots enclosed in the 
 lines below, and find how many there are in each en-. 
 closure. Observe, that the figures standing over the 
 several enclosures, represent the number of dots con- 
 tained therein. 
 
 eeeeu 
 e@eeon 
 
 eeeea 
 eveea 
 
 @eeae6 
 esves eeace 
 
 4 
 @se0n8 | veees ¢ eue tt 
 eeaee eee00 hs 4 tay 
 
 Bpeeese eeens 
 eceese @eaaee eeecae 
 
 escoe Dpecee Cennd 
 seece seaee 20008 
 &@ seee08 pease sesee 
 oecee geeee sacag 
 
 sess Seeen Gages 
 @esae 6 eeeee @eee00 @asag 
 
 peges eooo0 eeese euese 
 @e0ooe eeses 4 @eece @eeaee 
 @eeen Seene eeeee 
 @eace geece saceea seese 86888 
 @acne Qovee eo08e seeee Seese Geese 
 aenne 4 eeece ansee .. Bsase maces 
 
 Example 1. Which of these numbers is the greatest, 
 One, or Ten, or One Hundred, or One Thousand 2. 
 2. How many ones are there in a ten? 
 
ene 
 
 eh, . ara, 
 Ted P 
 
 See. 2. -NUMERATION. apa 
 
 3. How many tens are there in a hundred? 
 
 4. How many hundreds are there in a thousand ? 
 
 5. Ten ones make what number? Ten tens make 
 what number? Ten hundreds make what number ? 
 
 6. What figures stand to represent the number ten? 
 
 7. What figures stand to represent one hundred ? 
 
 8. What figures stand to represent one. thousand ? 
 
 Section Y. 
 
 If one hundred scholars were in school, and one 
 scholar more should come in, the number of scholars 
 would then be one hundred and one; and would be ex- 
 pressed in figures thus;—101. Again, if you had one 
 hundred books, and you should buy two books more, 
 you would then have one hundred and two books, and 
 their number would be expressed in figures thus ;—102."° 
 
 In Part First, you learned to read figures expressing all 
 numbers, from One to One Hundred. You will now see, 
 in the following columns, how the figures stand to express 
 numbers, from One hundred, to Two hundred. 
 
 100 One hundred, 120 one hund. and twenty, 
 
 101 one hund. and one, 121 one hund. and twenty-one, 
 102 one hund. and two, 122 one hund. and twenty-two, 
 103 one hund. and three, 123 one hund.and twenty-three, 
 104 one hund. and four, 
 
 105 one hund. and five, 130 One hund. and thirty. - 
 
 106 one hund. and six, 
 
 107 one hund. and seven, 140 One hund. and forty. 
 108 one hund. and eight, 
 
 109 one hund. and nine, 150 One hund. and fifty. 
 110 one hund. and ten, Le 
 111. one bund, and eleven, 160 One hund. and sixty. 
 112 one hund. and twelve, e 
 113 one hund. and thirteen, | 1'70 One hund. and seventy, 
 114 one hund. and fourteen, 
 
 115 one hund. and fifteen, 180 One hund. and eighty. 
 116 one hund. and sixteen, 
 
 117 one hund. and seventeen, 190 One hund. and ninety. 
 118 one hund. and eighteen, 
 119 one hund, and nineteen, 200 Two hundred. 
 
F 
 
 8 ORAL ARITHMETIC. I, 
 
 Edward’s mother gave him one hundred walnuts, his 
 sister gave him sixty, and his brother gave him eight; 
 making together, one hundred and sixty-eight. Being 
 required to tell what figures would express the number of 
 his walnuts, Edward looked over the columns of figures 
 on the last page, and discovered, (as you may), that 1 
 means one hundred, whenever two figures are standing 
 at the right hand of it; and, that 6 means sixty, whenever 
 one figure is standing at the right hand of it. He there- 
 
 '. fore said, ‘‘1, 6, 8, are the figures.” 
 
 1. How many tens does the figure 6 represent, when 
 there is one figure standing at the right of it? 
 
 2. Whatare 6 tens usually called, in reading numbers ? 
 
 3. How many tens does the figure 4 represent, when 
 there is one other figure standing at the right of it? 
 
 4. What are 4 tens usually called, in reading numbers ? 
 
 5. What number does the figure 1 represent, when 
 there is one other figure standing at the right of it? 
 
 6. What number does the figure 1 represent, when 
 there are two other figures standing at the right of it ? 
 
 7. What are 1 hundred and 5 tens usually called? 
 
 8. What are 1 hundred and 9 tens usually called? 
 
 9. What are 1 hundred and 3 ones usually called ? 
 
 10. What are 1 hundred and 8 ones usually called ? 
 
 11. What are 8 tens and 2 ones usually called ? 
 
 12. What are 1 hundred, and 7, tens, and 5 ones usu 
 ally called, in reading numbers ? 
 
 Note to Teachers. Require the learners to read the numbers expressed in 
 the following columns, without recourse to the preceding columns. 
 
 109 172 104 168 113 
 127 wh 90 110 140 147 
 145 » 12] 132 122 169 
 163 143 155 195 183: 
 181 165 176 177 103 
 118 187 198 159 125 
 136 154 186 131 158 
 
 The comparisons on the next page will show you, 
 that all the hundreds are expressed in the same manner 
 that one hundred is expressed. 
 
— °C r adh 
 
 ty - ADDITION. rf) 
 
 100 One hundred. 133 One hund. & thirty-three. 
 200 Two hundred. ' 633 Six hund. & thirty-three. 
 106 One hund. & six. 149 One hund. & forty-nine. 
 306 Three hund. & six. 749 Seven hund. & forty-nine. 
 
 117 One hund. & seventeen. 154 One hund. & fifty-four. 
 417 Fourhund. & seventeen. 854 Hight hund. & fifty-four. 
 
 121 Onehund. & twenty-one. 199 One hund. & ninety-nine. 
 521 Five hund. & twenty-one. 999 Nine hund. & ninety-nine. 
 
 Note to Teachers. The learners may be required to read the several 
 numbers expressed in the following columns of figures. . 
 : 
 
 814 293 552 466 Sat * 
 372 947 444 664 767 
 528 ool 786 gnats 8 aa 579 
 451 619 3609 940 296 
 
 ~ CHAP. II. 
 
 ADDITION. 
 , Section 1. 
 J. The Humane Society gave Charles a premium of 
 ‘ shar Poets, ais 7 re , 4 2 : A 
 6 dollars, 1. °“Ving a poy irom urownui., and a lady 
 
 gave him 5 dollars more. How much did he receive? 
 
 Solution. 6 dollars and 5 dollars are 11 dollars. 
 9. A merchant sold 7 barrels of flour to one man, and 
 5 to another. How many barrels did he sell? 
 
 3. If you should pay 9 cents for a book, and 4 cents 
 for a pencil, how much would you pay for both: 
 
 4. A farmer paid 10 dollars for a plough, and 9 dol- 
 lars for a harrow. How much did he pay for both? 
 5. A baker bought 8 barrels of flour of a merchant, 
 and 3 more of a miller. How many did he buy ? 
 
 6: Thomas gave 9 cents for a purse, and had 7 cents 
 left to put in it. How many cents had he at first ? 
 
 ~. A farmer sold 5 cows, and then had 6 cows left. 
 How many cows had he at first? 
 
 % 
 
10 ORAL ARITHMETIC. Rete ‘ 
 
 8. If you should receive 9 dollars from one man, and 
 5 from another, how many dollars would you receive? 
 
 Section Y. 
 
 1. Two little boys went into a shop to be weighed. 
 The oldest of them weighed 40 pounds, and the youngest, 
 30 pounds. How many pounds would they weigh both 
 together ? | 
 
 Solution. 40 is the same as 4 fens, and 30 is the same 
 as 3 tens. Then 4 tens and 3 tens are 7 tens;—and 7 
 tens are the same as 70. 3 
 
 2. There were 40 oranges in one basket, and 20 in 
 another. How many were there in both baskets? 
 
 3. What is the whole number of scholars in a school, 
 that consists of 20 boys and 30 girls? 
 
 4. A baker paid 50 dollars for a horse, and 30 dollars 
 for acart. How many dollars.did he pay for both? 
 
 5. If I read 50 pages of history, and 40 pages of 
 poetry, how many pages do I read of both? 
 
 6. If a man has lived 20 years in the city, and 10 
 years in the country, how old must he be? 
 
 7. James paid 60 cents. for his Reader, and 40 for 
 his Arithmetic. How many cents did they both cost? 
 
 8. Suppose you should buy 60 quills at one store, 
 and 50 at another; how many quills would you have? 
 
 Solution. 60 is 6 tens, and 50is5tens. 6 tens and 
 5 tens are 11 tens. 11 tens are 1 hundred and 1 ten;— . 
 that is, 110. 
 
 9. Suppose 70 books are upon my table, and I put 
 on 50 more; how many will then be on the table? 
 
 10. If a gold watch cost 90 dollars, and the chain 40 
 dollars; how many dollars do they both cost? 
 
 11. In a certain orchard, there are 80 pear trees and 
 60 peach trees. How many trees in the orchard ? 
 
 12. If 90 persons should enter a hall at one door, and 
 60 at another; how many would there be in the hall? 
 
 13. If I purchase 80 barrels of flour from one man, 
 and 80 from another; how many barrels shall I have? 
 
 14. A miller had 90 bags of wheat on hand, and res 
 ceived 80 bags more. How many bags had he then ? 
 
— "7 
 
 . 
 
 De I es bine 
 2. nit ADDITION. 11 
 
 (15. If a horse cost 90 dollars, and a gig 90 dollars, 
 how much do the horse and gig both cost? 
 
 16. How many pounds of honey in two jars;—there 
 being 70 pounds in one jar, and 60 in the other? 
 
 Section 3. 
 
 1. A gardener called three boys to the garden gate to 
 give them some grapes. To the first boy he gave 40 
 grapes, and to the second 40; but the third boy attempted 
 to push the others aside, and the gardener seeing it, gave 
 him only 6. How many did he give them all? 
 
 Solution. 40 grapes and 40 grapes are 80 grapes. 
 Then 80 grapes and 6 grapes are 86 grapes. 
 
 2. John, James, and Henry went a fishing. John 
 caught 30 fishes, and James caught 40; but Henry caught 
 only 9. How many did they all catch? | 
 
 3. How many are 30 and 40 and 9? 
 
 4. A traveller gave 70 dollars for his horse, 20 dollars 
 for his saddle, and 5 dollars for his bridle. How many 
 dollars did he give for the whole ? | 
 
 5. How many are 70 and 20 and 5? 
 
 6. A farmer kept 50 sheep in one pasture, 30 in 
 
 toy 
 
 another, and 7 in another. If he had kept them all in one 
 pasture, how many would there have been together ? 
 
 7. How many are 50 and 30 and 7? 
 
 8. How many cents will it take to buy a seal, a 
 blank-book, and a pencil; supposing the seal to cost 60 
 cents, the blank-book 20 cents, and the pencil 8 cents? 
 
 9. How many are 60 and 20 and 8? 
 
 10. An escort went out to meet Gen. Layfayette: 40 
 men rode on horseback, 30 rode in gigs, and 10 rode in 
 
 ~ coaches. Of how many did the escort consist? 
 
 11. How many are 40 and 30 and 10? 
 12. How many are 40 and 30 and 3? 
 13. How many are 60 and 20 and 5? 
 14. How many are 30 and 30 and 7? 
 15. How many are 50 and 40 and 9? 
 16. How many are 50 and 50 and 8? 
 17. How many are 60 and 40 and 4? 
 18. How many are 70 and 30 and 6? 
 
12 ORAL ARITHMETIC. IL. 
 
 Srotron 4, 
 
 yy 
 1. A certain class consists of 11 studious boys, and 2 # 
 idle boys. How many arethere inthe class? 
 2. Howmanyarelland2? 11and3? 1land4? 11 and 
 5? l1and6? iland7? 1land8? 1land9? 11 and10? 
 8, Alfred paid 11 cents for a pen-knife, and 10 cents 
 me a writing-book. How much did he pay for both ? 
 
 . If you should pay 12' cents for a slate, and 3 cents 
 for an orange, how many cents would they both cost? 
 5. Howmanyare12and2? 12and3? 12and4? 12 and 
 5? 12and6? 12and7? 12and8? 12and9? 12and10?' 
 6. If 12 boys play at foot-ball on one side, and 8 boys 
 on the other, how many are there in the play? 
 
 7. A certain class consisted of 13 small boys, and 4 
 large boys. How many were there in the class? 
 
 ~ 8. Howmanyarel3and2? 13and3? 13and4? 13and 
 
 5? 13and6? 13and7? 13and8? 13and9? 13and10? © 
 9. A number of sheep are in a fold;—13 are lying 
 
 down, and 6 are standing up. How many are there? 
 
 10. There were 14 hats hanging up,” 15 more lying 
 down. How many hats were there in’ 
 
 11. Howmany are 14and2? 14and3? aan} 14and 
 5? 14and6? 14and7? 14and8? 14and9? 14and10? 
 
 12: If you give 14 cents for a bow, and 4 cenis ior 
 aty arrow, how much do the bow aiid arrow cost? 
 
 13. A wagoner drove 15 miles in the forenoon, and 6 
 in the afternoon. How many miles in the day? 
 re How many are 15and2? 15and3? Sand? 15and 
 5? 15and6? I5and7? I5and8? 15and9? 15and102° 
 15. If a cow be worth 15 dollars, and a sheep»2 dol- 
 lars, what are the cow and sheep together worth? | 
 
 16. David wrote 16 lines in the forenoon, and 7 in “the ey 
 afternoon. How many lines did he write in the day? 
 17. Howmanyare 16and2? 16and3?\ 16and4? 16and 
 ' 5? I6and6? 16and7? 16and8? 16and9? 16and10? 
 
 18. A trooper gave 16 dollars for his saddle, and’9 
 dollars for his bridle!’ How much did he pay for both? 
 
4, 5. ADDITION. 13 
 
 19. A man lost 8 dollars, and still had 17 dollars left. 
 How many dollars had he before he lost any? 
 
 20. Howmanyarel7and2? 17and3? 17and4? 17and 
 5? 1W7and6? 1l7and7? l7and8? 17and9? 17and10? 
 
 21. If a time-piece cost 17 dollars and a looking-glass 
 7 dollars, how. many dollars do they both cost ? 
 
 22. While 18 doves were upon a roof, 9 doves more lit 
 among them. How many were then upon the roof? 
 
 23. Howmanyare 18and2? [8and3? 18and4? 18and 
 5? 18and6? 1Sand7? 18and8? 1S8and9? 1Sand10? 
 
 24. A man rolled 18 barrels of flour out of a mill and 
 a boy rolled out 5 more. How many did both roll out ? 
 
 25. A young man began studying law at the age of 19 
 years, and studied 3 years. At what age did he finish ? 
 
 26. Howmanyare19and2? 19and3? 19and4? 19and 
 5? 19and6? 19and7? 19and8? 19and9? 19and10? 
 
 27. A farmer mixed 19 bushels of oats with 10 of corn. 
 How many bushels were there of the mixture ? 
 
 Note to Teachers. The follewing combinations may be embraced in 
 separate questions by. she teacher ; thus,— How many are 19 and 4? 
 
 19 and 4 Hyg lt and 2 19 and 9 15 and 9 
 16and3 19 and 6 16 and 8 13 and 7 
 18 and 5 16 and 6 13.and 5 .%, 4.and 4 
 12 and 2 15 and 4 18 and 8 14 and 8 
 hiegi1'7 and 7 18 and 2 14 and 6 12 and 5 
 19 and7 17 and 6 12 and 9. 14 and 7 
 “15:and. 5 19 and 3 13 and 3 17 and 8 
 19 and 8 16 and 5 12 and 7 12 and 6 
 17 and 9. 15 and 8 16 and 6 16 and 9 
 12.and 8. 16 and 4 17 and 5 13 and 8 
 
 ' Section 5. 
 
 1. Charles had 25 books in his library, and his father 
 gave him 8 more. How many had he then? 
 Suggestion. You will easily perceive how many 25 
 and 8 are, since you already know that 5 and 8 are 13, 
 and that 15 and 8 are 23. 
 B 
 
14 ORAL ARITHMETIC. Il. 
 
 2. A father said to his son, ‘ You are 7 years old, and I 
 am 47—How old shall we each of us become, in 9 years 
 from this time?’ What should have been the answer? | 
 
 3. James bought a small book for 6 cents, and David 
 bought a large book for 56 cents. For how many cents 
 must each boy sell his book, in order to get 4 cents more 
 than he gave? 
 
 4. Julia was returning from a walk in the garden, with 
 8 red roses, and 68 white roses. She met her brother, 
 who gave her 6 more red roses, and 6 white ones. How 
 many of each kind had she then? 
 
 5. William has 9 cents, and John has 79 cents. If 
 - they should each of them get 10 cents more, how many 
 would each boy then have? 
 
 Note to Teachers. The following combinations may be embraced in ques- 
 tions by the teacher; thus,—How many are 3 and 9? 
 
 3 and 9 54 and 6 41 and10 38 and 8 
 13 and 9 67 and 8 53 and 9 Aland 7 
 
 7 and 6 72 and 9 65 and 6 53 and 9 
 27 and 6 8) /and.7 77 and. 65 and 2 - 
 
 8 and 8 90 and 5 89 and 5 77 and 10 © 
 38 and 8 18and4  . 92and 7 89 and 6 
 
 1 and 7 26 and 7 14 and 10 92 and 4 
 41 and 7 39 and 2 26 and 7 14 and 8 
 
 Section 6. 
 
 1. A trader paid 29 dollars for a chest of tea, 4 dollars 
 for a box of lemons, and ‘5 dollars for a box of raisins. 
 What did he pay for the whole? 
 
 2. How many are 29 and 4 and 5? 
 
 3. If I pay 38 dollars to one man, 6 to another, and 3 
 to another, how many dollars do I pay out ? 
 
 4. How many are 38 and 6 and 3? 
 
 5. Stephen had 47 books; he bought 5 more, and then 
 his uncle gave him 6 more. How many had he at last? 
 
 6. How many are 47 and 5 and 6? 
 
 7. ‘On a'certain day, a passenger travelled 56 miles in 
 the stage, 4 miles in a wagon, and 7 miles‘on foot. ‘How 
 many miles did he travel on that day? 7 
 
 8. How many are 56 and 4 and 7? 
 
6. 7. ADDITION. 15 
 
 9. If ayokeof oxen be worth 65 dollars, a sheep 8 dol- 
 lars, and a lamb 2 dollars, how much are they all worth? 
 
 10. How many are 65 ‘and 8 and 2? 
 
 11. Aschool boy paid 74 cents for a reading book, 
 7 cents for a writing book, and 9 cents for some quills. 
 How many cents did he pay for the whole ? 
 
 12. How many are 74 and 7 and 9? 
 
 13. A meeting was held in a country village, to which 
 83 persons walked, 9 rode on horseback, and 8 rode in 
 gigs. How many ‘attended the meeting ? 
 
 14. How many are 83 and 9 and 8? 
 
 15. A market man received 92 dollars for butter, 9 
 dollars for cheese, and 5 dollars for poultry. How many 
 dollars did he receive for the whole ? 
 
 16. How many are 92 and 9 and 5? 
 
 Section 7. 
 
 1. The captain of a steam-boat received the following 
 passengers;— 45 gentlemen, 20 ladies, and 8 children. 
 How many es ery there in all? 
 
 Solution. 45 and 20 are 65; then 65 and 8 are 73. 
 tina 73 passengers. 
 
 . If a quire of paper cost 23 cents, a book 30 cents, 
 ae a pencil 9 cents, what do they all cost ? 
 
 3. How many are 23 and 30 and 9? 
 
 4. Alfred paid 25 cents for his penknife, and 20 cents 
 for his wallet, and then had 5 cents left. How many 
 cents had he at first ? 
 
 5. How many are 25 and 20 and 5? 
 
 6. A lady gave 57 cents for a fan, 30 cents for a work 
 bag, and 4 cents for some needles. How many cents 
 did she lay out ? 
 
 7. How many are 57 and 30 and 4? 
 
 8. A fowler went out one morning to shoot birds;— 
 he shot 46 plovers, 50 snipes, and6 quails. How many 
 birds did he shoot ? 
 
 9. How many are 46 and 50 and 6? 
 
 10. If a cart cost 26 dollars, a plough 10 dollars, and 
 a chain 5 dollars, what do they all cost? 
 
 11. How many-are 26 and 10 and 5? 
 
16 ORAL ARITHMETIC. Il. 
 
 12. A farmer sold a horse for 75 dollars, a cow for 30 
 dollars, and a sheep for 5 dollars. How many dollars did 
 he get for the whole ? 
 
 13. How many are 75 and 30 and 5? 
 
 14. William gave 64 cents for a handkerchief and 40 
 cents for a pair of gloves, and then had 9 cents left. 
 How many cents had he at first ? 
 
 15. How many are 64 and 40 and 9? 
 
 -16. How many are 5 and 9 and 2 and 8 and 6 and 4? 
 17. How many are 8 and 3 and 7 and 6 and 5 and 3? 
 18. How many are 6 and 8 and 4 and 9 and 7 and 5? 
 19. How many are 9 and 7 and 2 and 8 and 3 and 6? 
 20. How many are 17 and 5 and 0 and 9 and 6 and 8? 
 21. How many are 23 and 8 and 1 and 0 and 9 and 7? 
 22. How many are 48 and 6 and 7 and 4 and 0 and 2? 
 23. How many are’71 and 3 and 9 and 0 and 6 and 9? 
 
 CHAP. III. 
 SUBTRACTION. 
 
 Secrion 1. 
 
 1. There were 9 passengers in a stage; 3 of them 
 got out to walk: how many remained in the stage? 
 
 Solution. 3 from 9 leaves 6. Answer. 6 passengers. 
 
 2. A boy having 10 cents, paid 6 cents for a kite, and 
 lost the remainder. How much did he lose? 
 
 3. Ann has 12 books andJuliahas7. _Howmany more 
 must Julia have, to make her number equal to Ann’s? 
 
 4. Andrew has 11 cents, and James has only 5 cents. 
 How many cents has Andrew more than James? 
 
 5. Stephen has 8 cents, and wishes to buy a knife worth 
 16 cents. How many more cents does-he want? 
 
 6. A lady went to buy goods, carrying 13 dollars; she 
 returned with 9 dollars. How much did she spend ? 
 
 .», 7, A merchant bought a box of goods for 10 dollars, 
 
 and sold it for 14 dollars. How much did he gain? 
 
1, 2. SUBTRACTION. 17 
 
 §. Jonathan is 7 years old, and his brother is 11 years 
 old. What is the difference in their ages? 
 
 9. Henry bought a book and a pencil for 19 cents: he 
 gave 10 cents for the book; what did the pencil cost ? 
 
 10. A man who owed a debt of 12 dollars, paid 5 dol- 
 lars of it. How many dollars remained unpaid? 
 
 11. John sold a knife for 18 cents, which was 9 cents 
 more than he gave for it. How much did he give for it ? 
 
 12. A farmer agreed to give 17 dollars for a cow: and 
 he paid 8 dollars down. How much did he still owe ? 
 
 Section 2. 
 
 1. Asloop of war went out with a crew of 70 men, and 
 fell into an engagement, in which 30 of her men were 
 killed. How many of the crew were still living? 
 
 Suggestion. Consider the numbers to be, 7 tens, and 
 3 tens;—you may then take 30 from 70 as easily as you 
 can take 3 from 7. : 
 
 2. A market woman had 60 oranges, and sold 20 of 
 them. How many had she remaining? 
 
 3. 20 from 60 leaves howmany? How many are 20and 40? 
 
 4. A certain school consists of 50 scholars, 30 of 
 whom are girls. How many boys are there ? 
 
 5. 30from 50leaveshow many? How many are 30 and 20? 
 
 6. A baker had 80 dollars to lay out for a horse and 
 cart. After having paid 50 dollars for a horse, how many 
 dollars had he left to purchase the cart? 
 
 7. 50from 80 leaves how many? How many are 50 and 30? 
 
 8. If your lesson for the whole day be 40 questions in 
 this book, and you answer 20 questions in the forenoon, 
 how many are there left for the afternoon ? 
 
 9. 20from 40 leaves how many? How many are 20 and 20? 
 
 10. I have read 40 pages, ina book which contains 90 
 
 ages. How many pages remain to be read? 
 
 11. 40 from 90leaveshowmany? Howmanyare 40 and 50? 
 
 12. James had 70 cents, and paid 40 of them for a 
 _school-book. How many cents had he left? 
 
 13. 40from70leaveshow many? Howmany are 40 and 30? 
 
 Be : 
 
18 ~~ ORAL ARITHMETIC. III. 
 
 Section 3. 
 
 1. A man received 12 dollars for work, and paid 2 
 dollars for his board. How many dollars did he save ? 
 2. How many will remain, if we take 2 from 12? 2 
 from 13? 2from14? 2from15? 2from16? 2 from 
 17? 2from18? 2from19? 2 from 20? | 
 
 3. Astable keeper owned 14 fine horses. After sell- 
 ing off 3 of them, how many had he remaining ? 
 
 4. How many will remain, if we take 3 from 13? 3 
 from 14? 3from15? 3from16? 3from17? 3 from 
 18? 3from 19? 3from 20? 3 from 21? 
 
 5. 16 boys were dismissed, but 4 of them were called 
 back for being noisy. How many were allowed to go? 
 
 6. How many will remain, if we take 4 from 14? 4 
 from 15? 4from16? 4from17? 4from18? 4 from 
 19? 4 from 20? 4 from 21? 4 from 22? 
 
 7. Aman, who had 18 dollars, paid 5 dollars for a 
 pair of boots. How many dollars had he remaining ? 
 
 8. How many will remain, if we take 5 from 15? 5 
 from 16? 5from17? 5from18?. 5from19? 5 from 
 20? 5 from 21? 65 from 22°? 5 from 23? 
 
 9. If you had just 20 cents, and you should lose 6 
 cents, how many cents would you then have ? 
 
 10. How many will remain, if we take 6 from 16? 6 
 from17? 6from18? 6from19? 6from 20? 6 from 
 21? 6from 22? 6 from 23? 6 from 24? 
 
 11. A man who had 22 dollars on hand, lent 7 dollars 
 to his neighbour. How many dollars had he remaining ? 
 12. How many will remain, if we take 7 from 17? 7 
 ' from18? 7from 19? 7 from 20? 7 from21? 7 from 
 22° 7 from 23? 7 from 24? 7 from 25? 
 
 13. 24 peaches grew upon a young peach tree, and the 
 owner took off 8 of them. How many remained on? 
 14. How many will remain if we take 8 from 18? 8 
 
 ~ from 19? 8from20? 8Sfrom21? Sfrom 22? 8fror 
 
 23? 8 from 24? 8 from 25? 8 from 26? 
 
} —_* 
 
 Ss aL 
 
 15. Suppose you had 26 cents, and paid 9 of them 
 for a dozen of quills; how many cents have you left ? 
 
 16. How many will remain, if we take 9from 19? 9 
 from 20? 9from21? 9 from22? 9 from 23? 9 from 
 24? 9 from 25? 9 from 26? 9 from 27? 
 
 17. James received 28 cents, and Charles received 10 
 cents less than James. How many did Charles receive ? 
 18. How many will remain, if we take 10 from 20? 10 . 
  from21? 10from22? 10from23? 10from24? 10from 
 _ 25? 10.from 26? 10 from 27? 10 from 28? 
 
 CORRESPONDENT EXAMPLES. 19 
 
 Note to Teachers. The following combinations of numbers may be em- 
 braced in quesions by the teacher, thus,—2 from 17 leaves how many? 
 
 2 from 17 8 from 19 7 from 24 5 from 23 
 7 from 21 3 from 20 9 from 21 6 from 24 
 9 from 24 9 from 26 3 from 18 8 from 23 
 3 from 16 7 from 18 8 from 22 3 from 21 
 ~ 8 from. 26 2 from 15 6 from 17 9 from 27 
 6 from 19 6 from 22 5 from 18 7 from 25 
 5 from 22 5 from ¥9 4 from 16 2 from 20 
 4. from 20 4 from 15 2 from 19 4 from 22 
 10 from 25 10 from 27. 10 from 26 10 from 29 
 
 Section 4. 
 CORRESPONDENT EXAMPLES. 
 
 1. A farmer, who‘had 19 dollars on hand, received 5 
 dollars for a sheep. _How many dollars had he then? 
 
 2. A butcher, who had 24 dollars on hand, paid out 5 
 dollars for a sheep. How many dollars had he left ? 
 
 3. A jeweller gave 17 dollars for a silver watch, and 
 sold it for 6 dollars more than he gave for it. For how 
 many dollars did he sell it? 
 
 4. A young man gave 23 dollars for a watch, and was 
 
 obliged to sell it for 6 dollars less than he gave. For ._. 
 
 how much did he sell it? 
 
 5. It was 4 years ago, that Samuel left the academy, 
 and he was then 15 years old-. How oldishe now? 
 
 6. Sarah is 19 years old; her father died when she 
 was 15. How many years is it, since her father died? 
 
gc = tee eee mae 
 
 re re ae 
 
 20 ORAL ARITHMETIC. Til. 
 
 7. A farmer who had 26 sheep, purchased 8 more. 
 How many sheep had he then? 
 
 8. A farmer who had 34 sheep, sold 8 of his flock. 
 How many had he remaining ? 
 
 9. A merchant who had 9 dollars on hand, received 
 27 dollars more, for a quantity of goods. How many dol- 
 lars had he then? 
 
 10. A merchant who had 36 dollars in his pocket, paid 
 a small debt, and hee had 27 dollars left. How many 
 dollars did he pay ? 
 
 11. A wagon passed icine carrying 88 empty barrels 
 and 7 full ones. How many barrels in all ? 
 
 12. In a. store-room there were 45 barrels, only 7 of 
 which were filled. How many were empty? 
 
 13. Edward paid 46 cents for a book, and then had 9 
 cents left. How many cents had Edward before he 
 purchased the book ? 
 
 14. Joseph’s father gave him 55 cents, to buy a book, 
 but he obtained the book for 46 cents. How many cents 
 did Joseph save ? 
 
 15. How many are 57 and 5° Then if we take 5 
 from 62, how many remain? 
 
 16. How many are 64 and 6° Then if we take 6 
 from 70, how many remain? 
 
 17. How many are 79 and 8? ‘Then if we take 8 
 from 87, how many remain ? 
 
 18. How many are 86 and 6? Then if we take 6 
 from 92, how many remain? 
 
 “ih. How many are 48 and 9? Then if we take 9 
 from 57, how many remain? | 
 " 90. How many are 75 and 7? Then if we take 7 
 from 82, how many remain? 
 
 vA fiw many are 36 and 5 ?— how many are 5 and 
 36? Then 5 from 41 leaves how many ?— 36 from 41 
 
 nalentrs how many? 
 
 +22. How many are 43 and 9?—how many are 9 and 
 48} ? Then 9 from 52 leaves how many?— 43 from 52 
 “leaves how many ? 
 
4 
 \ 
 
 5, MISCELLANEOUS EXAMPLES, 21 
 
 23. How many are 54 and 6 ?—how many are 6 and 
 54°? Then 6 from 60 leaves how many ?— 54 from 60 
 leaves how many? 
 
 24. How many are 68 and 42—-how many are 4 and 
 68? Then 4 from 72 leaves how many?— 68 from 72 
 leaves how many? Ba 
 
 25. How many are 79 and 8?— how many are 8 and 
 79° Then 8 from 87 leaves how many?—79 from 87 
 leaves how many? 
 
 26. How many are 87 and 5’—how many are 5 and 
 87% Then 5 from 92 leaves how many?—87 from 92 
 leaves how many? 
 
 Section §. 
 MISCELLANEOUS EXAMPLES. 
 
 1. George and David went out to gather lilies; George 
 ot 56, and David 49. On the way home, George gave 
 avid 8... How many had each boy then? 
 
 Solution. At first, George had 56; he gave away 8; 
 8 from 56 leaves 48...... At first, David had 49; he’ re- 
 ceived 8 more; 49 and 8 are 57. . 
 
 2. A clerk went out to collect some money. He re- 
 ceived 60 dollars from one man, 9 dollars from another, 
 and 20 from another; and he paid a debt of 7 dollars. 
 How many dollars had he to bring in? 
 
 Solution. 60 and 9 are 69, and 20 are 89;—this is 
 the number of dollars he collected. He then paid 7 
 dollars. 7 from 89 leaves 82. 
 
 3. Harriet answered 23 questions in arithmetic, and 
 Mary answered 7 more than Harriet. How many ques- 
 tions did they both answer ? 
 
 4. Edward answered 36 questions in arithmetic, and 
 Stephen answered 6 less than Edward. How many 
 questions did they both answer ? 
 
 5. A blacksmith who had 100 dollars, Jaid his money 
 out as follows—For iron 66 dollars, for steel 30 dollars, 
 and the remainder for coal. How many dollars did he 
 pay for coal? 
 
Q2 ORAL ARITHMETIC, Il. 
 
 6. A carpenter paid 31 dollars for boards, 10 dollars 
 for shingles, 6 dollars for nails, and 5 dollars for screws. 
 How many dollars did he spend? 
 
 7. A trader gave 48 dollars for a chest of tea, and 3 
 dollars for getting it home. For how much must he sell 
 a tea, in order to gain 8 dollars ? 
 
 . If I have 70 dollars on hand, and pay out 4 dollars 
 wh one man, 20 to another, and 30 to another, how many 
 dollars shall I have remaining ? 
 
 9. A gentleman travelled 8 miles fone breakfast, 30 
 more before’ dinner, and 40 more after dinner. oer 
 many miles did he travel during the day ? 
 
 10. A merchant, who had 80 barrels of flour, sold to 
 one man 52 barrels, to another 6 barrels, and to another 
 5 barrels. How many barrels had he left ? 
 
 11. Oliver’s penknife is worth 33 cents, and Edwin’s 
 is worth only 19 cents. Now if they exchange pen- 
 knives, how many cents must Edwin give Oliver? 
 
 12. Arthur’s penknife was worth 25 cents, and Wal- 
 ter’s was worth only 18 cents: still, A. gave W. 6 cents. 
 to exchange. How much did A: lose? 
 
 13. On the Fourth of July, Robert had 50 cents given 
 him. He spent 6 cents for fruit, 12 cents for confection- 
 ary, 20 cents for a picture of Gen. Washington, and gave 
 away 5 cents. How many cents had he left? 
 
 14. Leonard has 32 cents, and Albert has 49. How 
 many cents has Albert more than Leonard ? 
 
 15. Francis being asked how old he was, answered, 
 that in 14 years more, he should be 25 years old. How 
 old was he, at the time he was asked? é 
 
 16. If a cow be worth 22 dollars, and a calf 5 dollars, 
 how much more is the cow worth than the calf? 
 
 17. A jockey gave 85 dollars for a horse, and sold him 
 for 68 dollars. How much did he lose? 
 
 18. A trader gave $3 dollars fora hogshead of “sugar, 
 and sold it for 96 dollars. How much did he gain ? 
 
 19. A farmer gave 24 dollars for a cart, and 12 dollars 
 for a plough. How many dollars did both cost? 
 
 20. If a gold watch be worth 64 dollars, and a gold 
 chain 18 dollars, how much are they both worth? 
 
5. MISCELLANEOUS EXAMPLES. Q5° 
 
 21. A man gave 13 dollars for the improvement of a 
 piece of ground, paid 36 dollars for having it cultivated, 
 and then sold the produce for 48 dollars. How many 
 dollars did he lose? 
 
 22. A market-man bought some butter for 8 dollars, 
 some cheese for 15 dollars, and some poultry for 12 
 dollars; and then sold the whole for 39 dollars. Did he 
 gain or lose >— and how much? 
 
 23. John bought a penknife for 25 cents; he exchanged 
 it for a better one, paying 16 cents, and then sold the 
 better one for 40 cents. Did he gain or lose ?— and 
 how much? 
 
 24. A gentleman gave 32 dollars for a piece of cloth, 
 and 13 dollars for having it made into a suit of clothes. 
 How much did the suit cost? 
 
 25. A tailor gave 54 dollars for some cloth and trim- 
 mings; he made the whole into clothes, which he sold 
 for 72 dollars. How much did he gain by the work? 
 
 26. If a man, having 50 dollars, should buy a barrel 
 of sugar for 24 dollars, and a barrel of molasses for 13 
 dollars, how many dollars would he have left ? 
 
 27. A scholar gave 55 cents for a geography, and 42 
 cents for an arithmetic. What did he give for both? 
 
 28. Ellen had 30 cents; her father gave 16 more, and 
 her mother 10 more; she then bought a book for 45 cents. 
 How many cents had she remaining ? 
 
 29. James had 38 cents, and his father gave him 14 
 more—William had 33 cents, and his-father gave him 
 19 more. Which boy then had the most money? 
 
 30. Lucy has 75 cents, and she intends buying a book, 
 that will cost 63 cents. How much money has she more 
 than the book will cost? : 
 
 31. A grocer purchased some oranges for 18 dollars, 
 some lemons for 8 dollars, some raisins for 4 dollars, and 
 some figs for 6 dollars; and then sold the whole for 44 
 dollars. Did he gain or lose >— and how much? 
 
 32. A company marched 82 miles in three days. It 
 marched 25 miles the first day, 36 miles the second day, 
 and the remainder of the distance the third day. How 
 many miles did it march the third day ? 
 
yz. ORAL ARITHMETIC. ; IV. 
 
 CHAP. IV. 
 MULTIPLICATION. 
 
 Note to Teachers. In the second and third sections of this chapter, the 
 learners are required to find the products of factors as high as 10 and 20. 
 There are few scholars, who will easily commit these products to memory; and 
 it will, therefore, be necessary to adopt a mental process, by which they may 
 readily be found. ‘I'he following example will show the process. 
 
 Question. How many are 8 times 16% *Solution. 16 is made up of 10 
 
 and 6. Eight types ten are eighty; eight times six are forty-eight. 80 and 
 A8 are 128. 7 
 
 SECTION 1. 
 
 1. On the Fourth of July, George and Richard went 
 to the Celebration, and whenever George spent 1 cent, 
 Richard spent 7. In the course of the day, George 
 spent 6 cents. How many did Richard spend? 
 
 Solution. Richard must have spent six times seven 
 cents. 6 times 7 are 42. ) 
 
 2. If 4 yards of cloth are required to make 1 cloak, 
 how many yards are required to make 5 cloaks? 
 
 3. If 1 boat will carry 5 men across the river, how 
 many men will 3 boats of the same size carry? 
 
 4. If a man can earn 8 dollars in one week, how many 
 dollars can he earn in 3 weeks? 
 
 5. If a traveller ride 6 miles in one hour, how many 
 miles can he ride in 9 hours? 
 
 6. Ina garden, there are 5 rows of plum trees; 8 trees 
 in each row. How many trees are there in the garden? 
 
 7. In a field there are 8 rows of apple trees; 5 trees 
 in each row. How many trees are there in the field? 
 
 8. There were 7 boys, who gave a poor man, 4 cents 
 apiece. How many cents did the man receive? 
 
 9. How many merit-marks will Susan get in 6 days, 
 provided she gets 4 every day? 
 
 10. How many errors will Jane make in 8 days, pro- 
 vided she makes 3 errors every day? . 
 
 11. If the price of 1 quart of nuts be 7 cents, for how 
 many cents can you buy 7 quarts? 
 
 12. If you should read 9 pages every day, how many 
 pages would youreadinS days? \. 
 
 ge 
 
2. MULTIPLICATION, 4 
 
 13. How many dollars must I pay for 9 yards of cloth, 
 that is worth 6 dollars a yard? 
 
 14. How many dollars must I pay for 9 barrels of 
 flour, when the price is 7 dollars a barrel ? 
 
 15. If 4 bushels of wheat are required for 1 barrel of 
 flour, how many bushels are required for 8 barrels ? 
 
 16. What is the cost of 7 reams of letter paper, that 
 is sold at 6 dollars per ream? 
 
 17. How much will a market-man get for 10 melons, 
 if vi sell them at 9 cents ec ? ye 
 
 . If a mat can earn 9 dollars in one month, how 
 
 eo dollars can he earn in 6 months ? 
 
 Section 2. 
 
 1. John and Henry together, caught 13 fishes every 
 morning; and it always happened, that John caught 10 
 of them, and Henry 3. Now how many did each boy 
 catch in 6 pomines: ?—Then how many did they both 
 catch in 6 mornings? 
 
 2. 10 and what number make 13? How many are 6 
 times 10? 6 times 3? How many are 60 and 18?— 
 wl 6 times 13 are how many? 
 
 . If the diamond in a ring cost 10 dollars, and the 
 
 pe 4 dollars, what does the diamond-ring cost? What 
 would 5 diamonds cost? What would 5 rings cost >— 
 Then what would 5 diamond-rings cost ? 
 
 4. 10 and what number make 14? How many are 5 
 times 10° 5 times 4? How many are 50 and 20?— 
 Then 5 times 14 are how many?» 
 
 5. A Northern hunter received a bounty of 10 dollars 
 from the state, and 5 from the county, for killing a wolf: 
 how much did he receive from both? How much would 
 he receive from the state for killing 7 wolves? How 
 much from the county for killing 7?—Then how much 
 from state and county both for killing 7° 
 
 6. 10 and what number make 15? How many are 7 
 times 10? 7 times 5? . How many are 70 and 35 ?— 
 Then 7 times 15 are how many? 
 
 7. A man hired a horse and gig, to pay 10 cents a 
 mile for the horse, and 6 cents a mile for the gig. How 
 
 c . 
 
 3 
 
26 ORAL ARITHMETIC. IV. 
 
 - mucha mile did he pay for both? How much for the 
 horse 8 miles? How much for the gig 8 miles >—Then ~ 
 how much for the horse and gig, both 8 miles ? 
 
 8. 10 and what number make 16? How many are 8 
 times 10? 8 times 6? How many are 80 and 48 ?>— 
 Then 8 times 16 are how many? 
 
 9. If a man gather 10 barrels of apples, and a boy 7 
 barrels, in a day, how many barrels do they both gather ? 
 How many barrels can the man gather in9 days? How 
 many batt a can the boy gather in 9 me ?—Then how 
 many barrels can they both gather in 9 days? ' 
 
 10. 10 and what number make 17? How many are 
 9times 10? 9 times 7? How many are 90 and 63?— 
 Then 9 times 17 are how many? 
 
 11. Ifa man eat 10 ounces of meat in a day, and his 
 wife eat 8-ounces, how many ounces do they both eat in 
 a day? How many ounces will the man eat in 4 days? 
 How many ounces will the wife eat in 4 days ?>—Then 
 how many ounces will they both eat in 4 days? 
 
 12. 10 and what number make 18? How many are 
 4times10? 4times8? How many are 40 and 32 ?— 
 Then 4 times 18 are how many ? 
 
 13. If a company of soldiers march 10 miles in the 
 forenoon, and 9 miles in the afternoon, how many miles - 
 do they march ina day? How many miles would they 
 march in 6 forenoons? How many in six afternoons ?— 
 Then how many miles in 6 days? 64 
 
 14. 10 and what number make 19? How many are 
 6 times 10? 6 times 9? How hia are 60 and 54 ?— 
 Then 6 times 19 are how many? 
 
 _ 15. How many are 6 times 10? 6 times 2?—Then 
 how many are 6 times 12? — . 
 
 16. How many are 7 times 10: 7 times 3?—Then 
 how many are 7 times 13? 
 
 17. How many are 8 times 10? 8 times 4?—Then 
 how many are 8 times 14? — 
 
 18. How many are 9 times 10? 9 times 5?—Then 
 how many are 9 times 15? 
 
 19. How many are 10times10? 10 times 6 ?—Then 
 how many are 10 times 16? 
 
mS. MULTIPLICATION. Q7 
 
 20. How many are 3 times 10? 3 times 7?—Then 
 how many are 3 times 17? , 
 
 21. How many are 2 times 10? 2 times 8?—Then 
 how many are 2 times 18? i 
 
 22. How many are 5 times 10? 5 times 9 ?—Then 
 how many are 5 times 19? 
 
 23, How many are 4 times 10? 4 times 9 ?—Then 
 how many are 4 times 19? 
 
 Srecrion 3. 
 
 1. Albert spends 11 cents every month, for stationary. 
 How many cents will he spend in'3 months ? 
 
 2. Howmanyare2times11? 3timegll? 4times11? 
 5times 11? 6times 11? 7timesi1l? \8times11? 9 
 times 11? 10 times 11? , 
 
 3. If you should write 11 copy-lines every day, how 
 many copy-lines would you write in 10 days? 
 
 4. If a pound of Malaga raisins cost 12 cents, how 
 many cents will 4 pounds of raisins cost ? 
 
 5. Howmanyare2times12? 3times12? 4times12? 
 5 times 12? 6 times12? 7times12? Stimes12? 9 
 times 12? 10 times 12? 
 
 6. If you should read 12 verses every morning, how 
 many verses would you read in 9 mornings ? 
 
 7. Suppose a steam boat will go 13 miles in an hour;— 
 how many miles will it go in 5 hours? 
 
 8. Howmanyare2timesl3? Stimesl3? 4timesl3? 
 5times 13? 6times 13? 7times 13? Stimes13? 9 
 times 13? 10 times 13? ” 
 
 9. If a labourer can earn 13 dollars in a month, how 
 many dollars can he earn in 8 months? 
 
 10. If it take 14 men to navigate one ship, how many 
 men will it take to navigate 6 ships? | 
 
 11. Howmanyare2timesl4? Stimesl4? 4timesl4? 
 5 times 14° G6times14? 7times14? Stimes14? 9 
 times 14? 10 times 14? 
 
 12. If a pound of honey be worth 14 cents, how many 
 cents are 7 pounds of honey worth? 
 
VW 
 
 as ORAL ARITHMETIC. IV. 
 
 13. If a carpenter can make 15 hat boxes in a day, 
 how many hat boxes can he make in 2 days? 
 
 14. Howmanyare2times]15? Stimesl5? 4timesl5? 
 5 times 15? .6 times 15? 7times 15? Stimes15? 9 . 
 times 15? 10 times 15? 
 
 15. If ashoemaker make 15 pairs of shoes in a week, 
 
 * how many pairs will he make in 10 weeks ? 
 
 16. How much would a man earn in 3 months, pro- 
 vided his wages were 16 dollars a month? 
 
 17. Howmanyare2times16? 3timesl16? 4times16?: 
 5 times 16? 6times16? 7times16? 8 times16? 9 
 times 16? 10 times 16? 
 
 18. How much would a man spend in 9 months, if 
 his. expenses were 16 dollars a month? 
 
 19. If 17 barrels of flour can be carried on one wagon, 
 how many barrels may be carried on 4 wagons ? 
 
 20. Howmanyare2times17? Stimesl17? 4times17? 
 5times 17? 6times17? 7 times17? Stimes17? 9 
 times 17? 10 times 17? 
 
 21. If one hogshead of molasses be worth 17 dollars, 
 what is the value of 8 hogsheads of molasses ? 
 
 22. If 5 men should pay me 18 dollars apiece, how 
 many dollars should I receive from them all ? 
 
 23. Howmanyare2timesl8? 3times18? 4timeslS? 
 5times 18? 6times18? 7times 18? Stimes 18? 9 
 times 18°. 10 times 18?) «9% 
 
 24. If I should pay to 7 men, 18 dollars apiece, how 
 many dollars should I pay to all of them? | 
 
 25. How much would a farmer get for 3 cows, if he 
 should sell them for 19 dollars apiece ? 
 
 26. Howmanyare2times19? 3times19? 4times19? 
 5times19? 6times19? 7 times19? Stimes 19? 9 
 times 19? 10 times 19? 
 
 27. If you answer 19 questions at every recitation, 
 how many would you answer in reciting 6 times? 
 
 28. Paper is generally packed in reams, of 20 quires 
 each. How many quires are there in 4 reams? 
 
4. MULTIPLICATION. 20, 
 
 29. Howmanyare2times20? Stimes20? 4times20? 
 5 times 20? 6times 20? 7times20? Stimes20? 9 
 times 20? 10 times 20? 
 
 30. If a trader make 20 cents on every pound of tea 
 he sells, how much will he make on 5 pounds. 
 
 Section 4. 
 1. An ounce is a small weight, 16 of which make a 
 
 _ pound. How many ounces of tea are there i in 3 pounds 
 
 and 9 ounces of tea 
 Solution. In 1 pound there are 16 ounces, and in 3 
 
 pounds there are 3 times 16 ounces. °S times 16 ounces 
 
 are 48 ounces. 48 ounces and 9 ounces are 57 ounces. 
 
 2. How many ounces in 8 pounds and 4 ounces ? 
 
 3. 20 penny-weights of gold make 1 ounce. How 
 many penny-weights in 4 ounces and 13 penny-weights ? 
 
 4. How many Byeny pevrens are there in 6 ounces 
 and 9 penny-weights ? 
 
 5. The brewer sells his beer by the firkin, and a fir- 
 kin holds as much as 9 gallon measures. How many 
 gallons are there in 10 firkins and 6 gallons ? 
 
 6. In 7 firkins and 3 gallons, how many gallons ? 
 
 7. 40 rods, measured by a surveyor’s chain, make 1 
 furlong. How many rods in 3 furlongs and 17 rods? 
 
 8. In 4 furlongs and 8 rods, how many rods? 
 
 9. There are 12 months in a year. How many 
 months are there in 6 years and 6 months? 
 
 10. In 9 years and 10 months, how many months ° 
 
 11. 4 pecks of oats, peas, beans, or any other dry 
 commodity, make 1 bushel. How many pecks of wheat 
 are there in 6 bushels and 3 pecks ? 
 
 12. In 10 bushels and 1 peck, how many pecks? 
 
 13. 12 pence, in English money, make 1 shilling. 
 How many pence are there in 8 shillings and 6 pence? 
 14. In 10 shillings and 9 penee, how many pence? 
 
 15. 10 cents, in Federal money, make 1 dime. How 
 many cents are there in 7 dimes and 6 cents? 
 
 16. In 4 dimes and 8 cents, how many cents ? 
 
 17. In 1 month there are 30 Gays. How many days 
 are there ia 3 months and ‘ 5 days:2 | 
 
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 1. A lady divided 15 peaches among some little girls, 
 giving 3 to each girl. How many girls were there? 
 
 Solution. As many times as 3 peaches are eontained 
 in 15 peaches, so many girls there were. 
 
 2. If you had 16 cents to lay out in pencils, ade the 
 price of. the pencils were 4 cents aplene, oa many 
 could you buy for all the money ? 
 
 3. How many times is 4 contained in 16: 2 
 _ 4. If 4 horses are required to draw one wagon, how 
 
 many wagons might be drawn by 20 horses ? 
 
 BY et i How many times 4 in 20? How many are 5 times 4? 
 
 6. If a man can travel 4 miles in one hour, how many 
 hours will it take him to travel 12 miles? 
 
 7. How many times 41n 12? How many are 3.times 4? 
 
 8. How many yards of broadcloth, that is sold at 7 
 dollars a yard, can be purchased for 14 dollars ? 
 
 9. How many times 7 in 14? How many are 2 times 7? 
 10. How many lead pencils ‘could you buy for 18 
 cents, if they were sold at 6 cents apiece ? | 
 
 11. How many times 6 in 18? How memy are 8 times 6? 
 
 12. Inan orchard there are 35 trees; standing in rows, 
 7 trees in.a row. How many rows are there ° 
 
 13. How many times’7 in 35? How many are 5 times’ ? 
 
 14. A man bought sheep at 4 dollars apiece, and paid , 
 for them all, 24 dollars. How many did he buy ? 
 
 ai? How many times 4 in 24? How many are 6 times 4? 
 eeedo. A gardener set out 30 peach trees, in rows, put- 
 
 3 ting 5 trees in arow. How many rows were there? 
 
 17. How many times 5 in 30? How many are6 times 5? 
 
 18. A farmer got 36 dollars for some sheep, that he 
 sold at 6 dollars apiece. How many were there? 
 
 19. How many times 6 in 86? How many are 6 times 6? 
 
82 ORAL ARITHMETIC. Vy, 
 
 20. A trader wishes to pack 56 hats in boxes, putting 
 8 hats in a box:— how many boxes are wanted ? 
 
 21. How many times 8 in 56? How manyare7 times 8? 
 
 22. How many dozen of eggs can you buy for 63 
 cents, when they are sold at 9 cents a dozen? 
 
 23. How many times 9 in 63? Howmanyare7 times 9? 
 
 24. If an orange be worth 6 cents, and a lime 1 cent, 
 then how many oranges are 60 limes worth? 
 
 25. How many times 6 in 60? Howmanyare 10times 6? 
 
 26. If one silk bonnet be worth 7 handkerchiefs, how 
 many bonnets are 56 handkerchiefs worth ? 
 
 27. How many times 7 in 56? Howmanyare 8 times 7? 
 
 28. If I give a barrel of flour for 4 bushels of wheat, 
 how many barrels must I give for 36 bushels? 
 
 29. How many times 4 in 36? How many are 9 times 4? 
 
 30. If a man can build 8 rods of fence in a day, how 
 many days will it take him to build 72 rods ? 
 
 31. How many times 8 in 72? How many are9 times 8? 
 
 32. If 5 bushels of wheat will pay for a yard of broad 
 cloth, how many yards will 45 bushels pay for? 
 
 33. How many times 5 in 45? How many are 9 times 5? 
 
 34. Lafayette was 42 days on his passage from ‘Toulon 
 to New York. How many weeks was his passage ? 
 
 35. How many times 7 in 42? How many are6 times 7? 
 
 Srecrion Y. 
 
 1. Suppose 2 men have 8 biscuit to divide equally 
 between them;— how many must each man take ? 
 
 Observation. There are 2 men to share the biscuit, 
 and if there were only 2 biscuit to be divided, then 1 
 man would take 1 biscuit. ‘Therefore, 1.man will now 
 take 1 biscuit of every 2 biscuit. 
 
 Solution. As many times as 2 is contained in 8, so 
 many biscuit must each man take. 2 is contained in 8, 
 4times. | 
 
 2. If 12 dollars be divided equally between 2 men, 
 how many dollars does each man receive ? 
 
 3. If 18 chestnuts should be divided equally between 
 2 boys, how many would each boy receive ? 
 
g. DIVISION. 33 
 
 » 4. Atenant cultivated a piece of corn, agreeing to give 
 the owner of the land 1 bushel of every 2 bushels that 
 he might raise. He raised 22 bushels. How many 
 bushels should the owner of the land receive ? ) 
 
 5. Suppose 3 boys have 12 oranges to divide equally 
 between them;— how many must each boy take ? 
 
 Observation. If the 3 boys had only 3 oranges to di- 
 vide, each boy would take 1 orange;—if they had 2 times 
 3 oranges, each boy would take 2 times 1 orange:—and 
 thus, each boy will take as many times 1 orange, as there 
 are threes in the number to be divided. 
 
 Solution. As many times as 3 is contained in 12, so 
 many oranges must each boy take. 3 in 12, 4 times. 
 
 6. If 15 biscuit be divided equally between 3 men, 
 how many biscuit does 1 man receive? 
 
 7. 3 careless boys must pay 24 cents for breaking a 
 square of glass. What must each boy pay? 
 
 8. A man set out 27 trees, in 8 rows; an equal num- 
 ber in each row. How many were there in one row? 
 
 9. 4 boys have 12 oranges to divide equally between 
 them. How many will each boy receive? 
 
 Observation. If the 4 boys had only 4 oranges to di- 
 vide, then each boy would receive 1 orange. Therefore 
 each boy must receive 1 orange of every 4 oranges that 
 there are in the number to be divided. 
 
 Solution. As many times as 4 is contained in 12, so 
 many oranges will each boy receive. 4 in 12, 3 times. 
 
 10. I have 32 minutes to spend on 4 lessons. How 
 many minutes can I spend on each lesson ? 
 
 1i. Suppose I wish to give 28 quills to 4 boys;—how 
 many must I give to each boy? 
 
 12. 4 men received 20 dollars for doing a piece of 
 work. How much was each man’s share ? 
 
 13. A fisherman hired a boat, agreeing to give the 
 owner, | fish of every 5, that he might catch: he caught 
 20. How many should he give the owner ° 
 
 14. If 35 pounds of beef be divided among 5 soldiers, 
 how many pounds does each soldier receive ? 
 
 15. 5 men have agreed to pay equal shares of 50 dol- 
 lars. How many dollars must one man pay? . 
 
34 ORAL ARITHMETIC. Vv; 
 
 16. Charles was one of 6 boys, who owned together 
 42 books. They divided the books, and Charles receiv- 
 ed 1 book of every 6 books. How many did he receive? 
 
 17. If 24 books should be divided equally amare 6 
 boys, how many would each boy receive ? 
 
 18.6 men have agreed to pay 36 dollars in ool 
 shares. How many dollars’ must each man pay? 
 
 19. Edward is one of 7 boys, who are to have 28 
 peaches. divided equally among them.. How many will 
 Edward receive for his share? 
 
 20. If 7 writing-books be made of 42 sheets of paper, 
 how many sheets are there in each book ? 
 
 21. 8 boys owned together 72 quills; and, in order to 
 share them equally, each boy took 1 quill from every 8 
 quills in the number... How many did each boy take? 
 
 22. I have 48 dollars to divide among 8 men. How 
 many dollars must I give to one man? 
 
 23. 9 men shared 45 bushels of corn among them, 
 each man taking for his share, 1 bushel of every 9 bush- 
 els. How many bushels did each man take ? 
 
 24. 9 persons have agreed to make up a purse of 72 
 dollars. How many dollars must each one put in? 
 
 25. 10 sailors are to receive 90 dollars for retaking | 
 their ship. How much will each sailor receive ? 
 
 Section 3. 
 
 1, Charles has 25 cents, which he has engaged to 
 appropriate as follows. Whenever he blots his writing- 
 book, he is to lay it aside, and pay 6 cents for anew one. 
 Now how many books can he pay for; and how many 
 cents will he have remaining, after his number becomes 
 too small to buy another book. 
 
 Observation. If his whole number of cents were 30, 
 he could then pay for five books; because, 6 cents are con- 
 tained in 30 cents, 5 times. Again, if His whole number 
 of cents were only 24, he could then pay for 4 books; 
 because, 6 cents are contained in 24 cents, 4 times. 
 
 2. Suppose it takes 8 buttons to trim a vest:— how 
 many vests can the tailor, who has only 34 buttons, trim; 
 and what number of buttons will he have remaining ? 
 
DIVISION. 35 
 
 jany times 8 in 34; and how many over? 
 | aany glass tumblers, at 10 cents apiece, can 
 a woman, that has only 53 cents, buy;. and how many 
 cents will she have remaining ? 
 
 Solution. As many times as 10 is contained in 53, SO 
 many tumblggs she can buy. 10 is contained in 53, 5 
 times, and there is three over. 
 
 5. How many kegs, that will hold ‘7 gallons apiece, 
 may be filled from a cask of ivine containing 46 gallons; 
 and how many gallons will remain in the cask ? 
 
 6. How many times 7 in 46; and how many over ? 
 
 7. A hat-maker has 53 hats finished: and, in order to 
 send them to market, he must pack them i in boxes, that 
 will hold 8 hats apiece. How many full boxes can he 
 send; and how many hats will remain on hand? 
 
 8. How many times 8 in 53; and how many over? 
 
 9. A trader has 69 dollars with which he wishes to 
 purchase hats. If he should pay 7 dollars apiece for the 
 hats, how many could he purchase; and how many dol- 
 lars would he have remaining ? 
 
 10. How many times 7 in 69;,and how many over ? 
 
 11. If 4 yards of cloth will make 1 cloak, how many 
 cloaks can be made from a piece of cloth containing 38 
 yards; and-how many yards will there be over? 
 
 12. How many times 4 in 38; and how many over? 
 
 13. How many times is 4 contained in 29; and how 
 ae over? How many are 7 times 4, and 1 more? 
 
 14. How many times is 6 contained in 53; and how 
 many over? How many are 8 times 6, and 5 more? 
 
 15. How many times is 9 contained in 575 and how 
 many over? How many are 6 times 9, and 3 more? 
 
 16. How many times is 7 contained in 68; and how 
 many Over? How many are 9 times 7, and 5 more? 
 
 17. How many times is 5 contained in 49; and how 
 many over? How many are 9 times 5, and 4 more? “ 
 
 18. How many times is 3 contained in 26; and how 
 many over? How many are 8 times 3, and 2 more? 
 
 19. In 15, how many times 4; and how many over? 
 Ini7?. 1n26? In33? In27? In 42? 
 
36 ORAL ARITHMETIC. V. 
 
 20. In 27, how many times 5; and how many over? 
 In 29? In 36? In 32? In 44? In 48? 
 21. In 28, how many times, 6; and how many over? 
 
 In 37? In38? In46? In49?. In 22? - 
 22. In 30, how many times 7; and how many over! ? 
 
 In 36? In43? In48? In 51? In 59 sep 
 
 23. In 28, how many times 8; and how many over? 
 Ino? In 46? In 522° 1n 61? Un w75e 
 
 24. In 31, how many times 9; and how many over? 
 In 34? In 42? In50? In67? In 70? 
 
 25. A gallon measure, used for measuring wine, beer, 
 milk, &c. will contain as much as 4 quart measures. 
 Suppose I have 15 quart measures full of water;—how 
 many gallon measures can I fill from them; and how 
 many quarts will there be over? 
 
 26. How many gallons are there in 34 quarts ? 
 
 27. 3 feet, measured on a line, are the same as 1 yard. 
 How many yards are there in 29 feet ? 
 
 28. How many yards are there in 17 feet ? 
 
 29. 60 minutes, by the clock, make 1 hour. How 
 many hours are there in 128 minutes? 
 
 80. 12 inches, on the carpenter’s rule, make 1 foot. 
 How many feet long is a board, that is 65 inches long ? 
 
 31. How many feet are there in 38 inches? 
 
 32. 8 drams of medicine, weighed by the apothecary, 
 are the same as 1 ounce of medicine. How many ounces 
 are there in 46 drams? 
 
 33. How many ounces are there in 30 dramg? 
 
 _ 34. 9 square feet, measured upon the floor, make 1 
 square yard. How many square feet are there in 20 
 square yards ? 
 
 35. How many square yards in 51 square feet? 
 
 36. 7 days are 1 week. How many weeks in 33 days ? 
 
 37. How many weeks are there in 52 days? 
 
 38. 12 pence, in Englishmoney, make 1 shillmg. How 
 many shillings are there in 69 pence ? | 
 
 39. How many shillings are there in 46 pence ? 
 
 40. 10 cents, in Federal money, make 1 dime. How 
 many dimes are there in 48 cents? 
 
 41. How many dimes are there in 95 cents ? 
 
4. MULTIPLICATION AND DIVISION. 37 
 
 Section 4. 
 CORRESPONDENT EXAMPLES. 
 
 1. How much will 5 pounds of dates cost, when the 
 price of them is 7 cents a pound? 
 
 Solution. If one pound cost 7 cents, 5 pounds wil 
 cost 5 times 7 cents. 5 times 7 are 35. 
 
 2. How many pounds of dates can you buy for 35 cents; 
 the price being 7 cents a pound? 
 
 Solution. I can buy as many pounds of dates as 7 is 
 contained times in 35. 7 in 35, 5 times. 
 
 3. How many quarts of wine are there in 10 gallons; 
 there being 4 quarts in one gallon ? 
 
 4. How many gallons of wine are there in 40 quarts; 
 ~ every 4 quarts making one gallon? > 
 
 id 
 
 _._. 5. How many pence are there in 5 shillings; there 
 being 12 pence in 1 shilling? 
 6. How many shillings are there in 60 pence; there 
 _ being 12 pence in 1 shilling ? 
 7. In 1 penny there are 4 farthings. How many far- 
 things in 9 pence and 3 farthings ? 
 8. How many pence are there in 39 ferthings ;—and 
 how many farthings are there over? 
 
 9. A gentleman went on a journey of 9 days, and paid 
 for his expenses, 4 dollars per day. How much were 
 his expenses during the whole journey ? 
 
 10. A gentleman, who had been away on a journey 
 for 9 days, found on his return, that he an spent 36 dol- 
 lars. How much did he spend a day 
 
 Suggestion. 9 dollars would allow fi 1 dollar a day. 
 
 11. If 6 bushels of onions grow upon 1 square rod of 
 ground, how many bushels will grow upon 10 rods? 
 
 12. A man raised 60 bushels of onions upon 10 rods 
 of ground. How many bushels grew upon 1 rod? 
 
 13. If a ship sail 7 miles an hour, how many miles 
 will she sail in 7 hours ? 
 
 14. If a ship sail 49 miles in7 hours, how many miles 
 _ does she sail in 1 hour? ... 
 D 
 
 " 
 
 te 
 
38 ORAL ARITHMETIC. . V. 
 
 Section 5. ¢ 
 CONNECTED OPERATIONS. _ 
 
 1. A market man sold 10 pounds of cheese at 8 cents 
 a pound, and received his pay in sugar at 10 cents a 
 pound. How many pounds of sugar did he receive ? 
 
 Solution. The price of 1 pound of cheese being 8 
 cents, the price of 10 pounds is 10 times 8 cents, or 80 
 cents. —80 cents will pay for as many pounds of sugar, 
 as there are times 10 in 80. 10 in 80,8 times. 
 
 2. In 10 times 8, how many times 10? 
 
 Solution. 10 times 8 are 80.—10 in 80, 8 times. 
 
 3. 4 coaches went from Baltimore to Washington, 
 each carrying 6 boys: the same boys returned, riding 8 
 inacoach. In how many coaches did they return? 
 
 4. In 4 times 6, how many times 8? . phi 
 
 5. How many boxes of raisins at 6 dollars a box, will — 
 pay for 4 kegs of tobacco at 9 dollars a keg? 
 
 6. In 4 times 9, how many times 6? , oe 
 
 7. How many sheep worth 4 dollars a head, must be 
 given for 6 tons.of hay, worth 8 dollars a ton? 
 
 8. In 6 times 8, how many times 4? 
 
 9. How many reams of paper at 3 dollars a ream, will 
 pay for 5 dozen of books at 6 dollars a dozen ? 
 
 10. In 5 times 6, how many times 3? . 
 
 11. A hunter, in Michigan, sold 7 pelts at.5 dollars a 
 pelt, agreeing to take His pay in muskets at 8 dollars apiece. 
 The purchaser counted out as many muskets as the pelts 
 would pay for, and finding there was still a balance due. 
 to the hunter, he paid this in money. How many mus- 
 kets and how much money did the hunter receive ? 
 
 12. In 7 times 5 how many times 8; how many over? 
 
 13. In 3 times 4 how many times 5; how many over? 
 
 14. In 8 times 5 how many times 7; how many over? 
 
 15. In 7 times 7 how many times 5; how many over? 
 
 16. In 5 times 6 how many times 4; how many over? 
 
 17. In 9 times 3 how many times 6; how many over? 
 
 18. In 4 times 8 how many times 9; how many over? © 
 
 19. In 6 times 9 how many times 8; how many over? 
 
5. 6. MISCELLANEOUS EXAMPLES, 39 
 
 Note to Teachers.° In performing oral solutions which involve divert op- 
 erations, it will be found convenient, although not absolutely necessary, to use 
 the terms plusand minus. ‘These terms, however, should not be adopted until 
 they are perfectly understood; and the duty of explaining them is here confided 
 to the Teacher. It will not suffice, merely to tell the learner, that “plus means 
 more, and minus means less,”’ for the idiom of our language does not allow him 
 to use more and less, as he is called upon to use plus and minus. The ex- 
 pressions, ‘7 more 5 is 12,”’ and, “10 less 4 is 6,” although true, are not. 
 very likely to meet the under standing of a young scholar. Perhaps it will be 
 found necessary to resort to illustrations like the following. 
 
 Place 8 books in a pile before you, and say,—* Here 1 is a pile of 8 books, 
 and I shall make the number of books in the pile 3 more.”’ .'Then, placing 3 
 additional books upon the pile, say,—*‘ 8 books plus 3 Bees are 11 books.’” 
 Again proceed to say,—** I shall now make the number 2 less.” Then, taking 
 off 2 books ,» say,—** 1] books, niinus 2 books are 9.books.”’ 
 
 Section 6. 
 MISCELLANEOUS EXAMPLES. 
 
 1. How many days in the three Summer months;— 
 there being 30 in June, 31 in July, and 31 in August? 
 
 Solution. 30 days plus 31 days are 61 days; 61 days 
 plus 31 days are 92 days. 
 
 2. There were 42 gallons of wine in a cask; but, the 
 cask not aene Se 7 Liebe neve leaked out. How 
 
 ESolitsivt, 42 minus 7 is 35. Dunia 35 a om 
 
 3. A boy that had 97 cents, paid 62 cents for a book, 
 18 cents for a morocco wallet, and 6 cents for a pencil. 
 How many cents. had he remaining? 
 
 Solution. 62 cents (for book), plus 18 cents (for 
 wallet), is 80 cents; 80 cents plus 6 cents (for pencil), 
 is 86 cents. 97 cents minus 86 cents is 11 cents. 
 
 4. A black-smith bought 9 tons of coal, at 4 dollars 
 per ton, and gave 3 dollars for having it drawn to his 
 shop. How much did the coal cost him? 
 
 Solution. If the price of 1 ton was 4 dollars, the price 
 of 9 tons was 9 times 4 dollars, or 36 dollars; 36 dollars 
 
 plus 3 dollars (for having it drawn) is 39 dollars. 
 
 _ 5. A schoolmaster laid out 96. cents in writing-books, 
 at 8 cents apiece, and then gave away 5 of them. How 
 many books had he remaining? : 
 
 Solution. He bought as many books, as 8 is pulitlaed 
 times in 96, whichis 12. Then, 12 books minus 5 books, 
 (that he gave away), are 7 books. 
 
- 
 
 40 ORAL ARITHMETIC ¥, 
 
 6. A trader gave 16 dollars for a keg of tobacco, and 
 after selling it, found he had gained 6 dollars. For how 
 much did he sell it ? | 
 
 7. Arich farmer in Vermont had a flock of 100 sheep; 
 they went upon a mountain, and the wolves destroyed 18 
 of them. How many sheep had he remaining ? 
 
 8. Ifa man spend 4 dollars in a week, haw many dol- 
 lars will he spend in 9 weeks? 
 
 9. How many dozen of eggs can you buy for 64 cents, 
 when the price of them is 8 cents per dozen? 
 
 10. A trader gave 48 dollars for 7 barrels of flour, and 
 sold it for 6 dollars a barrel. What did he lose? 
 
 11. How many weeks are there in 35 days? 
 
 12. Four men made up a purse of 40 dollars, for a — 
 charitable purpose. The first man put in 9 dollars, the 
 second 12 dollars, and the third 7 dollars;—how much — 
 did the fourth man put in? 
 
 13. A sum of money was divided equally among 8 
 sailors; and Jack, who was one of the number, received 
 for his share, 15 dollars. What was the sum divided? 
 
 14-..How manv davs are there in18 weeks and 5 dayg? 
 
 15. A trader bought 3 reams of paper, at 5 dollars per 
 ream, and 7 maps, at 5 dollars apiece. How much did 
 he give for the whole? 
 
 16. If 49 bushels of corn should be divided equally 
 among 7 men, how much would one man receive ? | 
 
 Solution. As many times as 7 is contained in 49, so 
 many bushels would one man receive. 
 
 17. If 45 dollars be divided equally between 5 men, 
 how many dollars does each man receive ? 
 
 18. A man bought a turkey weighing 10 pounds, for 8 
 cents a pound, and then sold it for 3 cents a pound more 
 than he gave. For how much did he sell it ? 
 
 19. Charles had 25 cents; his father gave him 4 mel- 
 ons, which he sold for 6 cents apiece; he then paid 12 . 
 cents for a book. How many cents had he left ? 
 
 20. If a man earn 6 dollars a week, how many weeks 
 will it take him to earn 48 dollars ? 
 
 21. Geographers consider the United States in four 
 classes. ‘There are 6 Eastern states, 4 Middle states, 
 
6. MISCELLANEOUS EXAMPLES. 4l 
 
 8 Southern states, and 6 Western states. How many 
 states are there in the Union? 
 
 22. A merchant paid 43 dollars for some iron, and sold 
 it for 35 dollars. How many dollars did he lose? 
 
 23. A man paid 78 dollars for a piece of land, and 16 
 dollars for having it fenced; and he then sold it for 100 
 dollars. Did he gain or lose;—and how much ? 
 
 _ 24. A cabinet-maker sold 6 tables, at 14 dollars apiece. 
 How many dollars did he receive? 
 
 25. If t buy 10 yards of cloth, at 7 dollars a yard, how 
 many five-dollar bills must I pay for it? 
 
 26. How many boxes of strawberries can you buy for 
 36 cents, when they are sold at 9 cents a box? 
 
 27. Suppose a trader, who has 12 barrels of flour on 
 hand, should lay out 35 dollars in buying more flour, at 
 5 dollars a barrel; how many barrels would he have? 
 
 28. If I pay 19 dollars to one man, 13 to another, 
 and 31 to another, how many dollars do I pay out? 
 
 29. If a laborer can earn 7 dollars in a week, how 
 many weeks will he be in earning 42 dollars? 
 
 30. How many hats, that are sold at 6 dollars apiece, 
 can a man who has 50 dollars pay for;—and how many 
 dollars will he have remaining ? 
 
 31. If you should perform 19 examples i in arithmetic, 
 every day, how many would you perform in 6 days? 
 
 * 39, Samuel Moderate earns 7 dollars a month, and 
 John Smart earns 15 dollars a month. How much more 
 will John earn than Samuel, in 6 months ? 
 
 33. If 1 mando 1 day’s work in 1 day, how many mea 
 will it take to perform 7 days’ work, in 1 day? 
 
 34. If 4 men will perform 4 days’ workin 1 day, how 
 many days’ work will 4 men perform in 9 days? 
 
 35. How many days will it take 4 men to dig a cellar, 
 that 1 man would be 36 days in digging? 
 
 36. How many days will it take 7 men to clear a piece 
 
 of wood-land, that 28 men can clear in one day ? 
 87. How many men will it take to perform as much 
 work in 1 day, as 11 men can perform in 6 days? 
 
 38. How many days will it take 4 men to apap the. 
 same work, that 12 men can perform in 3 days ? f 
 
 p* 
 
42 ORAL ARITHMETIC. - V. 
 
 39. A trader has three bundles of bank notes;—23 
 dollars in one bundle, 15 dollars in another, and 34 dol- 
 lars in another; but in one. of the bundles there is a 
 note of 5 dollars, which is counterfeit. How many dol- 
 lars of good money has he? 
 
 40. Stephen has lost 30 cents, and has found 10 cents; 
 he now has 18 cents. How much had he at first ? 
 
 41. A farmer went to the city with 8 barrels of cider, 
 which he sold at 4 dollars a barrel. He then purchased 
 3 hogsheads of salt, at 3 dollars per hogshead, and paid an 
 old debt of 12 dollars. How many dollars had he to 
 carry home? 
 
 42. If I pay 3 dollars apiece for 7 umbrellas, and 6 
 dollars apiece for 6 hats, for how many dollars must I 
 sell the whole, in order to gain 7 dollars? 
 
 43. A man borrowed 75 dollars, and the next day paid 
 all but 14 dollars of it. How much did he pay? 
 
 44. A. spent 5 dollars as often as B. spent 3 dollars. 
 How much did A. spend, while B. spent 27 dollars? 
 
 Solution. As many times as 9 dollars are contained 
 in 27 dollars, so many times 5 dollars did B. spend. 3 
 dollars are contained in 27 dollars 9 times; therefore A. 
 spent 9 times 5 dollars. 
 
 45. A man and a boy were gathering corn;—the man 
 gathered 7 rows, in the same time that the boy gathered 
 4 rows. How many rows would the man gather, while 
 the boy was gathering 32 rows? 
 
 46. A man and a boy were digging potatoes;—the 
 man dug 11 bushels in the same time that the boy dug 6 
 bushels. How many bushels would the boy dig, while 
 the man was digging 55 bushels ? 
 
 47. Suppose butter to be worth 12 cents a pound, and 
 
 ‘tea 42 cents a pound;—how many pounds of butter must 
 be given for 2 pounds of tea? 
 
 48. A farmer sold 2 cows at 23 dollars apiece, and 9 
 sheep at 5 dollars apiece; he received in payment, 3 
 ploughs at § dollars apiece, and the rest in money. How 
 much money did he receive? 
 
 49. 4 boys found a purse containing 29 dollars. They 
 paid 2 dollars for advertising it; and, as no owner ap- 
 
6: MISCELLANEOUS EXAMPLES. 43 
 
 peared, they agreed to take 6 dollars apiece to themselves, 
 and give the remainder to a poor woman. How much 
 was there remaining for the woman? 
 
 50. What sum of money must be divided among 16 
 men, in order that one man shall receive 4 dollars ? 
 
 51. Two classes are studying arithmetic. The first 
 class is 81 examples in advance of the second; the sec- 
 ond performs 40 examples in a day, and the first, 31. In 
 how many days will the second overtake the first ? 
 
 52. A lady paid 6 dollars for silk, 9 dollars for cam- 
 
 _bric, 7 dollars for linen, and then had 13 dollars remain- 
 
 ing. How many dollars had she at first ? 
 
 53. How many barrels of flour, at 6 dollars per barrel, 
 can the baker who has 45 dollars, purchase; and how 
 many dollars will he have remaining ? 
 
 54. A trader, that has 48 dollars, wishes to buy all the 
 boots he can pay for, at 5 dollars a:pair, and then lay out 
 the remainder of his money in shoes, at 1 dollar a pair. 
 How many pairs of boots, and of shoes, must he buy? 
 
 55. What sum of money must be divided among 18 
 men, in order that one man shall receive 7 dollars ? 
 
 56. Three men made up a purse of 40 dollars. The 
 first man put in 6 dollars, and the second 3 times as much 
 as the first. How much did the third put in? 
 
 57. Eliza gave a poor woman 4 cents, Augusta gave 
 her 3 times as much as Eliza, and Lucy 3 times as much 
 as Augusta. How much did the woman receive ? 
 
 58. If a mandig 30 bushels cf potatoes in a day, anda 
 boy 13 bushels, how many bushels will they both dig ina 
 day? How many will they both dig in 3 days ? | 
 
 59. A farmer purchased 15 sheep;—he sold 8 of them 
 at 4 dollars apiece, and the remainder at 3 dollars apiece; 
 and then found that he had gained 7 dollars. How much 
 did he give for the sheep? 
 
44 ORAL ARITHMETIC. VI. 
 
 CHAP. VI. 
 FRACTIONS. 
 
 SecTION Il. 
 
 Note to Teachers. The subsequent progress of the learner, will depend 
 much on a proper conception of the division of unity, and a correct application 
 of the nomenclature of fractions. Therefore, thissection, however simple it may 
 appear, should not be slighted. It should be recited with the books closed. 
 
 The picture of a board. 
 
 This board, as it is presented above, is a whole thing. 
 The same board appears hereafter divided into parts; and 
 the parts are named according to their number and size. 
 
 Divided now into 2 equal pars.§ SSS = 
 
 One of these parts is one-hal/, === 
 1. How many halves are there in the whole of any thing? 
 2. Suppose I can write a letter on 1-half of a sheet of 
 
 paper; how much paper shall I use, in writing 2 letters ? 
 3. How much is 1-half and 1-half, added together? 
 
 Divided now into 3 equal parts. Bass BSS SSS 
 One of these parts is one-third. == SS====z 
 
 4. How many thirds are there in the whole of any thing? 
 5. If a carpenter can make 3 door-panels of 1 board, 
 
 what part of one board will he use, in making 1 panel ? 
 6. Which is the greater part, 1-half, or 1-third? 
 
 Divided now into 4 equal pars. Sas SSS SSeS 
 
 One of these parts is one-fourth, aE 
 7. How many fourths are there in the whole of 1 thing? 
 8. I gave 1-fourth of an orange to John, and 2-fourths 
 
 to Frances. How much of the orange did I give away ? 
 9. Which is the greater part, 1-third, or 1-fourth? 
 
 Divided now into 5 equal pars... 55> SS SSS 
 
 One of these parts is one-fifth, SSS SSS SE = 
 10. How many fifths are there in the whole of any thing? 
 11. Charles divided a melon, equally among 5 boys. 
 
 What part of the melon, [how many fifths,] had 2 boys? 
 12. Which is the smaller part, 1-fourth, or 1-fifth ? 
 
i FRACTIONS. 
 
 Divided now into 6 equal parts. SSS SS SS ESS SS S= 
 i a= eee ee eee = 
 One of these parts is one-sirth == SS ae SSS SSS SS 
 ——SS_—EESSSS-—_ SSS Eee 
 
 13. Howmany sixths are there in the whole of any thing? 
 14. If 3 girls and 2 boys should each of them eat 1-sixth 
 
 of a pie, what part of the whole pie would they all eat ? 
 15. Which is the greater part, 1-fifth, or 1-sixth? 
 
 Divided now into 7 equal pars. SS === SS SSS 
 One of these parts is one-seventh. 
 16. How many sevenths are there in the whole of 1 thing? 
 17. John broke off 2-sevenths of a new pencil, and cut 
 off 1-seventh more. How much of it was then wasted? 
 18. Which‘is the smaller part, 1-sixth, or 1-seventh? . 
 
 Divided now into 8 equal parts. 
 One of these parts is one-eighth. B= —— 
 
 19. How many eighths are there in the whole of 1 thing? 
 20. If a boy earn 3 eighths of one dollar, and find 4- 
 eighths more, what part of one dollar will he then have ? 
 21. Which is the’smaller, 1-seventh, or 1-eighth ? 
 
 Divided noidinto 9 equal parts. B33 
 One of these parts is oné-ninik. ==: 
 
 22. How many ninths are there in the whole of 1 thing? 
 
 23. Stephen paid 3-ninths of all his money for a slate, 
 and 6-ninths for a blank-book. How much had he left? 
 
 24. Which is the greater part, l-eighth, or 1-ninth? 
 
 | 
 
 Divided now into 10 equal parts. = 33 3 3 Ss SS Ss SS Ss SS 
 
 i 
 
 © 
 =] 
 ae) 
 io) 
 um) 
 ot 
 — 
 @) 
 io) 
 oO 
 0" 
 rat) 
 rt 
 er 
 ior 
 te 
 2 
 _ 
 far) 
 on 
 Oo 
 ay 
 ~— 
 ao 
 | 
 I 
 
 cost 4-tenths, what part of 1 dollar will they both cost? 
 27. Which is the greater part, 1-ninth, or 1-tenth? 
 
 Remark 1st. It appears fromthe examples above, that, 
 ONE-HALF of any thing, is one of two equal parts of the 
 thing;—-ONE-THIRD of any thing, is one of three equal 
 parts of the thing;—ONE-FOURTH of any thing, is one of 
 four equal parts of the thing; and so on. att 
 
 Remark 2nd. The greater the number of parts 1s, into 
 which any thing is divided, the smaller the parts are. 
 
46 ORAL ARITHMETIC. VL 
 
 Section 2. 
 
 Note to Teachers. One object in this section is, to lead the pupil to apply 
 correctly the terms expressing fractional parts. Every answer, therefore, must 
 be given in a vulgar fraction, unreduced. For example, two fourths is the 
 answer which must be given to the 3d question. The books to be closed dur- 
 ing the recitation of this section. 
 
 1. If we divide any thing into 2 equal parts, and take 
 
 away 1 of the parts, how f a 
 much of the thing is left ? —_—— 
 
 . If we divide any thing into 3 equal parts, and take 
 fia ofthe parts, how — 
 Oe of the thing is left? ——_ 
 
 . If we divide any thing into 4 equal parts, and take 
 rae: 2 of the parts, how set eae 
 
 Se 
 Seen ee 
 
 ~ mouch of the thing is left ? : ss 
 
 4. If we divide any thing into 5 SNe parts, and take 
 away 3 of the parts, how 
 much of the thing is left ? 
 
 5. If we divide any thing into 6 spiel parts, and take 
 away Ri OL ine par tS, now eo 
 much of the thing is left ? 
 
 6. If we divide any thing into 7 equal parts, and take 
 
 away 2 of the parts, how = SS SS SSS 
 much of the thing is left? it =e 
 
 . If we divide any thing into 8 eae parts, and take 
 nus 5 of the parts, how bi 
 much of the thing is left ? 
 
 if we divide any thing into 9 ii parts, and take 
 Riri: 3 of the parts, how pen 
 iia of the thing is left? 
 
 . If we divide any pate into + ian parts, and take 
 a 4 of the parts, how ~—7—7 > 
 much of the thing is left ? 
 
 10. Into how many parts must any adie be ‘divided 
 so that 1 part shall be 1-eleventh ?—Into how many, so 
 that 1 part shall be 1-twelfth ?—1-thirteenth ? 
 
BB, FRACTIONS. AY 
 
 Section 3. 
 
 Note to Teachers. The Jearners may be referred to Remark 1st. under 
 the first section of examples in this chapter, for a correct form of expression 
 to be adopted in answering the Ist., 4th., 7th., and other similar questions in 
 this section. Books to be closed during the recitation of this section. 
 
 1. What is meant ‘by one-half of any thing? 
 
 _ 2. Suppose you have I-half of 1 dollar;—what part 
 of a dollar more must you gét, to make up 1 dollar? 
 
 3. How many halves are equal to a whole one? 
 
 4. What is meant by one-third of any thing ? 
 
 5. If I should cut 1 orange into thirds, and give you 
 2-thirds of it, what part of an orange would you still want, 
 to make up 1 orange by joining the parts together ? 
 
 6. How many thirds are equal to a whole one? 
 
 7. What is meant by one-fourth of any thing? 
 
 8. Suppose you have 1-fourth of 1 dollar,—what part 
 of a dollar must you get, to make up 1 dollar? 
 
 9. How many fourths are equal to a whole one? 
 
 10. What is meant by one-fifth of any thing? 
 
 11. If I should cut 1 apple into fifths, and give you 
 4-fifths of it, what part of an apple would you still want, 
 to make up 1 apple by Joining the parts together ? 
 
 -12. How many fifths are equal to a whole one? 
 
 13. What is meant by one-sixth of any thing? 
 
 14. If I own 2-sixths of 1 acre of land, and I wish to 
 own 1 acre, what part of 1 acre must I buy? 
 
 15. How many sixths are equal to a whole one? 
 
 16. What is meant by one-seventh of any thing? 
 
 17.-A man bought 4-sevenths of a pound of tea at one 
 shop, and enough more at another shop to make 1 pound. 
 What part of 1 pound did he buy at the last shop? 
 
 __ 18. How many sevenths are equal to a whole one? 
 
 19. What is meant by one-eighth of any thing? 
 
 20. James had 5-eighths of a dollar given him, and he 
 earned 3-eighths more. How much money had he then? 
 
 21. How many eighths are equal to a whole one? 
 
 22. What is meant by one-ninth of any thing? 
 
 23. If I have 7-ninths of 1 acre of land, and I wish to 
 own 1 acre, what part of 1 acre must I buy ? 
 
 24. How many ninths are equal to a whole one? 
 
 7? : (i j 
 
48 ORAL ARITHMETIC. VI. 
 
 25. What is meant by one-tenth of any thing? 
 
 26. Suppose you have 8-tenths of 1 dollar, what part 
 of a dollar must you get, to make up 1 dollar? 
 
 27. How many tenths are equal to a whole one? 
 
 RELATIONS OF NUMBERS. 
 
 Section 4. 
 
 Note to Teachers: The object of this section is, to show the correspondence 
 of the division of a unit, with the division of a collection of units. The ques- 
 tions that inquire, what part of one number is another number, must be answered 
 in the terms of vulgar fractions. » For mstance,—the answers required in the 
 9th example are,—I i is 1-fourth of 4; 2 is 2-fourths of 4; 3 is 3-fourths of 4. 
 
 A collection of units is now to be viewed as a single oe therefore. the 
 verb singular will be used thus=3 times 4 is 12. 
 
 1. If 1-half of a sheer of p Pe be poet 1 cent, what 
 is a whole sheet worth? 
 
 2. Suppose 2 cents are lying upon the desk before us; 
 —what part of the 2 cents is 1 cent? 
 
 3.. What part of 2is 1? 
 
 4. If 1-third of a loaf of bread be worth 1 cent, what 
 is 2-thirds of it worth? What is a whole loaf worth ? 
 
 5. Suppose 3 cents are ina pile before us;—what part. 
 
 of the pile is 1 cent? What part of the ne is 2 cents? 
 
 if What part of 3is 1? What part of 3 is 2? 
 
 If 1-fourth of a yard of ribbon cost ccc what will 
 2- nike of a yard cost? What will 3- fourths of a yard 
 cost? What will a whole yard cost? ' 
 
 8. Suppose 4 cents are in a pile before us;—what part . 
 of the pile is 1 cent? is 2 cents? is 3 cents?. 
 
 a) Whatepatt of 44s 1? “is SY ger 
 
 10. If 1-fifth of a barrel of flour be worth 1 » deter: 
 what is 2-fifths of a barrel worth? 3-fifths of a barrel ? 
 4-fifths of a barrel? ..What is 1 barrel worth? 
 
 11. What part of 5is 1? is 2? is 3? is 4? 
 
 12. If 1-sixth of a yardof ribbon cost 1 cent, what will 
 Q-sixths of a yard cost? 38-sixths of a yard? 5-sixths 
 of a yard? What will 1 yard cost? 
 
 13. What part of 6is 1? is 2? is 3? is 4? is 5? 
 
 14. If a horse trot 1 mile in 1-seventh of an hour, how 
 
 # 
 
 many miles will he trot in 2-sevenths of an hour? in, 
 
 6-sevenths of an hour? How many miles in 1 hour? 
 15. What partof7is1? is2? is3? is4? is6? 
 
 ’ 
 
Mie. RELATIONS OF NUMBERS. 49 
 
 16. If 1-eighth of a bar of silver be worth 1 dollar, 
 what is 3-eighths of the bar worth? What is 5-eighths 
 of the bar worth? What is the whéle bar worth? 
 
 17. What partof 8isl? is2? Is 3? is5?.is 7? 
 
 18. If 1-ninth of a pound of sugar cost 1 cent, what 
 will 2-ninths of a pound cost ? What will 8-ninths of a 
 pound? What will 1 pound cost? 
 
 19. What partof 9isl? is2? is 4? is 6? is 8? 
 
 20. If a man can build.1 rod of fence in 1-tenth of a 
 day, how many rods can he build in 4-tenths of a day? 
 in Grtenths of a day? How many rods in 1 day ? 
 
 21. Whatpartof 10is1? is2? is3? isd? is6? 
 
 Secrion 5. 
 
 1. A carpenter having sawed a board into halves, finds 
 by measuring, that 1-half of the board is 2 feet long. 
 How long was the whole board? 
 
 2. Suppose 2 is 1-half of some number,—what is the 
 whole of the number ? , ) 
 
 3. If 1-half of a pound of rice be worth 3 cents, what 
 is a whole pound worth? 
 
 4. Sis 1-half of what number? 4 is 1-half of what 
 number? 7 is d-half of what number? 
 
 5. How many times 1-half of any number will make 
 the whole number ? 
 
 6. There is’ just room for 2 boys to sit upon 1-third 
 of a certain board... What number of boys could sit up- 
 on the whole of that board? 
 
 7. Suppose 2 is 1-third of some number,—what is the 
 whole of the number 
 
 8. If 1-third of a box of raisins be worth 3 dollars, 
 what is the whole box worth? 
 
 9, 3 is 1-third of what number? 4 is 1-third of what 
 number? 6 is 1-third of what number? — ‘ 
 
 10. How many times 1-third of any number will make 
 the whole number ? 
 
 11. If 1-fourth of a yard of broad-cloth cost 2 dollars, 
 what will a yard cost? 
 
 12. 2 is 1-fourth of what number ? 
 Solution. 2 is 1-fourth of 4 times 2. 4 times 2 is 8. 
 E 
 
50 /ORAL ARITHMETIC. VI. 
 
 13. If a ship sail 3 miles in 1-fourth of an hour, how 
 many miles will she sail in an hour? 
 
 14. 3 is 1-fourth of what number? 4 is 1-fourth of 
 what number? 10 is 1-fourth of what number ? 
 
 15. How many times 1-fourth of any number will make 
 the whole number ? 
 
 16. 3 men reaped 1-fifth of a field of wheat in a day. 
 What number of men would have reaped the whole field ? 
 
 Solution. If 3 men reaped 1-fifth, 5 times 3 men 
 would have reaped 5-fifths, or the whole. 
 
 17. If 1-fifth of a pound of loaf sugar be worth 4 cents, 
 what is 1 pound worth? 
 18. 4 is 1-fifth of what number? 5 is 1-fifth of what 
 number? 8 is 1-fifth of what number ? 
 
 19. How many times 1-fifth of any number will make 
 the whole number? 
 
 20. 4 sheets of paper is 1-sixth of a quire. How 
 many sheets are there in a quire? 
 
 21. 4is 1-sixth of what number? 2is 1-sixth of what 
 number? 3 is 1-sixth of what number ? 
 
 22. How many times 1-sixth of any number will make 
 the whole number ? 
 
 23. If 1-seventh of a ton of hay be worth 2 dollars, 
 what is a whole ton worth? 
 
 24. 2is 1-seventh of what number? 3 is 1-seventh 
 of what number? 9 is 1-seventh of what number? 
 
 25. 5 is l-eighth of what number? 3 is 1-ninth of 
 what number? 6 is 1-tenth of what number ? 
 
 Section 6. 
 
 1. Ifa yard of cloth be worth 2 dollars, what is 1 half 
 of a yard worth? What is 1-half of 2? 
 
 Observation. Since you: know that t-half of 2 is 1, 
 you will perceive, that 1-half of any other number must 
 be as many times 1 as there are twos in the number. 
 
 2. What is Il-half of 4°? of 12? of 18? 
 
 3. If a bar of silver weigh 3 pounds, what will 1-third — 
 of it weigh? What is 1-third of 3? 
 
 Observation. Here notice, that 1-third of any number 
 
 _ is aS many times 1, as there are threes in the number. 
 
6. RELATIONS OF NUMBERS. 51 
 
 > 
 
 4. If a peck of oats cost 9 cents what will 1-third of 
 a peck cost? What is 1-third of 9? 
 
 5. What is 1-third of 6? of 15? of 24? 
 
 6. If a man earn 4 shillings in 1 day, how much does 
 he earn in 1-fourth of a day? What is 1-fourth of 4? 
 
 Observation. Here notice that 1-fourth of any number 
 is of many times 1, as there are fours in the number ? 
 
 . If a pound Apitdisins cost 20 cents, what will 1-fourth 
 
 aft a Wound cost? What is 1-fourth of 20? 
 
 8. What is 1-fourth of 8? of 28? of 64? 
 
 9. Ifa yard of cambric if? 5 dimes, what will 1-fifth 
 of a yard cost?) What is 1-fifth of 5? 
 
 10. If 35 drums of figs will pay for a hogshead of su- 
 gar, how many drums will pay for 1-fifth ofa hogshead ? 
 
 11. What is 1-fifth of 835? of 26? of 40? 
 
 12. If a man earn 6 dollars in a week, how much does 
 
 . he earn in I-sixth of a week? What iS 1-sixth of 6? 
 
 13. Suppose writing paper costs 24 cents a quire;— 
 what will be the price of 1-sixth of a quire? 
 
 Solution., Ifa quire cost 24 cents, I-sixth of a quire 
 will cost 1-sixth of 24 cents. 1-sixth of 24 is 4. 
 
 14. What is l-sixth of 12? of 36? of 48? 
 
 15. What number of days is 1-seventh of a week ? 
 
 16. If you eat 21 meals in a week, Ay many do you 
 an y 1-seventh of a week, or 1 da 
 
 . What is 1-seventh of 14? of. « ? of 56? 
 
 ee If a melon weigh 8 pounds, what is the weight of 
 l-eighth of it? What is l-eighth of 8? 
 
 19. If a yard of silver wire cost 32 cents, what will © 
 1-eighth of a yard cost? 
 
 20. What is l-eighth of 16? of 32? of 64? 
 
 21. If a drum of figs weigh 9 pounds, what is the 
 weight of 1-ninth of a drum? What is 1-ninth of 9? 
 
 22. Suppose a watch-chain consists of 18 links;—how 
 many links are there in 1-ninth of the chain ? 
 
 23. What is I-ninth of 18? of 36?. of 72? 
 
 .24. What number of cents is 1-tenth of a dime? 
 
 25. If a chest of Souchong tea be worth 30 dollars, 
 what is 1-tenth of a chest worth? 
 
 26. What is I-tenth of 30? of 50? of 100? 
 
5 ORAL ARITHMETIC. VI. 
 
 SecTION 7. 
 
 Note to Teachers. In solving the following questions, the learner should 
 first state what proportional part of the number to be divided will be the answer, 
 and thence proceed to find the answer in the denomination of the dividend.— 
 See solution under example 2d. 
 
 1. If any number of oranges should be divided equally 
 between 2 boys, what part of the number would 1 boy 
 receive? What part would 1 boy receive, if the oranges 
 were dividedamong3boys? 4boys? 5boys? 6boys? 
 Tbhoys? 8boys? O9boys? 10boys? 
 
 2. 5 sailors received 40 dollars, which they divided 
 equally among them. What did 1 sailor receive ? 
 
 Solution. If 5 sailors received 40 dollars, 1 sailor 
 must have received 1-fifth of 40 dollars. 1-fifth of 40 
 dollars is 8 dollars ? 
 
 3. 2 fishermen caught 24 fishes, which they shared 
 equally. How many was each man’s share? 
 
 4. Ifa traveller spend 28 dollars in travelling a week, 
 how much does he spend a day? . 
 
 5. A farmer can keep 9 cows on 36 acres of land:— 
 how many acres would it take to keep 1 cow? 
 
 6. 3men have a bill of 30 dollars to pay:—how much, 
 must each man pay? 
 
 7. If a stage run 42 miles in 6 hours, what distance 
 does it run in 1 hour? 
 
 8. Suppose 8 dozen of biscuit to be worth 72 cents ;— 
 what is the value of 1 dozen? 
 
 9. A tailor made 10 cloaks of 40 yards of cloth. How 
 many yards did he put into each cloak ? 
 
 Section 8. 
 
 Note to Teachers. Require the learner, as in the last section, to com- 
 mence every solution by stating what proportional part of the given number is 
 to be taken for the answer. 
 
 1. If aman can travel 35 miles in a day, what distance 
 can he travel in 1-seventh of a day? What distance in 
 4-sevenths of a day? 
 
 Solution. If he can travel 35 miles in a day, he can 
 travel 1-seventh of 35 miles in 1-seventh of aday; 1-sev- 
 enth of 35 miles is 5 miles. He can travel 4 times 5 
 miles in 4-sevenths of a day; 4 times 5 miles are 20 miles. 
 
7.8. RELATIONS OF NUMBERS. 53 
 
 2. There are 24 sheets of paper'ina quire. How 
 many sheets are there in 1-eighth of a quire? How many 
 sheets in 3-eighths of a quire? 
 
 3. What is l-eighth of 24? 3-eighths of 247 
 
 Solution. 1-eighth of 24 is 3; 3-eighths is 3 times 3. 
 
 4. If a pound of coffee be worth 15 cents, what is 
 1-third of a pound worth? 2-thirds of a pound? 
 
 5. What is 1-third of 15? 2-thirds of 15? 
 
 6. Ifa bushel of barley cost 50 cents, what does 1-fifth 
 - of a bushel cost? 4-fifths of a bushel? 
 
 7. What is 1-fifth of 50? 4-fifths of 50? 
 
 8. Ifa yard of ribbon cost 28 cents, what, will 1-fourth 
 of a yard cost? 3-fourths of a yard? 
 
 9. What is 1-fourth of 28? 3-fourths of 28? 
 
 10. If an acre of land will produce 30 bushels of rye, 
 how much will 2-sixths of an acre produce? 
 
 Direction. First get what 1-sixth of an acre. will yield. 
 
 11. What is 5-sixths of 30? 
 
 Direction. First get 1-sixth of 30; thence 5-sixths. 
 
 12. If a stage run 81 miles in a day, what number of 
 miles will it run in 7-ninths of a day? 
 
 13. What is 7-ninths of 81? gai’ 
 
 14. There are 100 cents in a dollar. What number 
 of cents are there in 8-tenths of a dollar? 
 
 15. What is 8-tenths of 100? 
 
 16. Albert’s kite line was 32 yards long, and he cut 
 off 2-eighths of it for a fish line. What was the length 
 of the fish line? 
 
 17. Suppose a boy having 42 quills, should give away 
 3-sevenths of them;— how many would he give away ?—. 
 and how many would he have left? | | 
 
 18. A nfan having 40 dollars, paid away 3-eighths of 
 his money for a ton of hay. What was the price of the 
 hay ?—and how many dollars had he left ? 
 
 19. A boy, who had 45 cents, paid away 3-fifths of 
 his money for a quire of paper. What was the price of 
 the paper ?—and how many cents had he left? 
 
 20. If 75 men can build a mile of fence in a day, what 
 number of men must be employed, to build 2-thirds of a 
 mile in the same time : | 
 
 E* 
 
“BA ORAL ARITHMETIC. VI. 
 
 Section 9. 
 
 1. If48 dollars should be divided equally among 8 men, 
 what part of the money,—and what number of dollars 
 would 3 men receive? 
 
 Solution. 3 men would receive 3-eighths of the 
 money. 1-eighth of 48 dollars is 6 dollars; 3-eighths 
 is 3 times 6 dollars, or 18 dollars. 
 
 2. A tierce, holding 42 gallons of molasses, has been 
 emptied into 6 kegs, of equal size. What part of the 
 molasses,—and what number of gallons in 5 kegs ? 
 
 3. What part of 6 is 5? What is 5-sixths of 42? 
 
 4. Ifa piece of broad-cloth containing 30 yards will 
 make ten suits of clothes, what part of pi piece,—and 
 what number of yards, will make 6 suits ? 
 
 5. What part of 10 is 6? What is 6-tenths of 30? 
 
 6. 5 girls had 15 oranges, which they shared equally: 
 2 of the girls gave their shares to a sick woman: What 
 part of 15 oranges did the woman receive ?—and what 
 number of oranges did she receive ? 
 
 7. What part of 5 is 2? What is 2-fifths of 15:? 
 
 8. 7 men owned 56 sheep in company, and 3 of the 
 men took out their shares. What part of the flock,—and 
 what number of sheep did they take out? 
 
 9. What part of 7 is 3? What is 3-sevenths of 56 ?. 
 
 10. If 4 men eat 28 biscuit in a day, what part of 28 
 biscuit,—and what number of biscuit will 2 men eat ? 
 
 11. What part of 4is 2? Whatis 2-fourths of 28? 
 
 12. 3 brothers owned 60 acres of land together, and 
 the 2 younger sold their shares to the oldest. What part 
 of the land,---and how many acres did they sell ? 
 
 13. What part of 3is 2? What is 2-thirds of 60: > 
 
 Section 10. 
 
 1. If 3 men can fell 18 trees in a day, how many trees 
 can 4 men fell in the same time? 
 
 Solution. If 3 men can fell 18 trees in a day, 1 man 
 can fell 1-third of 18 trees, or 6 trees; 4 men can fell 4 
 times 6 trees, or 24 trees. 
 
 2. What is 4 times 1-third of 18 ? 
 
 Solution. 1 third of 18 is 6: then 4 times 6 is 24. 
 
9.10. 11. RELATIONS OF NUMBERS. 55 
 
 3. If 5 men will cut 20 cords of wood in a day, how 
 many cords will 3 men cut in the same time ? 
 
 4. What is 3 times 1-fifth of 20? 
 
 5. If 4 barrels of flour cost 24 dollars, how sill will 
 7 barrels cost, at the same price per barrel ? 
 
 What is 7 times 1-fourth of 24 ? 
 
 If 2 boats will carry 16 passengers across the river, 
 
 hil many passengers will 5 boats carry? 
 
 8. What is 5 times 1-half of 16? 
 
 9. Suppose a'cooper can make 27 barrels in 9 days;— 
 how many barrels can he make in 5 days? 
 
 10. What is 5 times I-ninth of 27? 
 
 11. Suppose 6 kegs will hold 36 gallons of molasses ;— 
 what number of gallons will 4 kegs hold? 
 
 12. What is 4 times 1-sixth of 36? 
 
 13. If 8 soldiers eat 56 pounds of beef in a week, how 
 many pounds will 9 soldiers eat ina week? — 
 
 14. What is 9 times 1-eighth of 56? 
 
 15. If a workman can earn 49 dollars in7 weeks, how 
 many dollars can he earn in 6 weeks ? 
 
 16. What is 6 times 1l-seventh of 49 ? : 
 
 17. If 10 casks of claret wine cost 80 dollars, what 
 would be the price of 8 casks of the same wine? 
 
 Section ll. 
 
 1. Suppose there are 10 links in 2-thirds of a watch 
 chain;—how many links are there in 1-third of the chain? 
 How many links in the whole chain? 
 
 Solution. If there be 10 links in 2-thirds of the chain, 
 there is 1-half of 10 links in 1-third of it: 1-half of 10 
 is 5.——If 5 links be 1-third of the chain, there are 3 
 times 5 links in the chain: 3 times 5 is 15. 
 
 2. 10 is 2-thirds of what number? 
 
 3. If 3-fourths of a pound of honey cost 15 cents, what 
 will 1-fourth cost? What will a pound cost? 
 
 4. 15 is 3-fourths of what number ? 
 
 Solution. Since 15 is 3-fourths of the required num- 
 ber, 1-third of 15 must be 1-fourth of thenumber: 1-third | 
 of 15is5. If 5 be 1-fourth of the number, 4 times 5, OF 
 20, is the whole number. 
 
56 ORAL ARITHMETIC. wVI). 
 
 5. If 2-fifths of a bushel of oats cost 18 cents, what 
 will 1-fifth cost? What will a bushel cost? 
 
 i 18 is 2-fifths of what number ? 
 
 If 4-sevenths of a kite line be 36 yards long, how 
 (oat is 1-seventh? How long is the whole line? 
 
 a 36 is 4-sevenths of what number ? 
 
 . If 8-sixths of a chest of tea cost 21 dollars, what 
 will ‘L-sixth cost? What will a whole chest-cost ? 
 
 10. 21 is 3-sixths of what number ? 
 
 11. If 5-eighths of a pipe of wine be worth 30 dollars, 
 what is the value of the whole pipe? 
 
 Direction. First find what 1-eighth 1s worth. 
 
 12. 30 is 5-eighths of what number? 
 
 13. If a man can earn 40 cents by working 4-sevenths 
 of a day, how much can he earn by working a whole day? 
 
 14. 40 is 4-sevenths ef what number? 
 
 15. If 7-ninths of a hogshead of sugar be worth 49 
 dollars, what is the whole hogshead worth? 
 
 16. 49 is 7-ninths of what number? 
 
 17. If a rail-road car run 24 miles in 8-tenths of an 
 hour, what distance will it run in an hour? 
 
 18. 24 is 8-tenths of what number? 
 
 19. Henry is 10 years old; and his age is equal to 
 5-sixths of Andrew’s age. How old is Andrew? 
 
 Suggestion. You may perceive that 1-fifth of Pei : 
 age must be equal to 1-sixth of Andrew’s age. 
 
 20. 10 is 5-sixths of what number ? 
 
 21. If 21 workmen will perform 3-fifths of a certain 
 piece of work in a week, what number of workmen 
 would it take to perform the whole work in a week? 
 
 22. 21 is 3-fifths of what number ? 
 
 23. A coach-man purchased a horse, and after paying 
 
 5-eighths of the price, he still owed 30 dollars. What 
 was the price of the horse ? 
 
 Solution.’ If he paid 5-eighths of the — price, the 30 
 dollars, which he still owed, was 3-eighths of the price. 
 80 dollars being 3-eighths of the price, 1-third of 30 dol- 
 lars, or 10 dollars, is 1-eighth. 10 dollars being 1-eighth 
 of the price, 8 times 10 dollars is the price. 
 
 24. 30 is 3-eighths of what number ? 
 
12, RELATIONS OF NUMBERS. : 57 
 
 25. If 2-fifths be taken from the whole of any thing, 
 how many fifths are there left ? 
 
 26. While George was fishing, a pickerel broke off 
 2-fifths of his line; he then had 12 feet of the line left. 
 How long was his line at first? 
 
 27. Suppose a laborer can earn 60 cents a day, by 
 working 5-sixths of the time;—how much could he earn 
 by working constantly ? 
 
 28. After 3-sevenths of a cask of wine had leaked out, 
 the owner drew off the remainder, and found there were 
 42-gallons. How many gallons had he lost ? 
 
 29. A farmer improved 3-ninths of his farm in tillage, 
 appropriated 4-ninths to pasturage, and had 18 acres of 
 wood-land. How many acres had he in all? 
 
 30. 2-eighths of Edward’s books are bound in leather, 
 3-eighths of them in marble paper, and 15 of them in 
 blue paper. How many has he of each description ? 
 
 Section 12. 
 
 Note to Teachers. This section embraces all the operations taught in the 
 preceding sections of this chapter. Prefixed to each example, is the number of 
 the section in which the operation involved in the example is taught. If the 
 pupil fail in any part of this section, he should be put back to the section whose 
 number is prefixed to the example in which he fails. 
 
 REVIEW. 
 
 1. (§1.) James found 4-eighths of a dollar, and earn- 
 ed 5-eighths. How much money had he then? 
 
 2. (§2.) If we divide any thing into 6 equal parts, 
 and take away 4 parts, how much of the thing is left? 
 
 3. (§ 3.) If you have 7-ninths of 1 dollar, what part 
 of a dollar must you get to make up 1 dollar ? 
 
 4. (§4.) Ifa man can walk 1 mile in 1-fourth of an 
 hour, how many miles can he walk in 1 hour? 
 
 5. (§4.) What part of 6 is 5? What part of 7 is 3° 
 What part of 10 is 4? What part of 18 is 7? 
 
 6. (§ 5.) If 1-fourth of an acre of land will produce 
 9 bushels of corn, how much will 1 acre produce? 
 
 7. (§5.) If 1-eighth of a barrel of beef be allowed 
 to 3 soldiers for a weck’s provision, what number of 
 soldiers will 1 barrel supply for a week ? 
 
 {he 
 
58 ORAL ARITHMETIC. VI. 
 
 8. (§ 6.) Suppose a yard of gold wire to be worth 
 28 dollars;—what is 1-fourth of a yard worth? 
 
 9. (§7.) If 50 day’s work is to be done by 5 men, 
 how many day’s work must each man perform ? 
 
 10. (§8.) If one pound of Hyson tea be worth 96 
 cents, what is 7-eighths of a pound worth? 
 
 11. ($ 9.) A company of 14 men gave 84 dollars for 
 a boat. What part of 84 dollars did 5 men pay? 
 
 12. (§ 9.) If 8 dollars will buy 72 pounds of brown 
 sugar, how many pounds will 6 dollars buy? 
 
 13. (§ 10.) Suppose 18 yards of cloth will make 6 ~ 
 
 coats;—how many yards are required for 10 coats? 
 
 14. (§ 11.) If 5-ninths of a yard of cotton cambric be 
 worth 50 cents, what is the value of one yard? 
 
 15. (§ 11.) Suppose a man by working constantly 
 can dig 40 bushels of potatoes in a day,—how many 
 bushels will he dig, if he be idle 2-fifths of the day ? 
 
 FRACTIONS AND RELATIONS. 
 
 Section 13. 
 
 'Noteto Teachers. The remainders, that will arise in the several examples 
 of division in this section, must be expressed in the language of fractions. See 
 answers under exainples 4th. and 8th. If the learner should not readily un- 
 derstand the process of converting the remainders into fractions, he may be 
 referred to section 4th. in this chapter, aud, after reviewing the examples 
 therein, may return iminediately to this section. 
 
 1. How much cloth, at 2 dollars a yard, can I buy for 
 1 dollar? How much for 3 dollars? 
 
 2. What part of 2 is 1? How many times 2 in 3? 
 
 3. How many yards of ribbon, at 2 cents a yard, can 
 you buy for? cents ?>—I mean,— how many whole yards, 
 and what part of another yard can you buy? 
 
 4. How many times 2 in 7 ?—I mean,—how many 
 twos are there, and what part of 1 more two, in 7? | 
 
 Solution. 2is contained in7,3 times, and 1 over: the 
 1 over is 1-half of another time 2. Ans. 2 and 1-half. 
 
 5. How many times 2in 9? in 12? in 13? 
 
 6. How much wine, at 3 dollars a gallon, can I buy 
 for 1 dollar? How much for 4 dollars ? 
 
 7. What part of 3is 1? How many times 3 in 4? 
 
13. FRACTIONS AND RELATIONS. 59 
 
 If a girl by setting types can earn 1 dollar in 3 
 ae how much can she earn in 20 days? 
 
 Solution. She can earn as many dollars as there are 
 threes in 20. 3 in 20,6 times and 2 over; the 2 over is 
 2-thirds of another three. Ans. 6 dollars and 2-thirds. 
 
 9. How many times 3in4? in 16? in 20? 
 
 10. If a pound of lead cost 4 cents, how much can I 
 buy for 1 cent? How many pounds for 9 cents? 
 
 11. If it take a man 1 hour to walk 4 miles, how many 
 hours will it take him to walk 15 miles? 
 
 12. How many times 4 in 9? in 15? in 34? 
 
 13. How much coal, at 5 dollars a ton, can be bought 
 
 *for 1 dollar? How much for 7 dollars ? 
 
 14. How many hogsheads of salt, at 5 dollars a hogs- 
 head, can be bought for 44 dollars 
 
 15. How many times 5 in 7? in 44? in 58? 
 
 16. How much ribbon, at 6 cents a yard, can you buy 
 for 10 cents? How much for 37 cents? 
 
 17. If it cost 6 cents a mile to ride in the stage, what 
 number of miles can you ride for 50 cents ? 
 
 18. How many times 6 in 10?, in 50? in 45? 
 
 19. tte much sugar, at 7 cents a pounds can I buy 
 for 9 cents? How much for 52 cents? 
 
 20. How many pounds of shot, at the rate of 7 cents a 
 pound, must be sold for 34 cents? 
 
 21. How many times 7 in 9? in 52? in 34? 
 
 22. How much hay, at 8 dollars a ton must be sold for 
 9 dollars? How much for 29 dollars ? 
 
 23. How many pounds of honey, a the rate of 8 cents 
 a pound, must be sold for 77 cents? | 7 
 
 24. How many times 8 in9? in29? in77?. 
 
 25. At 9 cents a pound, how much cheese must be 
 sold for 13 cents? How much for 31 cents? 
 
 26. If a man work for 9 cents an hour, how many 
 hours will it take him to earn 64 cents? 
 
 27. How many times 9in 13? in 31? in 64? 
 
 28. How much sugar, at 10 cents a pound, ean be 
 bought for 12 cents? How much for 64 cents ?- 
 
 29. Ifa workman can build 10 rods ofifence in'1 day; 
 how many days will it take him to build 48 rods? 
 
60 ORAL ARITHMETIC. Vi. 
 
 30. How many times 10 in 12? in 64?. in 48? 
 
 31. How much rice at 3 cents a pound, must be given 
 for 4 quarts of milk at 5 cents a quart ? 
 
 Direction. First find the value of 4 quarts of milk. 
 
 32. How many times 3 in 4 times 5? 
 
 Direction. First find how much 4 times 5 is. 
 
 33. How many pounds of flour at 4 cents a pound, 
 must be given for 5 pounds of honey at 7 cents a pound ? 
 
 34. How many times 4 in 5 times 7 ? 
 
 35. What quantity of butter at 10 cents a pound, will 
 pay for 6 combs at 8 cents apiece ? 
 
 36. If an active man earn 7 shillings a day, and a lazy 
 
 man 4 shillings, how many days must the lazy man work, — 
 
 to pay the active man for working 6 days ? 
 
 37. How many times 4 in 6 times 7 ? 
 
 38. How many yards of cloth at 5 dollars a yard, will 
 pay for 3 boxes of raisins at 9 dollars a box? 
 
 39. How many times 5 in 3 times 9? 
 
 40. What quantity of corn at 6 dimes a bushel, will 
 pay for 11 bushels of oats at 3 dimes a bushel ? 
 
 41, _ How many times 6 in 11 times 3? 
 
 Section 14. 
 
 Note to Teachers. 'The learners must now be led to observe, that the ex- 
 pressions, l-half, 1-third, 2-thirds, &c.areto be understood,—I-half of one, 
 1-third of one, 2-thirds of one, &c. in all cases where the number, of which 
 the fraction indicates a part, is not stated. 
 
 1. If I should cut each of 3 sheets of paper into halves, — 
 
 how many halves would they make ? 
 
 Solution. In 1 sheet there are 2-halves,—in 3 sheets 
 there are 3 times 2-halves, or 6-halves. ; 
 2. How many halves are there in 1? in2? in 3? 
 
 3. If I had 4 sheets and 1-half of a sheet of paper, how 
 many boys could I supply with half a sheet apiece ? 
 
 4. How many halves are there in 4 and 1-half? 
 
 5. If 2 slate pencils should each of them be broken 
 into thirds, how many thirds would they make ? 
 
 6. How many thirds are therein 1? in2? in4? 
 
 7. Suppose I had 3 pencils and 2-thirds, how many 
 
 mie could I supply with 1-third of a pencil each? 
 8. How many thirds are there in 3 and @-thinds £ 
 
 i 
 
 ~ 
 
14. FRACTIONS AND RELATIONS. 61 
 
 9. If 1-fourth of a yard of cloth will make a satchel, 
 how many satchels will 2 yards make ? 
 
 10. How many fourths are there inl? in2? in 3? 
 
 11. How many quires of paper, at 1-fourth of a dollar 
 a quire, can you buy for 3 dollars and 2-fourths ? 
 
 Solution. Ican buy as many quires as there are fourths 
 of a dollar, in 3 dollars and 2-fourths. In 1 dollar there 
 are 4-fourths,—in 3 dollars, 3 times 4-fourths, or 12- 
 fourths: 12-fourths plus 2-fourths is 14-fourths. 
 
 12. If a carpenter use 1-fifth of a board to make 1 book 
 shelf, how many book shelves can he make of a whole 
 board? of 2 whole boards? of 2 boards and 3-fifths ? 
 of 4 boards and 1-fifth ? 
 
 13. How many fifths are there ini? in2?. in2and 
 3-fifths ? In 4 and 1-fifth ? 
 
 14. If a bunch of quills cost 1-sixth of a dollar, how 
 many bunches can you buy for 1 dollar? for 1 dollar 
 and 5-sixths? for 3 dollars and 2-sixths ? 
 
 15. How many sixths are there inl? in 1 and 5- 
 sixths? in 3 and 2-sixths ? 
 
 16. Ifa stage run | mile in 1-seventh of an hour, what 
 number of miles will it run in 1 hour? in 2 hours and 
 1-seventh? in 4 hours and 4-sevenths ? 
 
 17. How many sevenths are there inl? in 2 and 
 l-seventh? in 4 and 4-sevenths ? 
 
 18. At l-eighth of a dollar a yard, how many yards ee 
 
 of ribbon can I buy for 1 dollar and 3-eighths? for 2 
 dollars? for 5 dollars and 7-eighths ? 
 
 19. How many eighths are there in 1 and 3-eighths ? 
 in 2? in 5 and 7-eighths ° 
 
 20. How many ninths are there inl? ini and 4- 
 ninths? im 2? in 2.and7-ninths? in 6? 
 
 21. How many tenths are there inl? in 4? in 3 
 and 5-tenths? in 5? in 8 and 3-tenths? 
 
 22. A laborer earned 9 dollars and a half, working at 
 half a dollar a day. How many days did he work ? 
 
 23. If 1-eighth of a yard of cloth cost a dollar, what 
 ee vi yards and 6-eighths cost? 
 
 If a man earn.a dollar in 1-sixth of a week, how 
 hak can he earn in 8 weeks and 4-sixths ? 
 F 
 
62 ORAL ARITHMETIC. VI. 
 
 25. If it take 1-fifth of a pound of fur to make a hat, 
 how many hats can be made of 4 pounds and 2-fifths ? 
 
 26. If 1-fourth of a yard of lace cost a dollar, how 
 much will 5 yards and 3-fourths of a yard cost ? 
 
 Section 15. 
 
 1. How many dollars in 2-halves of a dollar? in 3- 
 halves of a dollar? Ans. 1 dollar. 1 dollar and 1-half. 
 ' 2. How many dollars are there in 4,half dollars? «in 
 5 half dollars? in 9 half dollars ? Poe 
 
 3. How many whole ones in 2-halves? in 3-halves? 
 in 4-halves? in 5-halves? in 9-halves? 
 
 4. What will 13 pencils cost, at half a cent apiece ? 
 
 5. If 3-thirds of an orange be put together they make 
 up 1 orange. Now, if you had 6-thirds of an orange, 
 how many oranges could you make up? if you had 
 10-thirds? if you had 17-thirds ? 
 
 6. How many whole ones in 6-thirds? in 10-thirds? 
 in 17-thirds ? | 
 
 7. What cost 26 quills, at 1-third of a cent apiece? 
 
 Solution. If 1 quill cost 1-third of a cent, 26 quills 
 will cost 26-thirds of a cent. 26-thirds of a cent are as 
 many cents as 3 is contained times in 26. 3 in 26, 8 
 times and 2 over. Ans. & cents and 2-thirds. 
 
 8. How many whole apples could you:make up, if 
 you had 5-fourths of an apple? 14-fourths of an apple ? 
 
 9. What cost 31 cups, at 1-fourth of a dollar apiece ? 
 
 10. How many-whole ones in 5-fourths? in 14- 
 fourths? in 31-fourths ? 
 
 11. If 1 cotton ball be given for 1-fifth of a yard of 
 galloon, how much galloon must be given for 8 cotton 
 balls? for 17 cotton balls? for 44 cotton balls ? 
 
 _ 12. How many whole ones are there in 8-fifths? in 
 {7-fifths ? in 44-fifths ?- 
 
 13. If a quire of paper cost 1-sixth of a dollar, what 
 is the cost of 12 quires? 17 quires?. 19 quires? 
 
 14. How many whole ones in 12-sixths? in 17- 
 sixths? in 19-sixths ? | | : 
 
 15. How many whole ones in 18-sevenths? in 24- 
 tenths? in 3l-eighths? in 47-ninths? in 25-fourths ? 
 
16. 17. FRACTIONS AND RELATIONS. 63 
 
 Section 16. 
 
 1. Ellen paid, for the Young Ladies’ Class Book, 3- 
 fourths of a dollar; for the Boston School Atlas, 2-fourths 
 of adollar; and for the National Spelling- Book, 1-fourth 
 of a dollar. What did the whole cost? 
 
 2. How much is 3-fourths and 2-fourths and 1-fourth ? 
 
 3. A trader sold a piece of cloth for 19 dollars and 
 5-eighths, and a hat for 4 dollars and 7-eighths. How 
 many dollars did he receive for both? 
 
 Solution. 19 dols. plus 4 dols. are 23 dols. 5- 
 eighths of a dol. plus 7-eighths of a dol. are 12-eighths 
 of a dol., equal to 1 dol. and 4-eighths. Then, 23 dols. 
 plus 1 dol. and 4-eighths are 24 dols. and 4-eighths. 
 
 4. A traveller rode 31 miles and 3-fifths in the fore- 
 noon, and 25 miles and 4-fifths in the afternoon. How 
 many miles did he ride in the whole day ? 
 ~ 5, What is 31 and 3-fifths plus 25 and 4-fifths ? 
 
 6. A trader bought some goods for 64 dollars and 5- 
 sevenths, and paid 5 dollars and 3-sevenths for the post- 
 age of them. What was the whole expense? 
 
 “7. What is 64 and 5-sevenths plus 5 and 3-sevenths ? 
 
 8. A gentleman paid 33 dollars and 7-tenths for 
 some cloth, and 11 dollars and 6-tenths for having it 
 made into a suit of clothes. What did the suit cost ? 
 
 9. What is 33 and 7-tenths plus 11 and 6-tenths ? 
 
 10. What is‘16 and 6-ninths plus 8 and 5-ninths? 
 
 11. What is 40 and 5-sixths plus 41 and 3-sixths? © 
 
 Section 17, 
 
 1. Suppose a rail-road car to run 2-thirds of a mile 
 in 1 minute, what distance will it run in 10 minutes ? 
 
 Solution. In 10 minutes it will run 10 times 2-thirds 
 of a mile, or 20-thirds of a mile. 20-thirds of a mile are 
 equal to 6 miles and 2-thirds. 
 
 2. If 3-fourths of a gallon of wine leak out of a cask 
 in 1 hour, how much will leak out in 7 hours? | 
 
 3. How many whole ones in 7 times 3-fourths ? 
 
 4. If a yard of cambric muslin cost 4-fifths, of, a: dol- 
 
 lar, how much will 9 yards cost ? 
 5. How many whole ones in 9 times: 4-fifths ? 
 
64 ORAL ARITHMETIC. VI. 
 
 6. Suppose a man to eat 5-sixths of a pound of beef 
 ' .in one day, how many pounds will he eat in 5 se 
 7. How many whole ones in 5 times 5-sixths ¢ | 
 
 8. If 3-sevenths of a pound of gunpowder tea cost 1 
 dollar, how many pounds can I buy for $ dollars ? 
 
 9. How many whole ones in 8 times 3-sevenths ¢ 
 
 10. Suppose 5-eighths of a yard of cloth will make a 
 vest, how many yards will it take to make 6 vests ? 
 
 11. How many whole ones in 6 times 5-eighths ? 
 
 12. If 1 quire of letter paper be worth 4-ninths of a 
 dollar, how many dollars are 7 quires worth? 
 
 13. How many whole ones in 7 times 4-ninths? 
 
 14. Suppose a man to walk 1 mile in 2-tenths of an 
 hour, what time will it take him to walk 9 miles ? 
 
 15. How many whole ones in 9 times 2-tenths ? 
 
 Section 18. 
 
 1. What will 6 yards of broad-cloth cost, at 7 dollars 
 and 3-eighths of a dollar per yard? 
 
 Solution. 6 yards will cost 6 times 7 dollars and 3- 
 eighths. 6 times 7 dollars are 42 dollars. 6 times 3- 
 eighths are 18-eighths, equal to 2 and 2-eighths. Then, 
 42 dollars plus 2 dollars and 2-eighths are 44 dollars 
 and 2-eighths. } 
 
 2. What will 4 hundred-weight of sugar cost, at 9 
 dollars and 2-fifths per hundred-weight ? 
 
 3. What is 4 times 9 and 2-fifths ° 
 
 4. Suppose a ship to sail 10 miles and I-half in one 
 hour, what distance will it sail in 7 hours ? 
 
 5. What is 7 times 10 and 1-half? 
 
 6. If a horse eat 1 bushel and 9-tenths of a bushel of 
 oats in a week, how much will he eat in 4.weeks? 
 
 7. What is 4 times 1 and 9-tenths ? 
 
 8. If 1 dime will buy 3 yards and 2-thirds of a yard 
 of ribbon, how many yards will 6 dimes buy ? 
 
 9. What is 6 times 3 and 2-thirds ? 
 
 10. Suppose the price of coal at the mine, is 3 dol- 
 Jars a ton, and the freight of it to the city is 3-fourths 
 of a dollar a tof, what will 10 tons cost at the city ? 
 
 11. What is 10 times 3 and 3-fourths ? 
 
18.19. FRACTIONS AND RELATIONS. 65 
 
 12. Suppose a boat goes 10 miles and 5-sixths of a 
 mile in 1 hour; what distance will it go in 8 hours ? 
 
 13. What is 8 times 10 and 5-sixths ? 
 
 14. If 3 yards and 7-eighths of cloth will make a 
 cloak, how many yards will it take to make 5 cloaks ? 
 
 15. What is 5 times 3 and 7-eighths ? 
 
 Section 19. 
 
 1. If 1-fifth of a chest of tea be worth 6 dollars and 
 7-eighths, what is a whole chest worth? 
 
 Solution. A whole chest is worth 5 times as much 
 
 1-fifth of a chest. 5 times 6 dollars are 30 dollars; 
 5 times 7-eighths of a dollar are 35-eighths of a dollar, 
 or 4 dollars and 3-eighths. 30 dollars plus 4 dollars 
 and 3-eighths are 34 dollars and 3-eighths. 
 
 2.°6 and 7-eighths is 1-fifth of what number? 
 
 3. Suppose I-ninth of a kite line to be 5 yards and 
 3-fourths of a yard long,—how long is the whole line ? 
 
 4. 5 and 3-fourths is 1-ninth of what number ? 
 
 5. A young man being asked his age, answered indi- 
 rectly, that 1-third of his age was 7 years and 2-sixths 
 of a year. What was his age? 
 
 7 and 2-sixths is 1-third of what number ? 
 
 Suppose a man can build 8 rods and 2-fifths of a 
 roi of wall in 1-sixth of a w eek,—how many rods. can 
 he build in a whole week ? 
 
 8. 3 and 2-fifths is 1-sixth of what number ? 
 
 9. If 1-tenth of a bushel of corn be worth 6 cents and 
 1-fourth of a cent, what is a bushel worth ? 
 
 10. 6 and 1-fourth is 1-tenth of what number ? 
 
 11. 1-fourth of Edmund’s kite line measures 8 yards 
 and 3-sevenths of a yard. How long is the line? 
 
 12. 8 and 3-sevenths is 1-fourth of what number ?, 
 
 13. If 1-half of a yard of lace cost 3 dollars and 4- 
 fifths of a dollar, what will a yard cost ? 
 
 14. 3 and 4-fifths is 1-half of what number ? 
 
 15. Suppose that l-seventh of an acre of land will 
 produce 6 bushels and 7-ninths of a bushel of barley; ~ 
 how many bushels will an acre produce? 
 
 16. 6 and 7-ninths is 1-seventh of what number ? $ 
 
 R* 
 
66 ORAL ARITHMETIC. VI. 
 
 Section 20. 
 
 2. Here we see 1-third{ 
 of 2 boards, placed over 2- 
 
 thirds of 1 board. Is itnot | = 
 plain, that 1-third of ba v : == 
 boards together, is equal to | 
 
 2-thirds ot 1 board? [| bea 
 
 3. 1-third of 2 is equal to what part ‘of 1? 
 
 4. There were 3 boys, who had 1 dollar apiece; and 
 each boy gave a decrepit soldier 1-fourth of his money. 
 What part of 1 dollar did the poor soldier receive ? 
 
 5. Here, we see 1-fourth : 
 of 3 boards placed over 3- 
 fourths of 1 board. Sup- 
 pose the fourths seen in the 
 3 boards should be placed 
 together end to end—Is it |___+___i _ 
 not plain, they would make a= 
 E-foarthis of board Hoa = 
 
 6. 1-fourth of 3 is equal to what part of Ll? 
 
 7. | have 4 oranges to divide among 5 boys.—lI first 
 cut 1 orange into fifths, and give each boy t-fifth; and 
 thus I proceed, dividing 1 orange at a time, until they 
 are all divided. Now, what part of a whole orange can 
 each boy make up, by joining his fifths together ? 
 
 8. 1-fifth of 4 is equal to what part of 1? 
 
 9. If 1 melon were divided equally among 6 boys, 
 what part of 1 melon would 1 boy receive? If 2 melons 
 were divided, how many sixths would 1 boy receive ? 
 
 10. 1-sixth of 2 is equal to what part of 1? 
 
 11. If 3 barrels of flour were divided equally among 
 7 men, how much would 1 man receive? 
 
 12. 1-seventh of 3 is equal to what part of I? 
 
 13. If 3 pounds of beef were divided equally among 
 8 soldiers, what part of a pound would I soldier get ? 
 
 14. l-eighth of 5 is equal to. what part of 1? 
 
 LSS = 
 —_—_—_—_—_ 
 
20. 21, FRACTIONS AND RELATIONS. 67 
 
 15. An ostler has 2 bushels of oats to divide among 
 9 horses;—how much must he give to each horse? 
 
 16. 1-ninth of 2 is equal to what part of 1? 
 
 ' 17. If 7 dollars were divided equally among 10 men, 
 what part of 1 dollar would each man have? 
 
 18. 1-tenth of 7 is equal to what part of 1? 
 
 19. 1-fourth of 2 is equal to what part of 1? 
 
 20. 1-sixth of 5 is equal to what part of 1? 
 
 21. 1-eighth of 3 is equal to what part of 1? 
 
 22. There were 36 oranges in a basket and Albert 
 was directed to take 1-fourth of them. Accordingly he 
 cut 1-fourth out of every orange, and took it to himself. 
 How many fourths of an orange did he get? He then 
 joined his fourths together, to make them into whole 
 oranges ;—how many whole ones had he? 
 
 23. 1-fourth of 36 is equal to how many fourths of 1? 
 —equal to how many whole ones? . 
 
 24. In another basket there were also 36 oranges, 
 and Benjamin was directed to take 1-fourth of them. 
 But, instead of cutting 1-fourth out of every orange, as 
 Albert did, he took 1 orange from every 4 in the basket. 
 How many oranges did Benjamin get? 
 
 25. Now tell me which is the most;—1-fourth of 36, 
 or 36-fourths of 1? 
 
 26. 1-half of 10 dollars is equal to how many halves 
 of 1 dollar?—equal to how many dollars? 
 
 27. 1-third of 18 oranges is equal to how many thirds 
 of 1 orange ?—equal to how many whole oranges? 
 
 28. 1-fifth of 17 oranges is equal to how many fifths 
 of 1 orange?—equal to how many whole oranges? 
 
 29. 1-sixth of 42 is equal to how many sixths of 1? 
 —equal to how many whole ones? 
 
 30. 1-seventh of 59 is equal to how many sevenths. 
 of 1?—equal to how many whole ones? 
 
 Section 2]. 
 1, If a chest of green tea be worth 27 dollars, what 
 is 1-fourth of it worth? 
 Solution. 1-fourth of the tea is worth 1-fourth of 27 
 dollars. 1-fourth of 27 dollars is 6 dollars, there being 
 
 IA 
 
68 | . ORAL ARITHMETIC. VI. 
 
 8 dollars over. 1-fourth of 3 dollars is equal to 3-fourths 
 of 1 dollar. 6 dollars plus 3-fourths of a dollar are 6 
 dollars and 3-fourths...... Or, we may say,—One fourth 
 of 27 dollars,is 27-fourths of 1 dollar; equal to 6 dollars 
 and 3-fourths. 
 
 2.. What is 1-fourth of 27° 
 
 3. 3 men bought a barrel of sugar for 23 dollars, and 
 divided it equally among them, each man taking 1-third 
 of the sugar, and paying 1-third of the price. How 
 many dollars did each man pay? 
 
 4. What is 1-third of 23? 
 
 5. Suppose a family to eat 26 loaves of bread in a 
 week;—what number of loaves would the family con- 
 sume in l-seventh of a week, or 1 day? 
 
 6. What is 1-seventh of 26? 
 
 7. Suppose 48 bushels of wheat are to be divided 
 among 5 men; how much will 1 man receive ? ° 
 
 8. What is 1-fifth of 48? 
 
 9. 6 men purchased a boat for 27 dollars: each man 
 paid 1-sixth of the money, and owned 1-sixth of the 
 boat. How many dollars did 1 man pay? 
 
 10. What is 1-sixth of 27° 
 
 11. Suppose a bag of coffee to weigh 65 pounds;— 
 ils is the weight of 1-ninth of it? 
 
 . What is I-ninth of 65? 
 
 is If it will take a man 60: days to: clear a piece of 
 wood-land, in what time will he clear 1-eiglith. of it? 
 
 14. What is 1- -eighth of 60? 
 
 15. A sailor was cast upon a desolate island, and 
 subsisted 10 days upon 34 biscuit, eating an equal quan- 
 tity each day. How many did he eat each day? 
 
 16. What is 1-tenth of 34? 
 
 17. Ifa bar of silver, that is worth 37 dollars, should 
 be cut into 3 equal parts, how many dollars would 1 of © 
 the Wa be worth? 
 
 . What is 1-third of 37? 
 
 in, Suppose a party of 9 gold hunters find a quantity 
 of ore, which i is worth 88 dollars; what! is the value of 
 each man’s share? 
 
 20. What is 1-ninth of 88? | 
 
21, FRACTIONS AND RELATIONS. 69 
 
 21. If it take a man 4 months to earn 38 dollars, how 
 much does he earn in 1 month? 
 
 22. What is 1-fourth of 38? ae 
 
 23. If 6 barrels of superfine flour cost 35 dollars, 
 what is the price of 1 barrel of it? 
 
 24. What is l-sixth of 35? 
 
 25. Suppose 39 bushels of corn to grow upon 1 
 acre;—how much corn will 1-fifth of an acre produce? 
 
 26. What is 1-fifth of 39? 
 
 27. If 2 dollars will pay for 13 pounds of butter, how 
 many pounds can be bought for 1 dollar? 
 
 28. What is 1-half of 13? 
 
 29. If 8 dollars will pay for 78 pounds of cheese, how 
 many pounds will 1 dollar pay for? 
 
 30. What is l-eighth of 78? 
 
 31. Suppose 10 men drink 55 gallons of beer in a 
 month;— how much will 1 man drink in a month? 
 
 32. What is 1-tenth of 55? 
 
 33. Suppose 7 acres of land to produce 60 dollars’ 
 worth of hay;—what is the value of the hay which 1 
 acre of the land produces? 
 
 34. What is l-seventh of 60? 
 
 35. If 1 man can clear a piece of wood-land in 29 
 days, in what number of days would 5 men clear it? 
 
 Instruction. Consider that 5 men can do 5 times as 
 much work in a day, as 1 man can do: consequently, it 
 will take 5 men only 1-fifth of the time that it will take 
 1 man to clear the land. 
 
 36. How many days will it take 7 men to do a piece 
 of work, that 1 man can do in 46 days? 
 
 37. If 1 man will drink a firkin of beer in 50 days, 
 how many days will it last 6 men? 
 
 38. Suppose 24 men can hoe apiece of corn in 1 day; 
 what number of men must be employed to hoe it in8 days? 
 
 Suggestion. Each man, that shall be employed, can 
 do 8 times as much work in 8 days, as he can in | day. 
 
 39. If 40 men can build a wallin 1 day, what number 
 of men must be employed to build it in 4 days? 
 
 40. If a cistern can be discharged by 1 faucet in 19 : 
 
 hours, in what time can it be discharged by 3 faucets? 
 
70 ORAL ARITHMETIC. VIL 
 
 Section 22. 
 
 1. Ifasmith can make 5 cups from 12 ounces of silver, 
 how much silver is required to make 3 cups? 
 
 Direction. First find how much silver would make 
 1 cup; then, 3 times that quantity would make 3 cups. 
 
 2. What is 3 times 1-fifth of 12? 
 
 Solution. 1-fifth of 12 is2 and 2-fifths. 3 times 2 
 is 6; 3 times 2-fifths is 6-fifths, or 1 and 1-fifth. Then 
 2 plus 1 and 1-fifth is 3 and 1-fifth. 
 
 8. If 22 bushels of wheat will make 4 barrels of flour, 
 how much wheat will make 6 barrels of flour? 
 
 4. What is 6 times 1-fourth of 22? | 
 
 5. Suppose the equipments for 8 soldiers to cost’75 dol- 
 lars; what would be the expense of equipping 5 soldiers? 
 
 6. What is 5 times l-eighth 6f 75? 
 
 7. If 29 tons of hay will keep 9 horses through the 
 winter, how many tons would 6 horses require? 
 
 8. What is 6 times 1-ninth of 29? 
 
 9. Suppose 7 acres of pasturage to be worth 65 dol- 
 lars; what is 3 acres of the same pasturage worth? 
 
 10. What is 3 times 1-seventh of 65? 
 
 11. If 8 acres of pasturage will keep 35 sheep, how 
 many acres would be sufficient to keep 6 sheep? 
 
 12. What is 6 times l-eighth of 35? , 
 
 13. Suppose a man to eat 50 pounds of beef in 8 
 weeks; what number of pounds would he eat in 9 weeks? 
 
 14. What is 9 times l-eighth of 50? 
 
 15. If it take 36 yards of broad-cloth to make 10 suits 
 of clothes, how many yards would make 4 suits? 
 
 16. What is 4 times 1-tenth of 36? 
 
 17. A trader gave 59 dollars for 9 barrels of flour, and 
 sold 3 barrels of it, at the same price per barrel that he 
 gave. For how much did he sell the 3 barrels? 
 
 18. What is 3 times 1-ninth of 59? 
 
 19, If 6 pounds of brown sugar be sold for 52 cents, 
 _.. what would be the price of 5 pounds of it? 
 
 20. What is 5 times 1-sixth of 52? 
 
 21. If 8 scholars use 18 quires of paper in a month, 
 how many quires would 10 scholars use in a month? 
 
 . 2a. What is 10 times I-eighth of 18? 
 
22) 23, FRACTIONS AND RELATIONS. 71 
 
 23. Suppose a stage to run 58 miles in 7 hours; what 
 distance does it run in 6 hours? 
 
 24. What is 6 times 1-seventh of 58? 
 
 25. Ifa mill grind 17 bushels of corn in 2 hours, howe 
 many bushels will it grind in 7 hours ? 
 
 26. What is 7 bikes 1-half of 17? 
 
 27. Albert paid 61 cents for 9 writing-books, and 
 William bought 7 writing-books, paying at the same rate. 
 ron much did William’s books cost him ? 
 
 . What is 7 times 1-ninth of 61? 
 
 20. Suppose a hunter gets 8 pounds of gunpowder in 
 exchange for 44 pounds of venison; how many pounds 
 of venison must he give for 10 pounds of powder ? 
 
 30. What is 10 times 1-eighth of 44? 
 
 Section 23. 
 
 1. When writing paper is sold at 20 cents a quire, 
 ee is the price of L-third of a quire ? 
 If 1-third of a quire of paper is worth 6 cents and 
 2- thirds. what is 2-thirds of a quire worth ? 
 3 What j is 1-third of 20? 2-thirds of 20? 
 4. Suppose a yard of ribbon to be worth 23 cents; 
 what is 1-fourth of a yard worth? 
 5. If 1-fourth of a yard of ribbon is worth 5 cents 
 and 3-fourths, what is 2-fourths of a yard worth? 
 Solution. 2-fourths of a yard is worth 2 times 5 
 cents and 3-fourths. 2 times 5 cents are 10 cents; 2 
 times 3-fourths of a cent are 6-fourths of a cent, or 1 
 cent and 2-fourths. 10 cents plus l-cent and 2-fourths, 
 are 11 cents and 2-fourths. 
 6. What is 1-fourth of 23? 2-fourths of 23? 
 7. Suppose a pound of white sugar to be worth 23 
 ae what is 1-fifth of a pound worth? 
 If 1-fifth of a pound of sugar is worth 4 cents and 
 scfifths, what is 3-fifths of a pound worth? 
 9. What is 1-fifth of 23? 3-fifths of 23°? 6° ~~ 
 Solution. 1-fifth of 23 is 4 and 3-fifths...... 3-fifths 
 of 23 is 8 times 4 and 3-fifths. 3 times 4 is 12: 3 times 
 3-fifths are 9-fifths, or 1 and 4-fifths. 12 plus 1 and 4- 
 fifths is 18 and 4-fifths. = he 
 
 ZY 
 
 ¥ 
 
a 
 4 
 % 
 % 
 
 %, 
 
 72 ‘\  ORAL ARITHMETIC. VI. 
 
 10. Suppose a man can walk 34 miles in a day, what 
 
 distance can he walk in 1-sixth of a day ? 
 11. If a man walk 5 miles and 4-sixths, in 1-sixth of 
 
 _ day, how far will he walk in 5-sixths of a day? 
 
 12. What is 1-sixth of 834? 5-sixths of 34? f 
 
 13. Suppose a bushel of corn to be worth 65 cents; 
 what is 1-seventh of a bushel worth? - 
 
 14. If 1-seventh of a bushel of corn cost 9 cents and 
 2-sevenths, what will 3-sevenths of a bushel cost ? 
 
 15. What is 1-seventh of 65? 3-sevenths of 65? 
 
 16. Suppose 1 dollar will pay for 35 pounds of rice; 
 how much rice will 1-eighth of a dollar buy ? 
 
 17. If 1-eighth of a dollar will buy 4 pounds and 3- 
 eighths, how much will 5-eighths of a dollar buy ? 
 
 18. What is l-eighth of 35? 5-eighths of 35? 
 
 19. Suppose a man earns 70 cents a day; how much 
 does he earn in I-ninth of a day ? 
 
 20. If a man can earn 7 cents and 7-ninths, in 1-ninth 
 of a day, how much can he earn in 8-ninths of a day ? 
 
 21. What is l-ninth of 70? 98-ninths of 70? 
 
 22. Suppose an acre of land will produce 43 bushels 
 of oats; what will 1-tenth of an acre produce ? 
 
 23. If 1-tenth of an acre produce 4 bushels and 3- 
 tenths, what will 7-tenths of an acre produce? 
 
 24. What is l-tenth of 43? 7-tenths of 45? > 
 
 25. If a yard of cloth will pay for 30 pounds of cheese, 
 how many pounds will 3-fourths of a yard buy? 
 
 Direction. First find how many pounds 1-fourth of 
 a yard will pay for. 
 
 26. A farmer sold 4-fifths of a ton of hay, for oats, 
 allowing 32 bushels of oats to be worth the same as a 
 ton of hay. How many bushels of oats did he receive ? 
 27. What is 4-fifths of 32? 
 
 28. Suppose 1 dollar will pay for 38 pounds of rice; 
 for how many pounds will 8-tenths of a dollar pay ? 
 
 29. What is 8-tenths of 38? 
 
 _ $0. A man bought a piece of land containing 1 acre 
 and 4-sixths, and paid at the rate of 40 dollars per acre. 
 How much did he pay for the land? . 
 
 31. What is 40 plus 4-sixths of 40? 
 
24, | FRACTIONS AND RELATIONS, 73 
 
 Section 24. 
 
 1. Suppose 3-fourths of a yard of flannel to cost 32 
 cents; what does 1-fourth of a yard cost? What would 
 a yard cost? 
 
 Solution. If 3-fourths of a yard cost 32 cents, 1- 
 fourth of a yard costs 1-third of 32 cents. 1-third of 
 32 cents is 10 cents and 2-thirds of a cent...... 4-fourths, 
 or a whole yard would cost 4 times 10 cents and 2-thirds. 
 4 times 10 cents are 40 cents; 4 times 2-thirds are 8- 
 thirds, equal to 2 and 2-thirds. Then, 40 cents plus 
 2 cents and 2-thirds are 42 cents and 2-thirds. 
 
 2. 32 is 3-fourths of what number? 
 
 Solution. Since 32 is 3-fourths of the number, 1- 
 third of 32 is 1-fourth of it. 1-third of 32 is 10 and 
 2-thirds. 4 times 10 and 2-thirds are 42 and 2-thirds. 
 
 3. If 2-fifths of an acre of land will produce 9 bushels 
 of rye; how many bushels will 1-fifth of an acre produce ? 
 How many bushels will an acre produce? 
 
 4. 9 is 2-fifths of what number ? 
 
 Instruction. Observe, that 1-half of 9 must be 1-fifth 
 of the required number. 
 
 5. If aman drink 6 gallons of beer in 5-sixths of a 
 month, how many gallons does he drink in 1-sixth of a 
 month? How many gallons will he drink in a month? 
 
 6. 6 is 5-sixths of what number ? 
 
 7. A man, who spends 43 cents a day, finds his ex- 
 penses to be 5-sevenths of his wages. What is. 1-sev- 
 enth of his wages? What is the whole of his wages ? 
 
 8. 42 is 5-sevenths of what number ? 
 
 9. If 5-eighths of a dollar will pay for 24 pounds of 
 flour, how many pounds will 1-eighth of a dollar pay 
 for? How many pounds will a dollar pay for ? 
 
 10. 24 is 5-eighths of ;what number? 
 
 11. Suppose 6 gallons of wine to leak from a cask in 
 
 8-ninths of an hour; how much will leak out in 1-ninth 
 of an hour? How many gallons in 1 hour? 
 
 12. 6 is 8-ninths of what number ? 
 
 13. If 4-tenths of a yard of cloth be worth 33 éents, 
 how much is 1 yard worth ? 
 
 Direction. First find what 1-tenth of a yard is worth. 
 
 pe 
 
74 “ORAL ARITHMETIC. VI. 
 
 14. If 3-eighths of a bale of cotton be worth 17 dol- 
 lars, what is the whole bale worth? 
 
 15. A laborer spent 80 cents a day, and still saved 
 3-sevenths of his wages. How much was his wages? 
 
 16. Suppose that I have read 5-ninths of the pages in 
 a certain book, and there are 35 pages more to be read; 
 —how many pages are there in the book ? 
 
 NOTATION. OF FRACTIONS. 
 
 Learners will now attend to the meaning of the words, 
 FRACTION, DENOMINATOR, and NUMERATOR. 
 
 A Fraction is any part of one. For example, one-half 
 of an orange is a fraction of 1 orange; three- -fourths of 
 an orange is another fraction of 1 orange. 
 
 In this book, fractions have been expressed by a 
 number joined with a word; thus, 4-ninths. Fractions 
 are commonly expressed by two numbers, standing one 
 above the other, with a line between them; thus, 3 jar, 
 
 1 one- 2 two- 1 one- 4 four- 3 three- 
 3 third, 3 thirds, 6 sixth, 5 fifths, 9 ninths. 
 
 17. What fraction is expressed, when there is a 4 with 
 aloverit? 7 with 2over it? 8 with 5 over it? 10 
 with 6 over it? 
 
 18. Which is the greater fraction; 3 or 
 yore? torqy? tory? a 
 
 19. Uae is the greater fraction; 4} or 3? £or 2? 
 
 Zori? ¢ord? for ¥;? 
 
 The Pe cine of a fraction, is the number of equal 
 parts into which a whole one is ivitad. For example, 
 if a whole orange be divided into 4 equal parts, the de- 
 nominator is 4; the parts being denominated fourths. 
 
 The Numerator of a fraction is the number which 
 shows how many of the equal parts the fraction ex- 
 presses. For example, the fraction ¢ expresses 3 of 
 the four equal parts; therefore 3 is the numerator. 
 
 20. What numerator, and what denominator, would 
 express the fraction, four-fifths? two-eighths?  six- 
 ninths ? one-fifteenth? _five-eighteenths ? 
 
 wh 
 wv 
 Uy 
 jo) 
 Le 3 
 ool 
 vw 
 
 1) aes 8 
 Vey 
 f 
 
OB. Me FRACTIONS. — "5 
 
 When the numerator is equal to the denominator, 
 thus, 4, then the fraction is equal to 1; as 4-fourths of 
 an orange, when joined together make 1 orange. 
 
 When the numerator is greater than the denominator, 
 thus, 3, then the fraction is equal to as many times 1 as 
 the denominator is contained times in the numerator. 
 
 21. How many times 1, [how many whole ones], in 3? 
 in’? milf? in??? info? ings? 
 
 92. How many tities ». the what bibles over, ing? 
 
 né? in$? inl?? in %? in 23? 
 
 93. Where have you observed the numeratce of a frac- 
 tion to stand;— above, or below the denominator ? 
 
 Section 25. 
 
 1. James has 3 of a dollar, and Hen his 2 4 of a 
 dollar :— which wi them has the most money ? 
 
 Compare the fraction 4 —= 
 with other fractions. a 
 2. 4 is equal to how ma- a =a 
 
 ny fourths : ? st 
 
 3. 518 Paue to how ma- 
 ny sixths ? 
 
 4. 51s equal'to how ma- 
 ny eighths ?. 
 
 5. 41s equal to how ma- 
 ny tenths? 
 
 6. 4 is equal to how many twelfths? h 
 teenths ? how.many twentieths? 
 
 7. Edward broke a slate pencil into 3 equal pieces, 
 and Albert broke one into 6 equal pieces. How many 
 of Albert’s pieces were ae to 1 of Edward’s pieces ? 
 
 Compare the fraction } 
 with other fractions. C= 
 
 8. 41s pauat to how ma- [~~ ae | 
 ny sixths ? 3 
 
 9. $ is equal to how ma- | 
 ny ninths ? 
 
 many six- 
 
"6 ORAL ARITHMETIC. ey VE 
 
 10. 4.is equal to how many twelfths? how many 
 eighteenths? how many thirtieths? 
 
 Suggestion. 4 of 1 is equal to 4 of 12-twelfths. 
 
 11. 4 is equal to how many eighths? how many 
 twelfths? how many sixteenths ? 
 
 12. 41s equal to how many tenths? how many twen- 
 tieths? how many twenty-fifths ? | 
 
 13. + is A to how many twelfths? how many 
 Keture. how many thirtieths ? 
 
 14. 4 is eae to how many fourteenths ? how many 
 twenty-eighths ?. how many thirty-fifths ? 
 
 15. + is equal to how many twentieths ? 
 
 Solution. + is Sia to 34,5 7 1s equal to 3 times 5- 
 Wrenn eu, which is 42. 
 
 16. $ is equal to how ial twelfths ? 
 
 17. A boy, who had 2.of an orange, cut each fifth 
 into 2 parts, (making ent: his brother gave him 
 
 %.,70 more. What fraction of an orange had he at last? 
 
 * 18. Into how many parts must you cuta sivth of an 
 Punting to make the parts eighteenths?...... Why? 
 99. 21s it ene to how many eighteenths ? 
 
 20. ee 4 to fourteenths, ae then add +; to it. 
 
 21. Z is equal to how many twenty- -fourths ae 
 
 22. Change 3 to eighteenths, and then take + from it. 
 
 Section 26. 
 
 1, What is meant bya Fraction : ?,—_—How is a frac- 
 tion commonly expressed ?. What is the Denomina- 
 tor of a fraction ?. What is the Wumerator ? 
 
 2. If the denominator of a fraction be 9, and the 
 numerator 7, how should these numbers be written ?— 
 and what would the fraction be called in reading it ? 
 
 3. Suppose two fractions have numerators alike, and 
 denominators different—which is the greater fraction— 
 that with the greater, or the smaller denominator ? 
 
 4. Suppose two fractions have denominators alike, 
 and numerators different—which is the greater fraction 
 —that with the greater, or the smaller numerator ? - 
 
f 
 
 26. 27. 
 
 Observation. - 
 
 FRACTIONS. 
 
 77 
 
 If an orange be cut into eighths, and 
 
 then 4 of the eighths be joined together, these 4-eighths 
 
 become 1-half of an orange. 
 
 sia reduced to its lowest terms, is 4 
 
 . Reduce ¢ to its lowest at, is, find the 
 aa numerator: and denon ingae that will express. a 
 quantity equal to 3. 
 2 to its lowest terms. 
 
 6. Reduce 
 7. Reduce 
 
 8. Reduce 2 
 
 9. Reduce 
 
 3 
 6 
 
 2 
 8 
 ry 
 9 
 
 Observation. 
 
 est terms. 75- 
 
 to its lowest terms. 
 to its lowest terms. 
 to its lowest terms. 
 
 Reduce 
 Reduce 
 Reduce ¢. 
 
 And ngps the fraction, 4 4, 
 
 B]D ay}ede 
 
 A fraction is reduced, by dividing the 
 numerator and denominator by any number, which will 
 divide them both without a remainder. Fo 
 we reduce ° thus; 2 in 6, 3 times, 3 is a new numera- 
 tor: 2 in 10, 5 times, 5 is a new denominator. 
 
 10. Reduce cms of the following eg mons to its low- 
 
 LBS 
 io: E aoe 
 
 0m <a 
 ike a is: 5: 
 
 Lt: ape hed s knife cost -3; of a dollar, 
 
 cost 3% of a dollar. 
 12. Reduce the fractions, + and 
 
 terms, and then add them together. 
 13. Reduce, and then add together, 4 20 an 
 14. Reduce, and then add together, $2 an 
 
 Section 27. 
 1. 4 of a water melon was divided equally among 3 
 aha © What part of the whole melon did 1 si receive ? 
 4 of }$ is equal to 
 ited part of 1? 
 f 1 be divided into 3 equal ae it will 
 
 Solution. 
 
 I 
 
 r example, 
 
 30... 
 rs 
 
 and John’ s 
 
 Whose knife cost the most? - 
 7% to their lowest 
 
 On 
 
 dk. 
 and 
 
 in 
 Dy? 
 
 take 12 such birt to make a whole one. 
 [- times z is qq-] 
 
 3. What ona of a whole one is ¢ of $? 
 If 4 of an orange ure cut into 5 equal 
 
 ae Ie 
 3 Of Fis 45 
 
 - Illustration. 
 
 Thefefore, 
 
 parts, it would tape 6 times 5 such parts to make a 
 
 whole orange. — 
 
 Operation. 
 G* 
 
 - times 4 is 30° 
 
Ex 
 SS 
 
 3 an \. ORAL ARITHMETIC. VI. 
 
 4. What jartof 1 is 3 of 3? “ua > Zoft? tof 
 2? lofi? Pots? 
 me 181 | ddllans {18 and } } dotlans} be divided equal- 
 
 ly abi 3 men, what will ne man receive ? 
 
 6. bien is + of wei 
 
 Sol. 4 of 18 j is 6; 4 of tis 4; 6 plus +4 is 644. 
 
 if What is } of 304? 4 of 245? 4g of 184? 
 
 8. A boy, having @ 4 “af a dollar, ade of his money 
 for a knife. What part of a dollar did he pay? 
 
 9. 2 of 4 is equal to (77 = ae 
 what part of Ie ia 
 
 li 
 a 
 
 Solution. One-fourth of $ is equal to 3; three-fourths’ 
 
 of 4 is equal 3 times 3, which is 3. 
 10. What partof lisfof4? fof? ¢ofd? of 
 BP ROLF! FOF Yo 
 11. A girl having $ of a dollar, paid 5 of her money 
 fora book. What part of a dollar did shie pays ? 
 
 12. 3 of + is equal to =a = 
 what part of 1? [i oe 
 
 said 1 of one-fourth [5 times z is g] is equal to 
 
 4; 4 of 3 is 3 times 3, which Is 2. 
 
 Ts 
 
 13. Which i is eh - pihenie fraction of a dollar,—# of 4 
 
 of a dollar,— or, 4 of 3 of a dollar? 
 14. ane gee zof $? dof ge i 
 of $2? tof? tof 
 15. if 4 andes ae 16 be made from 122 yards of 
 cloth, how many yards must be put into each’ cloak? . 
 
 16. What 5 + of 123? E 
 Solution. {of 12is 3: tof diss, tof 2 iss: 
 
 then 3 plus #5 age 335° 
 17; What is $ of 2032 4 of 24? $of 457? 
 18. A boy having 2 of a dottad: paid 3 of his money 
 for a book. What part of a dollar did he pay? 
 19. # of 2 is equal to [7 
 what ‘part of 1? : pill __ HEEB 
 ihe t ony + is cal to 73; Goffis yy; Z of F 
 is 2 times 7, or yy. fz is equal to 4. 
 
 * rc aie 
 
98, - FRACTIONS. (all ”2 79. : 
 
 20. 2 of anacre of land was divided i to a pa lot? 
 and a dasileher bought 3 of the fot. hat part of an 
 acre did he buy ? 
 
 Direction. First find what part of an acre there was 
 in one lot;—then, what part in 3 lots. 
 
 21. What part of 1 is 3 of 2? 
 
 Direction. First find what part of a whole one 4 of 
 4 is;— then find 4 of 2,—and then 2 of 2. 
 
 22. Whatpart of lis Zof2? Zoff? 4o0f2? 2of. 
 2? 2of #?. 2 of 2? . 
 at ewe a O8 G p 
 
 23. A merchant, who owned 3 of a ship, sold 4 of 
 his share. What part of the ship did he sell ? 
 
 24. What partof lis?ofZ? Zof3? Zof2? Aof 
 3? Sof $2? tof? 
 
 25. Suppose a piece of broad-cloth to contain 322 
 yards ;— how many yards are there in 3 of the piece? 
 
 Direction. First find 2 of 32; then fing. 70,3. 3 
 
 26. What is 2 of 2022." 3 of 368? 4. of 403? $ of | 
 35%? Sof 542? 345 of 502? 
 
 Section 28. 
 
 1. Suppose you have 4 of an orange and 4 of an or-' 
 ange,—into how many parts must you cut “the third, 
 and into how many “parts the fourth, so that the parts of 
 the third, and of the fourth shall be of one size ? 
 
 We here see, that when 
 1 is divided into 4 parts, 
 and + into 3 parts, the 
 parts are all twelfths. LE te i 
 
 In this example 12 is found to be a Be aah Denomi- 
 nator; and the two fractions $ and 4, become +/; and # 
 
 2. Change 4 and 4 to a common denominator: that a, 
 find how many Bach. a half, and how many a third must 
 be divided into, so that the parts shall be equal: also 
 find how many of these parts would make a whole one. 
 
 Observation. If two denominators be multiplied to- 
 
 gether they will produce a common denominator. 
 
 rast 
 iy, f: ¢ Ay on 
 Pe: a) ah gst r 
 t Ae 
 
A 
 
 a 
 
 a 
 qs 
 
 Y 
 
 aS 
 
 3 . 
 % 
 
 i 
 4 
 
 8. Change 
 
 /, ee 
 <7 _/ORAL ARITHMETIC. VI. 
 
 3. Change 4 and 4 $ toa common denominator. 
 Solution. 3 times ‘5 is 15, the ss acgion aE 
 of is 753; 4 0f 42 is 3. Answer. + and 3. 
 
 4. Change } and 1 i a Foon denominator. 
 
 5: Change 4 and ¢ to a common denominator. 
 
 6. Change nd to a common denominator. 
 
 7. Change ~ and 4 to a common denominator. 
 
 and 4 to a common denominator. 
 
 and + and + to twelfths. 
 
 and 4 1 and 2 to twenty-fourths. 
 
 11. Change ainda ‘anda +s to thirtieths. 
 
 12. Change $ and s to a common denominator. 
 Solution. 4 times 5 is 20, the common denominator. | 
 of 2° is 34; Libf 30 ts Mun atid BUM, 
 
 13. Change 4 and ¢ to a common denominator. 
 
 14. Change aba 1 to a common denominator. 
 
 15. Change 2 and 4 to a common denominator. 
 
 16. Change 4 and 4 to a common denominator. 
 
 17. Change # and # to a common denominator. 
 
 18. Change 2 and § to a common denominator. 
 
 19. Change 3 and 2 to a common denominator. 
 
 20. Change $ and ¢ to a common denominator. 
 
 21. How much is ¢ and # added together. 
 
 Solution, if is equal to 28. ’ oa # is $3: ie equal to 
 
 Co] Ca] fie a] Col oS 
 
 9. Change 
 10. Change 
 
 BH Of w]e 
 
 LO]D | UT] oho WH aun w]do “a 
 
 ss and#is ge. 3% Plus 25 2 is 28, A to +4 
 
 22. How mich is 3 aad added feecihtee 
 
 23. How much is 2 and 4 Zac together ? 
 
 24. How much is 2 and 3 added together ? 
 
 25. How much is # and 5 added together ? 
 
 26. How much is 3 and # added together ? 
 
 on 3 and 4 a 7 are how many twelfths? 
 
 28. 2 3 and < , are how many twelfths ? 
 
 29. + and ape >- are how many sixteenths ? 
 
 30. If 4 be an oe 3, how much will remain ? 
 
 ws ~ILo ado Ps 
 
 ; (Oe [7 times 5 is zs]. 7 is equal to 3, # is 3. 
 1 is equal to 75, 2is 33. Then 35 minus 33 is ys. 
 
29, FRACTIONS. | 81 
 
 33. Take 2 from $,—how much remains ? 
 34. Take 2 from ¢,—how much remains? 
 35. Take + from ?,—how much remains ? 
 36. Take 4 from $,—how much remains ? 
 37. Take 3 from 4,—how much remains ? 
 
 Section 29. 
 
 1. A farmer gathered 21% bushels of apples from one 
 tree, and 102 from ano tige® How many bushels did he 
 gather from both trees ? 
 
 Direction. First add together the whole bisttales 
 then change the fractions of a bushel to a common de- 
 nominator and add the new numerators. 
 
 2. Ifa bonnet cost 5# dollars and a’shawl 5 ar dollars, 
 how much do they both cost ? 
 
 3. Ona certain day, I travelled 302 miles in a stage, 
 154 miles in a gig, and 10 miles on horseback. How 
 at, i miles did I travel that Haye ? 
 
 4. A farmer sold a cow for 237 dollars, and a calf for 
 44 dollars. How much did he get for both ? 
 
 5. Three soldiers shared a loaf of bread as follows:— 
 the first man took 4 of it, the second took 4 of it, and 
 the third took the remainder. What part of the loaf did 
 the third soldier get ? : 
 
 6. Three men, A, B > and C, ae to reap a field of 
 wheat— A is to reap 3 3 of it, B +4 of it, and C the re- 
 mainder. What part ‘of the field is C to reap? 
 
 7. A trader, having 2 barrels of flour, sold ¢ of a 
 barrel to one man, and # of a barrel to another man. 
 What part of a barrel had he remaining? 
 
 8. A man, having 10 dollars, paid away 44 dollars 
 for a hat, and 34 dollars for a pair of boots. How 
 many dollars had he left ? 
 
 9. A miller, having 20 bushels of eorn, sold 6% bush- 
 els to one man, and 94 to another. How many bushels 
 
 had he remaining? 
 
 10. A man paid 25¢ dollars for a watch, and 2.3, dol- 
 lars for having it repaired, and then sold it so as to gain 
 3 dollars. For how much did he ie it? 
 
= 
 ce 
 
 82 ORAL ARITHMETIC. VI. 
 
 Section 30. 
 
 2, Suppose! I had 4 oranges,—to how many bor 
 could I give 4 of an orange apiece? 
 
 Direction. Find how many thirds of 1 orange in 4 
 oranges, then find how many times 2-thirds there are. 
 
 2. How many times is } contained in 4? 
 
 Solution. 1 is equal to 3, and 4 is equal to 4 times 
 3 or }°: then 2 is contained in 4, 6 times. 
 
 3." How many pairs of gloves can I buy for 6 dollars, 
 the price being } of a dollar a pair? 
 
 4. How many times 1s } contained in 6? 
 
 5. Suppose a man to walk 1 mile in 3 of an: hour,— 
 what distance will he walk i in 1 hour? 
 
 6. How many times is ¢ ¢ Pantained 3 in 1? 
 
 Solution. 1 is equal toy. % ing, 45 times. 
 
 How many yards of cloth, that is sold for 2 of a 
 
 dollar a yard, can be bought for 4 dollars ? 
 
 8. How many times is 3 contained in 4? 
 
 9. How many pounds of tea, that is sold for 2 of a 
 dollar a pound, can be bought for 44 dollars ? 
 
 10. How many times is 2 contained in 41? 
 
 11. If $ of a barrel of biscuit will last a ship? s crew | 
 week, how many weeks wal 33 barrels last them ? 
 
 12. How many times is 4 Pepitaineds in Sy 33? 
 
 13. How many yards of cloth, at 3 of a dollar per 
 yard, can be bought for $ of a dollar? 
 _ Solution. 4 of a dollar is equal to +% of a dollar; 2 
 of a dollar is equal to 42 of a dollar. As , many yards 
 can be bought as 7% Is contained times in 42 
 
 14. How many times is 4 contained in “ ? 
 
 15. If a man can hoe 4 of a field of corn int day, in in 
 how many days can he hoe # of the field ? 
 
 16. How many times is : contained in }? 
 
 17. How many times is 2 contained in $? 
 
 Direction. Change both fractions to a common de- 
 nominator; then divide one numerator by the other. 
 
 18. How many times is $ contained in 2? 
 19. How many times is 3 contained in 1? 
 4 
 5 
 
 20. How many times is # contained in 3%? 
 
 ¢ 
 
30. 31. FRACTIONS. © 83 
 
 _ 21. Suppose that 6 cloaks are to be made from 223 
 yards of broad-cloth;— what number of yards must be 
 put into each cloak ? 
 
 Solution. Each cloak must contain 1 of 223 yards. 
 1 of 224 is, 3, there being 4% over. 43 j is equal to. 
 4 of tis 3, ‘and 2 4 of Y is 19 times as much, or 2, 
 Then 3 yards plus 37 2 of a yard, are 337 yards. 
 
 22. If 302 pounds of bread will supply a family for 1 
 week, how many pounds will supply the family for 1 day ? 
 
 23. What is 4 of 302? 
 
 ‘24. If 8 yards of cloth cost 512 dollars, what will 1 
 yard cost? What will 3 yards cost? 
 
 25. What 1 is $ of 512? What is 3 of 513? 
 
 Section 3l. 
 
 Note to Teachers. | This section furnishes a test of the learner’s knowledge 
 of the several operations taught since the Review in Section 12. Should the 
 Jearner fail in any of these examples, he must be put back to the section, whose 
 number is prefixed to the example in which the failure appears. 
 
 REVIEW. 
 
 1. (§ 13.) How many hours will it take you to read 
 a book of 75 pages, if you read 9 pages an hour? 
 
 2. (§ 14.) Ifa bushel of oats be given in exchange for 
 4 of a bushel of grass seed, how many bushels of oats 
 must be given for 63 bushels of grass seed? 
 
 3. (§ 15.) If a man drink 4 of ‘a gallon of beer ina 
 day, how many gallons will he drink in 33 days? 
 
 4. (§ 16.) Suppose a watch to cost 17% dollars, and 
 a chain 12 dollars,— what is the cost of both ? 
 
 5. (§ 17.) If 1 quire of letter paper cost 53; of a dol- 
 lar, what will 7 quires cost, at the same rate? 
 
 6. (§.18.) Suppose a fire engine to throw from its 
 pipe, 42 barrels of water in 1 minute,— what number of 
 barrels will it throw in 10 minutes? 
 
 7. (§19.) A farmer sold + of a ton of hay for 35 
 dollars. What is the price of a ton at the same rate ? 
 
 8. (§20.) There were 9 men, who performed a piece 
 of work, for which they received 6 bushels of wheat. 
 What part of a bushel was the share of each man ? 
 
S4 ORAL ARITHMETIC. VI. 
 
 9. (§ 21.) A ship’s crew used 14 casks of water, 
 during a passage of 5 months, from Calcutta to New York. 
 How much did that quantity allow them per month? 
 
 10. (§ 22.) If 7 barrels of flour cost 30 dollars, what 
 will 9 barrels cost at the same rate ? 3 
 
 11. (§ 23.) A man’ purchased a farm, containing 98 
 ~ acres; but not being able to pay for the whole, he sold 
 off =4, of the land. How many acres did he sell? 
 12. (§ 24.) If a mill grind 9 bushels of corn in 4 of 
 an hour, how many bushels will it grind in 1 hour? 
 
 13. (§ 25.) If pen-knives are worth + of a dollar 
 apiece, and pencils s'5 of a dollar apiece, how many 
 pencils must be given in exchange for 3 knives? _ 
 
 14. (§ 26.) Reduce 3$ to its lowest terms. How 
 do you reduce a fraction to its lowest terms? 
 
 15. (§ 27.) A man, owning # of an acre of.land, sold 
 2 of what he owned. What part of an acre did he sell ? 
 
 16. (§ 28.) Change 2 and 2 to a common denomina- 
 tor. How do you change fractions to a com. denom. ? 
 
 17. (§ 28.) John gave 4 of a dollar for a book, and 
 x of adollar fora slate, and then sold them both for 3 
 of a dollar. Did he gain or lose >— How much? 
 
 18. (§ 29.) A farmer cut 182 tons of hay, and sold 
 2% tons of it. How many-tons had he left? 
 
 19. (§ 30.) When coffee is ¢ of a dollar per pound, 
 how many pounds can be bought for 2 of a dollar? 
 
 20. (§ 30.) A tenant raised 582 bushels of corn, and 
 gave his landlord ¢ of it for the use of the land: How 
 many bushels had the tenant for himself? 
 
 a J 
 
 Section 32. 
 MISCELLANEOUS EXAMPLES. 
 
 1. The Gulf Stream is a current in the ocean, running 
 3 miles an hour. Ifa steam boat, whose engine propels 
 her 124 miles an hour, should run in the stream, with 
 the current, what distance would it move in 8 hours? 
 
 2. If the above steam boat were running against the 
 current, what distance would it move in 8 hours ? 
 
32, MISCELLANEOUS EXAMPLES. &5 
 
 3. A trader bought 25 barrels of flour, paying 7 dol- 
 Jars a barrel for 11 barrels of it, and 9 dollars a barrel for 
 the remainder.. What did the whole cost? | 
 
 4. What sum of money must be divided among 10 
 men, so that each man shall receive 194 dollars ? 
 
 5. Suppose a man can perform a journey in 8 days, 
 travelling 10 hours a day,—in how many days can he 
 - perform it, travelling 12 hours a day? 
 
 6. Henry reads 12 pages in the same time that Wil- 
 liam is reading 7 pages;— how many pages will Henry 
 read while William is reading 60 ?. 
 
 7. If 72 dollars be divided. equally among 9 sailors, 
 how many weeks’ board, at 3 dollars a week, will each 
 sailor’s share pay for ? 
 
 8. A man failed in trade, and could pay only 4 dollars 
 on every 9 dollars that he owed. How much did he 
 pay on a debt of 100 dollars? | 
 
 9. There is a pole standing in a pond, so that 4,@f it 
 is under the water, and. 34 feet of it is above the water. 
 How long is the pole? 
 
 10. A pole is standing so that } of it is in the mud, 
 3 of it is in the water, and 24 feet of it is above the wa- 
 ter. What is the length of this pole? 
 
 11. If A borrow of B, 8 bushels of wheat, when the 
 price is 9 shillings a bushel; how much wheat must A 
 return, when the price is 7 shillings a bushel ? 
 
 12. A trader, having 100 dollars, laid out +5 of his 
 money for narrow-cloth at 5 dollars a yard, and the 
 remainder for broad-cloth at 7 dollars a yard. How 
 many yards did he buy of each sort ? 
 
 13. If 24 bushels of apples will fill a barrel, how many 
 bushels will it take to fill 8 barrels? 
 
 14. John can pick a quart of berries in an hour; Ann 
 can pick twice as fast;—how many can both pick in an 
 hour? In what time would they pick 10 quarts? 
 
 15. How many bushels of corn must a miller grind, 
 to get 1 bushel for himself—allowing, that he takes 2 
 quarts from every bushel before grinding it, and, that 32 
 quarts make a bushel? | 
 
 Suggestion. He gets 2qts. for grinding less thana bush- 
 
 H 
 
86 ORAL ARITHMETIC. VI... 
 
 16. If 1 monitor can mend 2 pens ina minute, how 
 long will it take 3 monitors to mend 28 pens? 
 
 17. It is worth as much to pasture 1 cow, as 5 sheep. 
 If I pay 1 dollar a month for pasturing a Mh what 
 must I pay for pasturing 35 sheep, 7 months? 
 
 18. If 3 horses eat 1 ton of hay in 1 month, how 
 long will 5 tons last 4 horses ? ’ 
 
 -.19. A drover sold a cow for 20 ddfass, and, in so 
 doing, he gained a sum equal to 4 of what he had paid 
 - for the cow. How much had he: paid for her ? 
 
 20. Suppose a man can dig a trench in 4 days, and a 
 boy in 6 days;— what part of it can each = in 1 day? 
 What part of it can both together dig in 1 day? In 
 what time can they both finish it ? 
 
 21. Suppose a cistern has one tap that will discharge 
 it in 5 hours, and another in 7 hours,—in what time 
 will they both discharge it ? 
 
 _., 9@. If 1 man can perform a piece of work in 35 days, 
 in what time can 6 men perform it? 
 
 23. If 4 men drink a barrel of cider in 20 days, in 
 what time will 9 men drink the same quantity ? 
 
 24. If 9 men can do a piece of work in 5 days, in 
 how many days will 7 men do the same work ? 
 
 25. A farmer kept his sheep in four pastures— In the 
 
 first pasture he had -#; of his flock; in the second, 4; 
 in the third, +53 and in the fourth he had 32 sheep. 
 How many sheep had he ? 
 . 26. There is a school, in which $ of the scholars 
 read in the Classical Reader, 4 read in the National 
 Reader, 4 read in Pierpont’s Introduction, and 36 little 
 boys read in the Young Reader. How many scholars 
 are there in the school ? 
 
 27. If a post 4 feet high cast a shadow 3 feet, at 
 - noonday, what is the height of a steeple, that casts a 
 aa: 90 feet, at the same time. 
 
 A and B are laborers—A earns 10 abllery. a 
 ‘nee and B 9; but A gives 4 of his earnings to B. 
 What will each lay up in 3 months ? 
 
 29. If 12 mencan perform a piece of work in 6 days, 
 in what time would: ae men perform the work ? | 
 
32. MISCELLANEOUS EXAMPLES. 87 
 
 30. How many men must be employed, to dig a 
 trench in 3 days, that 6 men can dig in 4 days? 
 
 31. Suppose 2 men start from the same place, and 
 travel in opposite directions, one at the rate of 5 miles 
 an hour and the other 3 as fast; ;— how far apart will they 
 be in 11 hours ? 
 
 32. A fox has 35 rods the start of a greyhound, but 
 the hound runs 10 rods while the fox runs 7. How 
 many rods must the hound run to catch the fox? 
 
 33. A started on a journey, and travelled 5 miles an 
 hour— B ‘started on the same journey, 2 hours after, 
 and travelled 74 miles an hour. In how many hours 
 did B overtake A? 
 
 34: A jockey paid 9 times as much for his horse as 
 he did for his saddle; he paid 3 times as much for his 
 saddle as he did for his bridle; and for his bridle he paid 
 5 dollars. What did the whole cost? 
 
 35. Suppose a man can reap 3 of a field of wheat in 
 a day, and his son can reap 4 of it in a day;— what part 
 of it can they both reap in a day? In what time can 
 they both reap the whole ?. 
 
 36. A boy being asked how much money he had, 
 bepuie des ‘If I had as much more, and 3 as much more, 
 and} as much more as I really have, I should then have 
 70 cents.” How much must he have had ? 
 
 37. A gentleman paid 85 dollars for 5 weeks’ board 
 of himself, his son, and one servant, at a hotel— His 
 own hoard cost twice as-much as his son’ S, and his son’s 
 cost three times as much as the servant’s. Mian? was 
 the expense of each, per week ? 
 
88 
 
 NOTE TO TEACHERS. 
 
 The teacher should now be provided with «A KEY TO THE NORTH 
 AMERICAN ARITHMETIC,” otherwise he must lose much time in examin- 
 ing operations. The Kry is.a small book designed exclusively for teachers, 
 and contains answers to all the examples in the Written Arithmetic. If the 
 Key cannot be obtained at every place where the Arithmetic is for sale, it 
 may still be obtained from the publishers of the Arithmetic, and from the 
 principal book-stores in the larger cities and towns. 
 
 A variety of expedient methods may be pursued, in examining written opera- 
 tions in arithmetic; and perhaps no one system can be adopted, from which it 
 will not be found advantageous, occasionally, to depart. My own practice for 
 several years, with occasional variation, has been as follows. 
 
 A certain number of examples having been assigned for a lesson the day pre- 
 vious, each scholar is supposed to be prepared with the solutions upon his slate, 
 and the class are paraded for recitation. | Every scholar passes his slate into the 
 hands of the scholar next above him, except the head scholar, who hands his to 
 the foot scholar. The first scholar then reads from the slate he holds, the answer 
 to the first example; and the teacher, holding the key, declares the answer to 
 be right, or wrong. When the answer has been pronounced right, it is the 
 duty of every scholar who finds a different answer upon the slate he holds, to 
 signify it, and the error is noted against the owner of the slate. The first ex- 
 ample being disposed of, the answer to the second example is read by the second 
 scholar, and disposed of in like manner. ‘Thus the reading of answers goes 
 through the class, and each scholar detects the errors of hisneighbour. Individ- 
 ual scholars are occasionally called upon to explain their work ina particular 
 example, and to give their reasons for the operation adopted. By this mode of 
 examination, the work of a large class is particularly inspected, in nearly the 
 same time that would be required to inspect the work of one scholar. Be- 
 sides the advantage of despatch in this inode of examination, the exercise it- 
 self is beneficial to the pupils.— Each scholar acts the part of an inspector— he 
 is interested to be critical— he acquires a facility in deciphering the work of 
 others— and thus his perceptive powers are cultivated, and a habit of alertness 
 is attained. hatin Moe, 
 
 Before the learners attempt to perform operations by figures, they should be 
 able to write figures with facility, and to arrange them regularly. To attain 
 this object, the arrangement of figures below, may be repeatedly copied upon 
 
 the slate, until a good degree of despatch and accuracy is acquired. 
 
 42:96 
 7E89IO4FG2 
 SZEATS 
 9O*S23S 
 567890 
 23456 
 789042 
 S45678 
 
 > 
 
 423456 
 7EIO4G? 
 
 I43 0.7 8 
 
 9OOS2ZI4L 
 567890 
 TEP 49 6 
 7EIOFGT? 
 S45678 
 
 T23456 
 TEIOF? 
 \PZIO678 
 9QOV2IL 
 567890 
 Z2I456 
 789042 
 S45 678 
 
WRITTEN ARITHMETIC. 
 
 CHAPTER I. 
 NUMERATION. 
 
 SecTion 1. 
 
 THEUNIT, which is the first thing to be considered in 
 numeration, signifies One. .The figure 1 stands for one 
 unit; D, for two units ; 3, for three units; 4, for four 
 units; 5, for five units ; 6, for six units ; ei for seven 
 units; 8, for eight units; 9, for nine units. 
 
 The TEN is a number which is made up of ten units. 
 One ten is expressed thus, 10; two tens, thus, 20; three 
 tens, thus, 30; four tens, thus, 40; &c. 
 
 The HUNDRED is a number which is made up of ten 
 tens. One hundred is expressed thus, 100; two hun- 
 dreds, thus, 200; three hundreds, thus, 300; &c. 
 
 Suppose the balls below, which are arranged i in three 
 places, to represent 8 units, 3 tens, and 1 hundred. 
 
 HUNDRED TENS UNITS 
 
 90080000 
 
 1 3 : 
 beat from the figures above, that the first or right 
 hand figure expresses units, the second figure expresses 
 tens, and the third figure expresses hundreds. 
 a* 
 
90 WRITTEN ARITHMETIC. I. 
 
 The THOUSAND is a number, which is made up of ten 
 hundreds. One thousand is expressed thus, 1000; two 
 thousand, thus, 2000; three thousand, thus, 3000; &c. 
 Observe, that a figure expresses thousands, when it 
 stands in the fourth place from the right; therefore ten 
 thousand is expressed thus, 10000; and a hundred 
 thousand, thus, 100000. 
 
 Examine the following Numeration Table. _ Begin at 
 the right hand, and observe, that every three figures may 
 be viewed by themselves;—the first three express so 
 many wnits, tens and hundreds; the second three, so 
 many Thousands; the third three, so many Millions; 
 the fourth three, Billions; the fifth three, Trillions.* 
 
 m n = 
 
 S rs S § 7” 
 ° re} se 2a 
 
 SE i ee Ss 
 
 Be 32 €8 S82 
 
 Pao ey O Sept e. 3A 
 
 SEO e243 84 eae 
 
 m5 Bae’ 4 & St ie , 
 Bsa BSS Bek BeS 3B m 
 
 Sad tod vat tao tee 
 
 Sas Gs sae] Sq Seah 
 
 Som Sou Sot SoG 554 
 
 Teh Cee Des Cee Gap 
 
 472156795 841526 
 
 To read the line of figures in this table, begin with 
 the left hand figure, and proceed as follows. 
 
 =) . 
 
 rs o i ae =| 
 a «i 
 & 29 ac sg § 3 
 Ss 3g § § 7-3 & a 
 § mM * m= 
 
 Spe & Sa,8 8 So 
 apes & So8 SB 
 BS oa SP Ebe os 
 SES Pex FES Ee Poy 
 Bas Oma BEAR TRS KS's 
 472156795 841526 
 
 This character, 0, called nought, or cipher, expresses 
 nothing of itself— it stands only to occupy a place, 
 where there is none of the denomination belonging to 
 that place to be expressed. For example, in the num- 
 ber 240, there are no units; therefore a cipher stands in 
 the units’ place. In the number 407, there are no tens; 
 therefore a cipher stands in the tens’ place. | 
 
 _ * The old method of embracing siz figures in a period, is of late abandoned. — 
 
2. - NUMERATION. 91 
 
 Note to Teachers. Require the learners to copy upon their slates the fol- 
 lowing figures expressing numbers. Then require them to read from their slates 
 the several numbers expressed. 
 
 (Ex. 1.) 508 | (19) 1000 001 
 (2) 3861 | (20) 90 040 
 (3) 1050 | (21) 107090 © 
 (4) 27 400: | (22) 6 000 304 
 (5) 13.008 | (23) 77 010 000 
 (6) 29111 | (24) 100100011 
 (7) 112600 | (25) 0, SS OO2 
 (8) 30 030 | (26) | 11 333111 
 (9) & 206 209 | (27) 216 090 900 
 (10) 500 088 | (28) 10.000 004 
 (11). 7432040 | (29) 8 000 000 500 
 (12) 200 005 | (30) 50 000 000 036 
 (13) 9 070638 } (31) 1 000 700 007 
 (14) » 3018103 | (32) $400052000 600 
 (15) 16 974036 | (33 8 631 008 000 
 (16) 340 007 140 | (34) 22 000 004 
 (17) 31 031 032 | (35) 919 000 000 060 
 (18) 9908000 | (36) 86000001 100018 
 
 Section 2. 
 
 " Note to Teachers. The following numbers written in words, are to be 
 written upon the slate infigures.. If the learner meet with difficulty in denoting 
 the larger numbers, he may be instructed to repeat the Numeration Table, 
 from units up to the highest denomination in the number to be denoted; and, 
 while repeating the table, he may make a dot for each denomination, arranging 
 _ the whole in aline. Then, the figure to express the highest denomination may 
 
 be written under the left hand dot, and there will be no difficulty in arranging 
 the figures of other denominations under their respective dots. 
 
 . Seventy. 
 
 . Forty-eight. 
 
 . One hundred and twenty-four. 
 
 . Six hundred and nine. 
 
 . Three thousand, and six hundred. 
 
 Two thousand, four hundred and fifty. 
 
 . Nineteen thousand, and sixty-eight. 
 8. Five thousand, seven hundred and thirty-one. 
 
 a3 D OP 69 to 
 
92 . WRITTEN ARITHMETIC. I. 
 
 9. Thirty-six thousand, seven hundred and forty. 
 
 10. T'wo hundred and sixty-eight thousand. 
 
 11. Nine hundred five thousand, and one hundred. 
 
 12. Eighteen thousand, seven hundred and thirty-five. 
 
 13. Seven hundred thousand and nine. 
 
 14. Thirteen million, sixteen thousand, and nineteen. 
 
 15. One hundred five million, two thousand, and one. 
 
 16, Six billion, forty million, and six thousand. 
 
 17. ‘Twenty-one billion, and one hundred million. 
 
 18. Five. trillion, fourteen billion, seventy roillion, 
 one thousand, two hundred and thirty-six. 
 
 19. One hundred twenty-two trillion, eight hundred 
 and forty-seven thousand. eH 
 
 20. Ten billion, nine hundred eighty-seven thousand, 
 ‘seven hundred and thirty, 
 
 21. Seven hundred trillion, and thirty-six thousand: 
 
 22. ‘Twelve billion, eight hundred forty-two thousand, 
 seven hundred and eighty. 
 
 23. ‘Twenty-nine trillion, eight hundred nine billion, 
 one thousand, and eighteen. 
 
 24. Eight hundred twenty-three billion, ten million, 
 eight thousand, and fifteen. 
 
 Questions to be answered Orally. 
 
 (1) What is a wnit? (2) What is the greatest 
 number, that can be expressed by one figure alone? 
 (3) In ‘what situation must the figure 9 stand, to 
 express 9 tens? (4) What is the greatest number, 
 that can be expressed by two figures? (5) Recite 
 the several denominations of numbers, from units to 
 trillions, as they stand in the Numeration Table. 
 (6) What denominations are expressed in the Ist. 
 three places of figures? (7) What denominations 
 are expressed in the 2nd. three places? (8) ‘Where 
 must the figure 7 stand to express 7 tens of thousands 
 —that is, seventy thousand? (9) What denomina- 
 tions are expressed in the 3rd. three places? 
 (10) Where must the figure 2 stand, to express two 
 hundred thousand?) 
 
12: ADDITION. 93 
 
 CHAP. IL. 
 ADDITION. 
 
 Section 1. 
 1. What is the whole sum of 6312 dollars, 8032 dol- 
 lars, 501 dollars, and 7123 dollars ? 
 We first write the numbers under one 
 
 A 
 
 ge another, so that all the units may stand in a 
 2223 column on the right hand. We then add 
 eres the units thus—3 and 1 are four, and 2 
 6312. are six, and 2 are eight; and we write 8 
 8032 . under the column of units. We next add 
 
 501 the column of tens, and, finding their, sum 
 7123 10 be G, we write 6 under the column. ° In 
 the same manner we add the hundreds, and 
 =~ -- the thousands. 
 
 Find the sum of the numbers in each of the following 
 examples, by addition upon the slate. 
 
 (2). 51 + (8). 783 (4). 6243... (5). 24031 
 4 120 4123 1320 
 60 12 9401 40214 
 
 : 63 130. 34314 
 ae "Pa ae Pah Fay hy ge f f 
 
 Section 2. 
 
 . Add the following numbers into one sum. 4638 
 216 and 8329 and 1212. } 
 _ Finding the sum of the units to be 25, or 
 2 tens and 5 units, we write only the 5 units, 
 “2 and presently add the 2 tens in with the 
 &5 column of tens.’ In adding the hundreds, 
 4638 we find their sum to be 13. Now if we 
 216 should write down 13, the 3 would stand 
 8329 under the column of hundreds, and the 1, 
 1212 under the column of thousands; therefore 
 we write the 3 only, and presently add the 
 1 in with the thousands. 
 
 jor 
 
 an 
 
94 WRITTEN ARITHMETIC. II 
 
 In the following examples, observe, that when the 
 sum of any column amounts to more than 9, you must 
 set down only the right hand figure of it, and, must add 
 the left hand figure to the next column. 
 
 (2). 6214 (8). 5221, (4). 7420 (5). 3150 
 
 2403 7940 | Oak 2 216 
 
 590 1368 cue kde at St 8481 
 8732 520 9103 275 
 MUN tie 5648 430 8610 
 
 2464 “kj BROOK» ae 1000 2541 
 
 RULE FOR ADDITION. Write the numbers, units under 
 units, tens under tens, §-c. dd each column separately, 
 beginning with the column of units. When the sum of 
 any column ts not more than 9, writé it under the column: 
 when the swm ts more than 9, write only the units’ figure 
 under the column, and carry the number of tens to the 
 next column. -Finally, write down the whole sum of the 
 left hand column. | 
 
 6. Add together the numbers, 143 and.8 and 56 and 7. 
 
 7. Add together the buiibers: 3 and 96 and 5 and 984. 
 — §. What is the whole sum of 46 9, 18, 153 and 728 ? 
 
 9. What is the whole sum of 8, 49, 728 and 4105? 
 
 10. Whatis the whole sum of va 536, 827 and 3480 ? 
 
 11. Whatis the whole sum of 1118, 6004, and 84932? 
 
 12. What is the whole sum of 61297,.58 and 389163% 
 
 13. Find the sum of 423, 315, 531, 414, 612, 284, 
 621, 414, 711, 144, 621 and 918. 
 
 14. Find the sum of 314, 90, 246518, 7, 1101, 47, 
 ee 8601520, 2004 and 5674. 
 
 . Find thee sum of 1728, 26510, 34, 100, 3261, 9, 
 odte 1640831, 6733 and 40000000. 
 
 16. A Wierk received from one man 94 Ao linee: from 
 another 361 dollars, and from another 113 dollars. 
 What was the whole sum of money received? 
 
 17. A merchant sent to the bank at one time 301 dol- 
 Jars; at another 214; at another 1109; at another 109. 
 How much did he send in all ? 
 
4 
 
 pe 
 2. ADDITION. 95 
 
 18. A certain lot of land has been divided into three 
 farms; one of the farms contains 112 acres, another 123 
 acres, and the other 147 acres. How many acres were 
 there in the original lot? 
 
 19. If you start on a journey, and travel on Monday 
 42 miles, on Tuesday 57, on Wednesday 49, on Thurs- 
 day 54, on, Friday 63, acidhtoui Saturday 75, how. far 
 will:you have travelled at the end of the week? 4 
 
 20. Suppose 477 dollars are in one bag, 8509 in 
 another, 1965 in another, and-956 in another; what sum 
 of money is there in the four bags ?* 
 
 21. A-merchant bought a quantity of sugar for 2075 
 dollars, and then sold it so as'to gain 415 dollars. For 
 how much did he sell the sugar? i | 
 
 22. There are four numbers, the first of which is 532, , 
 the second 895, the third 240, and the fourth as much 
 as the other three. What is the sum of them all ? 
 
 23. A broker, by selling a note for 836 dollars, lost 
 
 ‘140 dollars. What must he have paid for the note ? 
 
 24. A capitalist gave (to one of his sons, 13427 dol- 
 lars; to another, 13025 dollars; to another, 12947 dol- 
 lars. What did he give to all of them? 
 
 25. Sacred history shows, that thé time, frit the 
 creation of the world to the Deluge, was 1656 years; 
 thence to the building of Solomon's temple, 1344 years; 
 
 thence to the birth of Christ, 1004 years. How old is 
 _ the world the present year’ 
 
 26. George Washington was born in the year 1732, 
 and lived to be 67 years old. In what year did he die: ? 
 
 27. Three men united in trade;—the first man had 
 5136 dollars, the second had 1562 dollars, and the third 
 had 756 dollars. How much had they all ? 
 
 28. A trader bought four pieces of cloth: the first 
 piece.contained 86 yards; the second, 55 yards; the 
 third, 87 yards and the fourth 91 yards. What was the 
 Poe of the whole, at 1 dollar per yard ° 
 
 Pui ve a purchased a farm for 8257 dollars; 
 paid 953 dollars for having it fenced, and 300 dollars 
 for having a barn built upon it. For how much inust 
 he sell it, in order to gain 100 dollars ? 
 
es 
 
 96 WRITTEN ARITHMETIC. Il. 
 
 30. A drover paid 300 dollars for 100 sheep, 525 
 dollars for 150 sheep, and 1000 dollars for 250 sheep. 
 How many did he buy? What did the whole cost ? 
 
 31. What is the sum of two million, five hundred 
 
 thirty-one thousand, one hundred and twenty,— fourteen 
 
 thousand,— thirty thousand and twenty-four,— five hun- 
 dred and sixty,—and seven hundred and two? 
 32. The inhabitants of the British Islands, are stated 
 
 thus: England 11260555; Wales 717103; Scotland 
 
 2092014; Ireland 6 846 949; Army and Navy 310000; 
 Isle of Man 40981; Guernsey 20 827; Jersey 28 600; 
 Scilly Isles 2614. What is the whole number? | 
 33. The inhabitants of the United States, by the cen- 
 sus of 1830, were stated.thus: Maine 399 437; New 
 
 ,Hampshire 269 367; Vermont 280679; Massachusetts 
 
 610014; Connecticut 297513; Rhode Island 97210; 
 New York 1913508; New Jersey 320779; Pennsyl- 
 vania 1347672; Delaware 76739; Maryland 446 913; 
 Virginia 1211272; North Carolina 738470; South 
 Carolina 581458; Georgia: 516567; Ohio 937 679; 
 Kentucky 688 844; Indiana 341552; Illinois 157 575; 
 Missouri 140192; Tennessee 684833; Louisiana 
 215 762; Alabama 308 997; Mississippi 136806; Flo- 
 rida Territory 834723; Michigan Territory 31 260; Ar- 
 kansas Territory 30383; District of Columbia 39 858. 
 What was the whole number ? 
 il 
 
 Questions to be answered Orally. 
 
 (1) When you have several numbers to add to- 
 gether, in what order do youwritethem? (2) Which 
 column do you add first? (3) Do you add all other 
 columns in the same manner that you add the first? 
 (4). When the sum of any column is less than 10, 
 
 |.where is it to be written? (5) When the sum of 
 
 any column is more than 9 what is to be done? 
 (6) Why do:we carry as many ones to the next left 
 hand column, as there are fens in any column that we 
 have added? (7) Recite the rule for addition. 
 
RR. SUBTRACTION. 97 
 
 CHAP. III. 
 SUBTRACTION. 
 
 Section 1. 
 
 4. Subtract 632 from 1847; that is, take 632 from 
 1847, and find what number remains. 
 1847 We first write the smaller number under 
 632 the greater. Then, take 2 units from 7 units, 
 1215 3 tens from 4 tens, 6 hundreds from 8 hun- 
 dred, and nothing from 1 thousand. 
 
 Subtract the smaller number from the greater in each 
 
 of the following examples. 
 
 (2). 25 (3). 639 (4). 4258 (5). 705684 
 whan 2. 213 3215 4261 
 
 —_—— ——_—_ 
 
 6. A farmer having 359 sheep, sold 136 of them, and 
 kept the remainder. How many did he keep? 
 
 7. A trader having 2748 dollars, laid out 2616 dollars 
 for goods. How many dollars had he remaining ? 
 
 Section 2. , 
 1. Subtract the number 1528 from the number 8473. 
 We unite 1 of the 7 tens with the 3 units, 
 8473 making 13 units, and say, 8 from 13, leaves 
 1528 5. Then, having used 1 of the 7 tens, we 
 6945 take 2 tens from 6 tens. In the same way 
 ~~ we take 5 hundreds from 14 hundreds. 
 
 Do not pass from the above example without under- 
 standing it. Whenever an upper figure is smaller than 
 the figure under it, we use 1 from the next upper figure, 
 and this 1 becomes 10 when considered with the right 
 hand figure. Arithmeticians commonly call this process, 
 borrowing 10; and, instead of reckoning the figure from 
 which they have borrowed to be 1 less than it stands, 
 they pay 1 to the figure under it—reckoning the lower 
 figure to be 1 morethan it stands. 
 
 I 
 
98 §—-«.: WRITTEN ARITHMETIC. ~ III. 
 Perform subtraction in the following examples. 
 
 (2). 1853 (8). 5264 (4). 2657 (5). 6807 
 1370 762 349 4096 
 
 ————— 
 
 ——___ + 
 
 ee 
 
 6. Subtract 1268 from 1503. | 
 In subtracting the $ units, we use a ten, 
 1503 that we obtain by supposing 1 of the 5 hun- 
 dreds, (which is 10 tens,) to be where the 
 235 Ois. Then, having used 1 of the 10 tens, 
 "we presently subtract 6 tens from 9 tens. 
 7. Subtract 1146 from 2601. 
 8. Subtract 5428 from 8019, 
 9. Subtract 258 from 34307. 
 
 RULE FOR SUBTRACTION. Write the smaller number 
 under the greater, placing units under units, &c. Begin 
 with the units, and subtract each figure in the lower 
 number from the figure over it. When a figure in the 
 upper number is smaller than the figure under it, consider 
 the upper figure to be 10 more than it is, and the nezt 
 upper figure on the left hand, to be 1 less than it is. 
 
 PROOF. ddd together the remainder and the smaller 
 number: their sum will be equal to the greater number, 
 if the work be right. 
 
 10. Find the difference between 39 and 64, by sub- 
 tracting the smaller number from the greater. 
 
 11. What is the difference between 464 and 502 | ? 
 
 12. What is the difference between 99 and 200? 
 
 13. What is the difference between 35720 and 9100 ? 
 
 14. Subtract 44 from 10000. 
 
 15. I deposited 1450 dollars in the bank, and I have 
 since drawn out 835 dollars. How many ‘dollars. have 
 I remaining in the bank? 
 
 16.. Suppose. a man owes 1634 dollars, and possesses 
 property to the amount of 8150 dollars; how much, will 
 he have left, after paying his debts ? 
 
 17. Subtract. sixty-two thousand five hundred and 
 seven, from one million eighty thousand and forty-four. 
 
4 SUBTRACTION. 99 
 
 18. The number of inhabitants in the city of London 
 is 1 250000; the number in the city of Paris is 750 000: 
 How many more are there in London, than in Paris? 
 
 19. The population of Great Britain and Ireland is 
 21 500 000; the population of France is 32 000 000. 
 How many more inhabitants are there in France, than 
 in Great Britain and Ireland? 
 
 20. The Rocky Mountains, in North America, rise 
 12 500 feet above the level of the ocean; the Andes, in 
 South America, rise 21440 feet. How many feet 
 higher are the latter, than the former? 
 
 21. A merchant paid 13 745 dollars for a ship, and 
 sold it for 15 150 dollars. What did he gain? 
 
 22. A farmer sold a piece of wood-land for 396 dol- 
 lars, which was 78 dollars more than he gave for it. 
 How much did he give for the land? 
 
 23. Columbus discovered America in the year 1492. 
 How many years is it since the discovery? 
 
 24. The United States declared Independence in the 
 year 1776. How many years since the declaration? 
 
 25. A man bought 20 casks of wine, containing 2459 
 gallons, and sold 14 casks containing 1682 gallons. 
 How many casks, and how many gallons were left? 
 
 26. There are two numbers, whose difference is 758; 
 the greater number is 1524. What is the smaller number? 
 
 Questions to be answered Orally. 
 
 (1) How can you find what the difference is be- 
 tween two numbers? (2) When one number is to 
 be subtracted from another, in what order must the 
 numbers be written? (3) In what place do you 
 begin to perform the subtraction? (4) When a 
 
 | figure in the upper number is smaller than the figure 
 under it, what 1s to be done? (5) Where does the 
 remainder appear, after the subtraction is performed? 
 
 (6) Recite the rule for subtraction. (7) How can } 
 
 you prove that an operation in subtraction is per- 
 formed correctly? 
 
100 WRITTEN ARITHMETIC. ie i 
 
 Section 3. 
 MISCELLANEOUS EXAMPLES. 
 
 1. A man owing 379 dollars, paid at one time 47 
 dollars, at another 23, at another 84, and at another, 143. 
 How much did he still owe? 
 
 2. There are 1000 dollars in 4 bags; the first bag 
 contains 230 dollars, the second 245, the third 270. 
 What is contained in the fourth bag?» 
 
 3. Suppose the world to have been created 4004 
 years before the Christian era, how old is it at this date? 
 
 4. A man having in his desk 2000 dollars, took out 
 120 dollars to pay a debt, and afterwards put in 75 dols. 
 How much was there remaining in the desk? 
 
 5. A merchant bought a ship for 11 240 dollars, paid 
 305 dols. for repairing it, and sold it so that he lost 95 
 dols.. For how much did he sell it? 
 
 6. What is the sum of 58,45, and 70? Then, if you 
 subtract 43 from this sum, what. will be the remainder? 
 
 7. A merchant, who had 650 barrels of flour, sold 95 
 barrels to one man, 38 to another, and 225 to another. 
 How many barrels had he left? 
 ~ 8. A jockey bought a horse for 115 dollars; he ex- 
 changed him for a better horse, paying 23 dollars, and 
 then sold the better one for 137 dollars. Did he gain 
 or lose?—and how much? 
 
 9. If 654 be subtracted from 10000, and then 29670 
 be added to the remainder, what will be the sum? 
 
 10. A gentleman gave 972 dollars for a carriage and 
 two horses; the carriage was valued at 525 dollars. 
 What was the value of the horses? 
 
 11. Dr. Franklin died in the year 1790, and he was 
 84 years old when he died. In what year was he born? 
 
 12. A clerk went out with 240 dollars, to settle some 
 accounts: he paid 126 dollars to one man, received 37 
 dollars from another, and paid 94 dollars to another. 
 How many dollars had he then? ' 
 
 13. Add together two hundred, sixteen thousand, 
 thirteen million, and seven billion; and then subtract ten 
 thousand from the sum. 
 
2. 2. MULTIPLICATION. 101 
 
 CHAP. IV. 
 MULTIPLICATION. 
 
 SEcTION 1. 
 
 1. If a gunner shoot 72 pigeons every time he goes a 
 gunning, how many will he shoot in going 3 times ? 
 
 We might here obtain the answer by adding together, 
 72 and 72 and 72; but we shall obtain it more readily 
 by multiplying 72 by 3; that is, by finding 3 times 72. 
 Multiplicand 72 We write 72, and write 3 under 
 Multiplier 3 ate bat we multiply sa Fj units 
 
 fat and the 7 tens separately, thus, 3 
 Broduct as times 2 are 6; 3 sens Anite 91. 
 
 Observe, that the number which we multiply is called 
 the multiplicand; the number by which we multiply is 
 called the multiplier; and the number which we obtain 
 by multiplication is called the product. 
 
 Find the product in each of the following examples. 
 (2). 61 (8). 524 * (4). 9182 | (5), 420121 
 4 2 dy 4 
 
 —_—_—_ ——— 
 
 6. If a farm produce 230 bushels of wheat a year, 
 how many bushels will it produce in 3 years? 
 7. Multiply 512 by 4;—that is, find 4 times 512. 
 
 Section 2. 
 1. Multiply 743 by 6;— that is, find 6 times 743. 
 743 6 times 3 are 18, or 1 ten and 8 units; we 
 G write only the 8 units, (as in addition), and 
 4459 proceed;—6 times 4 are 24 and 1- we carry 
 s-°* are 25; we write the 5 and proceed. 
 Find the product in each of the following examples. 
 (2). 5236 (3). 1908 (4). 6175 (5). 3640 
 . 4 2 3) 8 
 
 —t___—. 
 
 ess ee : eee et eee 
 
 1* 1g 
 
 RR eo 
 
102 WRITTEN ARITHMETIC. IV. 
 
 6. What will 3 books cost, at 31 cents apiece ! ? 
 
 7. What will 4 slates cost, at 24 cents apiece ! ° 
 
 8. What will 5 baskets cost, at 17 cents apiece? 
 
 9. What will 6 cows cost, at 25 dollars apiece ? 
 
 10. What will 7 horses cost, at 115 dollars apiece? 
 
 11. How many are 8 times 9? 
 
 12. How many are 9 times 16? 
 
 13. How many are 5 times 342? 
 
 14. How many are 7 times 6453? 
 
 15. How many aré 3 times 42 908? 
 
 16. How many are 6 times 704 370? 
 
 17. Multiply 251 by 8, phat 3 is, find 8 times 251. 
 
 18. Multiply 475 by 4 
 
 19. Multiply 3086 by 6. 
 
 20. Multiply 15 350 by 8. 
 
 21. Multiply 430 039 by 7. 
 
 22. Multiply 7000005 by 9 
 
 23. Multiply 42 862 000 by 5 
 
 24. Multiply 928 064 309 by 4. 
 
 25. Suppose 8 to be a multiplicand, and 6 the multi- 
 plier; how much will be the product ? 
 
 26. Suppose 35 to be a multiplicand, and 7 the multi- 
 plier; how much will be the product ? 
 
 27. Suppose 491 to be a multiplicand, and 5 the mul- 
 tiplier; how much will be the product ? 
 
 Section 3. 
 
 1. Multiply 657 by 24. 
 We first multiply by the 4 units. Then 
 657 owe multiply by the 2 tens, and since this 
 ae product must be ten times greater than it 
 2628 — would be if the 2 were 2 units, we set the 
 1314 product one place to the left. At last, we 
 15768. add the two products together, and the sum 
 is the whole product of 657 by 24. 
 2. Multiply 75 by 16. 
 3. Multiply 6384 by 45. 
 4., Multiply 3291 by 63. 
 5. Multiply 71538 by 77. 
 6. Multiply 428 601 by 81. 
 
iB: “MULTIPLICATION. 103 
 
 RULE FOR MULTIPLICATION. Write the multiplier un- 
 der the multiplicand, placing units under units, §c. 
 
 When there is but one figure in the multiplier, begin 
 with the units, multiply each ‘figure in the multiplicand 
 separately, and place each product under the figure in the 
 multiplicand from which it arose; observing to carry the 
 tens to the left as in addition. | 
 
 When there is more than one figure in the multiplier, 
 multiply by each figuré separately, and write its product 
 in a separate line, placing the right hand figure of each 
 line under the figure by which you multiply; and final- 
 ly, add together the several products. The sum will be 
 the whole product. i 
 
 7. Suppose 5476 208 to be a multiplicand, and 3942 
 the multiplier; how much will be the product? 
 
 5476208 
 ity 9 4:2) 
 
 10952416 
 
 21904832 
 49285872 
 16428624 
 
 21587211936 
 
 8. Suppose 73 054 to be a multiplicand, and 548 the 
 multiplier; how much will be the product? 
 
 9. Suppose 295 to be a multiplicand, and 486 the 
 multiplier; what will be the product? _ 
 
 10. What is the product of 9351 by 765 ? 
 
 11. What is the product of 3008 by 254 ? 
 
 12. What is the product of 5603 by 6448 ? 
 
 13. How many are 74 times 6580? 
 
 14. How many are 236 times 3759 ? 
 
 15. There is an orchard containing 9 rows of trees, 
 and there are 57 trees in each row. How many trees 
 are there in the orchard ? 
 
 16. A merchant bought 75 pipes of wine, at 145 dol- 
 lars a pipe. What did the whole cost ? bis 
 
 17. A merchant bought 37 mules, for shipping, at 52 
 dollars per head. What did the whole cost | 
 
104 WRITTEN ARITHMETIC. IV. 
 
 "18. A man travelled 26 days, travelling 47 miles a 
 day. How far did he travel in the whole time? 
 
 19. A merchant sold 342 tons of iron, at 142 dollars 
 per ton. What was the price of the whole? 
 
 20. If a coach wheel turn round 346 times in 1 mile, 
 how many times will it turn round in the distance from 
 New York to Philadelphia, it being 95 miles? 
 
 21. A prize was divided among 47 men, and each 
 man received 25 dollars. . How much was the prize? 
 
 22. What sum of money must be divided among 45 
 men, so that each man shall receive 59 dollars? 
 
 23. A merchant bought 7 bales of cloth, each bale 
 containing 11 pieces, and each piece, 29 yards. How 
 many pieces, and how many yards were there? 
 
 24. A trader bought 9 pieces of cloth, each piece 
 containing 42 yards, at 6 dollars a yard. How many 
 yards were there, and what did the whole cost? _ 
 
 25. If hats are worth 7 dollars apiece, what are 15 
 boxes of hats worth, each box containing 24 hats? 
 
 26. The distance from Washington to Boston is 436 
 miles; and in each mile there are 320 rods. How 
 many rods is it from Washington to Boston? 
 
 27. The distance from Washington to New-Orleans 
 is 1255 miles. How many rods is it? f 
 
 28. What is the value of the hay, that is produced on 
 16 farms; allowing each farm to produce 62 tons, and 
 allowing the hay to be worth 12 dollars a ton? 
 
 29. There are 24 hours in a day, and 365 days in a 
 year. Ifa ship sail’7 miles in an hour, how many miles 
 will she sail in a year? | 
 
 30. How many days’ work can 9 men do in 24 days? 
 
 31. How many days will it take 1 man to perform a 
 piece of work, that 9 men will perform in 24 days? 
 
 32. How many days will it take 1 man to build a 
 piece of road, that 13 men can build in 47 days? 
 
 33. How many men must be employed to do a piece 
 of work in 1 day, that 11 men can perform in 18 days? 
 
 34. Suppose that a ship’s crew of 13 men will drink 
 82 gallons of water in 14 days, how long would the 
 same quantity of water last 1 man? 
 
4. MULTIPLICATION. 105 
 
 Section 4. 
 ABBREVIATIONS. 
 
 When there are ciphers standing between figures, in 
 the multiplier, they may be disregarded. 
 
 1. What is the product of 12318 12318 
 multiplied by 7004 ? 7004 
 49272 
 
 $6226 
 86275272 
 
 2. What is the product of 9651 multiplied by 304? 
 3. How many are 1001 times 57 906? 
 4. How many are 905 times 820 437 ? 
 
 Ciphers on the right hand of the multiplier or multi- 
 plicand may be disregarded till the multiplication is per- 
 formed, and then placed onthe right hand of the product. 
 
 5. What is the product of 5763. 5763 
 multiplied by 3600° 3600 
 34578 
 17289 
 20746800 
 
 6. What is the product of 158 multiphed by 350 ? 
 7. How many are 800 times 369? 
 8. How many are 40 times 4728? 
 
 Ciphers on the right hand of the multiplier and mul- 
 tiplicand both, may rall be disregarded in multiplying, 
 and finally placed on the right hand of the product. 
 
 9. What is the product of 46000 46000 
 multiplied by 340. 340 
 == 184 
 roe 
 15640000 
 
 10. What is the product of 8370 multiplied 4 240? 
 11. How many are 90 times 761000? 3 
 12. How many are 5700 times 6800? 
 
106 WRITTEN ARITHMETIC. IV. 
 
 When the multiplier is 10, 100, 1000, &c. merely 
 place the ciphers of the multiplier on the right hand of 
 the multiplicand, and it becomes the product. 
 
 13. What is the product of 5 multiplied by 10° 
 
 14. What is the product of 17 multiplied by 100? 
 
 15. What is the product of 49 multiplied by 1000? 
 
 16. In 1 dollar there are 100 cents. How many 
 cents are there in 6 dollars? ” 
 
 17. How many cents are there in 25 dollars? 
 
 18. If 1 box of lemons cost 7 dollars, how many 
 cents will it take to pay for 10 boxes? 
 
 When the multiplier is a number, that can be produc- 
 ed by multiplying two smaller numbers together, mul- 
 tiply the multiplicand first by one of the smaller numbers, 
 and the product thence arising by the other. 
 
 19. Find the price of 32 horses, at 96 dollars apiece. 
 
 96 price of 1 horse. 
 8 “ 
 768 price of 8 horses. . 
 4 nf 
 
 3072 price of 4 times 8 horses, or 32 horses. 
 
 Observe in the above example, that 32 can be pro- 
 duced by multiplying 4 and 8 together. ‘The 4 and the 
 8 are called the factors of 32. 
 
 20. A merchant bought 24 hogsheads of molasses at 
 19 dollars a hogshead. What did the whole cost? 
 
 In this example we consider 24 to be the multiplier. 
 For 24, we can find several different sets of factors; 
 Viz: Sy eicalso, 4, Hevalso, 22.53, Aealso, 12).2....6. hae 
 Either set of these factors may be used. 
 
 21. If a ship sail at the rate of 129 miles a day, how 
 many miles will she sail in 72 days? 
 
 22. If 1 man can dig 41 bushels of potatoes in a day, 
 how many bushels can 28 men dig? 
 
 23. Multiply 425 by 36, using the factors of 36. 
 
 24. How many are 63 times 540? 
 
 25. How many are 45 times 2807 ? 
 
er 
 eae 
 Ee 
 
 A, MULTIPLICATION. 107 
 
 Questions to be answered Orally. 
 
 (1) What is meant by multiplicand?— what by 
 multiplier?— and what by product? (2) When we 
 say, 5 times 8 are 40, which of these numbers is the 
 multiplicand ?— which the multiplier ?—and which 
 the product? (3) Can you obtain the product of 
 any two numbers, by means of addition? (4) Re- 
 cite the rule for multiplication. (5) When there 
 are ciphers between figures in the multiplier, what 
 may be done? (6) When there are ciphers on the 
 right of the multiplier, or multiplicand, or on the 
 right of both, what may be done withthem? (7) In 
 what manner can you multiply by 10, by 100, by 
 1000, &c.? (8) What is meant by the factors of a 
 number? (9) Name two factors of 24. (10) Name 
 three factors of 24. (11) Name two factors of 36. 
 (12) Name three factors of 36. 
 
 Perform the following examples by either of the fore- 
 going methods, which may be found convenient. 
 
 26. What is the value of a farm consisting of 200 
 acres of land, at 40 dollars an acre? 
 
 27. Suppose a book to contain 235 pages, 45 lines 
 in each page, and 50 letters in each line;—how many 
 letters are there in the book? , 
 
 28. Suppose an orchard to consist of 109 rows, 126 
 trees in a row, and 1007 apples on a tree;— how many 
 trees, and how many apples are there? 
 
 29. Suppose a crew of fifty men have provision for 30 
 days, allowing each man 20 ounces a day;— how many 
 days would it last, if each man ate 1 ounce a day? 
 
 30. Suppose a crew of fifty men have provision for 
 30 days, allowing each man 20 ounces a day;— how 
 many men would it serve for the same time, if each man 
 
 ~ ate one ounce a day? 
 
 31. How many fishes would be caught by 14 boats, 
 employed for 30 days, each boat drawing a net 15 times 
 a day, and taking 13 fishes each draught? 
 
 32. What is the product of 90042 multiplied by 9009 ? 
 
108 WRITTEN ARITHMETIC. Vv. 
 
 CHAP. V. 
 “DIVISION. 
 
 Section l. 
 
 1. How many yards of cloth, at 3 dollars a yard, can 
 be bought for 396 dollars ? 
 
 Here we must find how many times 3 dollars there 
 are in 396 dollars: that is, we must divide 396 by 3. 
 
 3)396 We first divide the 3 hundreds, then the 
 
 132. «9 tens, and then the 6 units; thus, 3 in 3, 
 ! once; 3 in 9, 3 times; 3:in 6, 2 times. 
 
 Observe in the above example, that the 3 which we 
 first divide, means 3 hundred; and the 1 which we place 
 under it means 1 hundred, showing that 3 is contained 
 in 300, 100 times. The 9 means 9 fens, and the 3 
 which we place under it means 3 tens, showing, that 3 
 is contained in 90, 30 times. 
 
 A. Dividend is a number which is to be divided; such 
 is the number 396 in the above example. A Divisor is 
 a number by which we divide; such is the number 3 in 
 the above example. The Quotient is the number of 
 times which the divisor is contained in the dividend; 
 such is the number 132 in the above example. . 
 
 Find the quotient in each of the following examples. 
 (2). 4)8 (3). 2)46 (4). 3)936 (5). 4)4884 
 
 6. A man laid out 69 dollars for sheep, paying 3 dol- — 
 lars a head for them. How many did he buy ? . 
 7. If 4 bushels of wheat will pay for 1 barrel of flour, 
 how many barrels will 848 bushels pay for ? 
 
 Section 2. 
 1. How many times is 4 contained in 3684? 
 
 4)3684 In this example we find that 4 is not 
 921 contained in 3, therefore we join the 3 
 ~—— with the 6, and say, 4 in 36, 9 times. 
 
“ DIVISION. 109 
 
 - How many times is 7 contained in 56? 
 - How many times is 9 contained in 639? 
 - How many times is 5 contained in 405? 
 - How many times is 4 contained in 3248? 
 . How many times is 8 contained in 1569? 
 - If 4 horses are required to draw 1 wagon, how 
 many wagons might be drawn by 168 horses? 
 8. How many yards of broad-cloth, that is sold at 6 
 dollars a yard, can be bought for 492 dollars? 
 9. If a man can travel 5 miles an hour, how many 
 
 IAB ow yw 
 
 f 5 hours will it take him to travel 205 miles? 
 
 -10. Suppose 69 to be a dividend, and 3 a divisor; 
 what is the quotient? ~ 
 11. Suppose 128 to be a dividend, and 4 a divisor; 
 what is the quotient? “a : 
 12. Suppose 486 to be a dividend, and 6 a divisor; 
 what is the quotient? Mh: fe 
 13. How many times is 4 contained in 8722. 
 4)872 4 in 8, 2 times; 4 in 7, 1 time, and 
 218 there is 3 over;. (we join this 3 with the 2, 
 == making 32,) then 4 in 32, 8 times. 
 14. How many times is 6 contained in 726? 
 15. How many times is 8 contained in $96? 
 16. How many times is 5 contained in 1605? 
 17. How many'times is 7 contained in 924? 
 - 18. How many times is 4 contained in 6732? 
 19. Suppose 1585 to be a dividend and 6 the divi- 
 sor; what is the quotient? 
 20. Suppose 4518 to be a dividend and 6 the divi- 
 » sor;. what is the product? 
 21. How many times is 7 contained in 742? 
 7742. The divisor not being contained once in 
 “= the ten’s place of the dividend we writea , 
 - 106 - 0 in the ten’s place of the quotient. 
 22. How many times is 3 contained in 609? 
 23. How many times is«8 contained in 1624? 
 24. How many times is 5 contained in 4015?, 
 25. How many times is 9 contained in 2880? 
 26. How many times is 7 contained in 10500? 
 K 
 
110 WRITTEN ARITHMETIC. Vv. 
 
 27. If I had 78 dollars to lay out for flour, and the 
 flour was 6 dollars a barrel, how many barrels could I 
 buy for all the money? 
 
 28. A drover received 268 dollars for sheep, that he 
 sold at 4 dollars a héad.. How many were there? 
 
 29. If 1 ton of hay be worth 9 bushels of corn, how 
 many tons of hay are 576 bushels of corn worth? 
 
 30. If 3 bushels of wheat will pay for a yard of cloth, 
 how many yards will 105 bushels pay for? 
 
 31. How many soldiers may be clothed from 5708 
 
 yards of cloth, allowing 4 yards to make a suit? 
 
 ’ . 32. How many muskets can be purchased for 2952 
 dollars; the price being 6 dollars apiece? = 
 
 33. If 76 dollars should be divided equally among 4 
 men, how many dollars would each man receive? 
 
 If there were only 4 dollars to be divided, each man 
 would receive just 1 dollar: therefore each man must 
 receive as many dollars as there are fours in 76. 
 
 34. Suppose 5 men have to pay a bill of 95 dollars, , 
 how many dollars must each man pay? | 
 
 35. If 171 biscuit be divided: equally among a crew 
 of 9 sailors, how many does each sailor receive? 
 
 36. A farmer planted 354 trees, in 6 equal rows. 
 How many were there in 1 row? ft 
 
 37. A fisherman hired a boat, agreeing to give the 
 owner | fish of every 7 that he might catch: he caught 
 434. How many should he give the owner? 
 
 38. 8 sailors received 1576 dollars for retaking their 
 ship. How much did each sailor receive? 
 
 39. A man intending to go a journey of 336 miles, 
 wishes to perform it in 6 days. How many miles must 
 he travel each day? ; ; 
 
 40. 9 men have agreed to make up a purse of 2178 
 dollars. How many dollars must each one put in? 
 
 41. Suppose A to spend 3 dollars as often as B spends 
 1 dollar; how many dollars will B spend while A is 
 spending 89004 dollars? = * ‘ 
 
 42. Suppose 3656 dollars have been equally divided 
 among a number of men, and each man has received 8 
 dollars; how many men were there? 
 
9, DIVISION, ee 
 
 43. A number of men contributed 9 dollars apiece, 
 and thereby made up a purse of 54 dollars. How many 
 men were there? 
 
 44. Suppose 9 has been multiplied by some number, 
 and the product is 54; what was the multiplier? 
 
 45. 5 men paid equal’ shares of a debt of 80 dollars. 
 How much did each man pay ? 
 
 46. Suppose some number has been multiplied by 5 
 and the product is 80; what number was multiplied ? 
 
 47. Two numbers have been multiplied together, and 
 their product is 126: one of the two numbers multiplied 
 is 7;—— what is the other ?» 
 
 48. Divide 348 by 4; then prove the work to be right, 
 by multiplying the quotient and divisor together ? 
 
 4)348 We find by the quotient, there are 87 
 - times 4 in 348: therefore we know that 87 
 37 ; 3 
 4 times 4, or 4 times 87, must make 348. 
 - Had our quotient been wrong, our product 
 348 and dividend would not be equal. 
 
 49. Divide 72 by 8, and pfove the work to be right. 
 
 50. Divide 5890 by 5, and prove the work to be right. 
 
 51. Divide 39781 by 7, and prove the work to be right. 
 
 52. Divide 90048 by 8, and prove the work to be right. 
 
 53. Divide 17604 by 9, and prove the work to be right. 
 
 54. A hatter has 130 hats finished; and, in order to 
 send them to market, he must pack them in boxes, that 
 will hold 8 hats apiece. How many full boxes can he 
 send; and how many hats will remain on hand? 
 
 8)130 We have 2 units over. This 2 is a re- 
 
 169 mainder; it shows that there are 2 hats, 
 which cannot be divided into eights. 
 
 55. How many sheep, at 4 dollars a head, can a 
 butcher, who has 747 dollars buy; and how many dol- 
 lars will he have remaining ° 
 
 56. If 5 yards of cloth will make a suit of clothes, 
 how many suits can be made from 96 yards; and how 
 many yards will there be over? 
 
 57. How many times is 6 contained in 4637; and 
 how many are there over ? 
 
 5 
 
112 WRITTEN ARITHMETIC. V. 
 
 58. How many times is 8 contained in 9150; and 
 how many are there over? 
 
 59. Suppose 568 to be a dividend, and 7 the divisor;: 
 - what is the quotient, and the remainder ? 
 
 60. Suppose 1953 to be a dividend, and 7 the divi- 
 sor; what is the quotient, and the remainder ? 
 
 61. Divide 564 by 7, and prove the work to be right. 
 
 The remainder, in division, is an undivided part of the 
 dividend: therefore, the remainder must be added to the 
 “product of the divisor and quotient, to make the product 
 equal to the dividend. 
 
 62. Divide 109 by 6, and prove the vital to be right. 
 
 63. Divide 817 by 5, and prove the work to be right. 
 
 Section 3.° 
 
 The method of dividing taught in the two preceding 
 sections, is called Short division: the method taught in 
 this section; is called Long division. In long division, 
 we place the quotient on the right hand of the dividend, 
 and perform some operations under the dividend, here- 
 tofore performed in the mind. 
 
 1. How many times is 4 contained in 95307 ? 
 
 b& b& Doms Perceiving that 4 is contained 
 Ss S in 9, twice, we place 2 in. the 
 fa a a i eae multiply the divisor by 
 Bey se aR ii 
 = of 2, and subtract the product (8) 
 4)95307(23826 from 9. This is the same as_ 
 
 8 saying in shortdivision, ‘4 in 9, 
 seh 2 times, and 1 over.’ Now, 
 
 2 since the 1 over must be joined 
 ea with the 5, we bring the 5 down 
 at to the right of the 1: and then, 
 52 perceiving that 4 is contained in 
 10 15, 3 times, we place 3 in the 
 
 3 quotient, multiply the divisor 
 
 ee by 3, and subtract the product 
 
 ; as before. Thus we proceed to 
 
 24 He 
 
 | oo ring down every figure of the 
 
 Remainder 3 dividend, and unite it with the © 
 i previous remainder. 
 
we % 
 3. DIVISION. 113 
 
 Perform the following examples by long division. 
 How many times 5 are there in 7163? 
 
 . How many times 7 are there in 88704 ?' 
 
 . How many times 6 are there in 97 547? 
 
 How many times 3 are there in 8 057 251? 
 
 How many times 4 are there in 8708 983 ? 
 
 How many times 5 are there in 6.457 080? 
 
 - How many times 8 are there in 25 648? 
 
 The divisor not being contain- 
 
 a teres 
 
 8)25648(3206 » ed once in the left hand figure 
 feo of the dividend, we join this fig- 
 16 ure with the next. After bring- 
 16x} ing down the 4, we find the divi- 
 
 48 sor is not contained in it; there- 
 
 48 fore, we place a 0 inthe quotient, 
 
 rt and bring down the next figure. 
 
 9. How many times 5 are there in 43 906? 
 10. How many times 9 are there in 70 223°? 
 11. How many times 6 are there in 901 500? 
 12. How many times 7 are there in 161 635? 
 13. How many times. 24 are there in 3762? 
 24)37 62(156 This operation is performed 
 in the same manner that it would 
 
 kre have been, if the divisor had 
 136 consisted of only one figure. 
 120 The two following examples 
 162 will show the method of deter- 
 144, mining when a figure placed in 
 Tia the quotient is too great, and 
 18 
 — when it:is too small. 
 
 14. How many times is 18 contained in 12532? 
 In this example, we have 
 18)12532(697 — chosen 7 for the last figure of the 
 
 108 quotient; but it appears, that 7 
 173 times 18 are more than head 
 162 therefore 18 is not contained 7. 
 
 times in 112. The 7 and the 
 112 product arising from it must be 
 126 rubbed out, and a smaller figure 
 
 must be placed in the quotient. . 
 
 K* 
 
114 WRITTEN ARITHMETIC. Vv. 
 
 15. How many times is 35 contained in 45817? 
 Here we have chosen 8 for 
 
 if ebhe LY{ESO8 the fast figure of the quotient; 
 fut but, after subtracting 8 times 
 108 35 from 317, there remains, 37. 
 POP ze . This renahder will contain 
 Rh7 35, once more; therefore, we 
 280 must rub out the 8 and the 
 37 work resulting from it, and. 
 
 must put 9 in the place of 8. 
 16. How many times is 47 contained in 804? 
 
 17. How many times is 53 contained in 1625 ? 
 
 18. How many times is 68 contained in 94 605? 
 19. How many times is 71 contained in 661419 ¢ 
 20. How many times is 108 contained in 216? 
 
 21. How many times is 325 contained in 7134? 
 22. How many times is 476 contained in 92 107 ? 
 23. How many times is 504 contained in 1008? 
 24. How many times is 651 contained in 43 126? 
 
 RULE FOR DIVISION. When the divisor does not exe. 
 ceed 9, draw a line under the dividend, find how many 
 
 times the divisor is contained in the left hand figure, or 
 two left hand figures of the dividend, and write the figure 
 expressing the number of times underneath: if there be a 
 remainder over, conceive it to be prefixed to the next fig- 
 ure of the dividend, and divide the next figure as before. 
 Thus proceed through the dividend. | 
 
 When the divisor is more than 9, find how many times 
 it is contained in the fewest figures that will contain it, 
 on the left of the dividend, write the firwre expressing 
 the number of times to the right of the dwidend, for the 
 first quotient figure; multiply the divisor by this figure, 
 and subtract the product from the figures of the dividend 
 considered. Place the next figure of the dividend on the 
 right of the remainder, and divide this number as before. 
 " Thus proceed through ‘the dividend. 
 
 PROOF. Multiply the divisor and quotient together, 
 and to the product add the remainder: the sum will be 
 equal to the dividend, if the work be right. 
 
 ne 
 
 4 
 p 
 
3 | DIVISION. 115 
 25. Divide 46242 by 252, and prove the operation. 
 
 252)46242(183 | i 252. 
 252 he 183 
 ign... &. by 756. 
 
 2016 2016 
 
 882 252 
 756 ; 126 
 126 | 46242 
 
 . 26. Divide 74 201 by 625, and prove the operation. 
 27. Divide 408 732 by 9, and prove the operation. 
 28. Divide 15 362 by 88, and prove the operation. 
 29. Divide 57 026 by 492, and prove the operation. 
 30. Divide 982 700: by 53, and prove the operation. 
 31. Divide 162 941 by 256, and prove the operation. 
 32. Divide 648 035 by 14, and prove the operation. 
 33. Divide 106 401 by 333, and prove the operation. 
 
 "34. Divide 62 509 by 4423, and prove the operation. 
 35. Divide 1 071 400 by 29, and prove the operation. 
 36. How many acres of land, at 22 dollars an acre, 
 
 can be bought for 8514 dollars ? 
 
 "eet. Suppose a man to earn 35 dollars a month; how 
 
 many months will it take him to earn 490 dollars: >» 
 
 38. If a man travel 48 miles a day, in how many days 
 will he perform a journey of 3264 miles? 
 
 39. If 774 dollars be divided equally among 18 sail- 
 ors, how many dollars will each sailor receive ? 
 
 40. If a man’s income be 2555 dollars a year, how 
 much is it a day, there being 365 days in a year? 
 
 41. The income of the Chancellor of England, ‘is 
 
 99 280 dollars a year. How much is it per day? 
 
 42. 63 gallons of water will fill a hogshead. How 
 many hogsheads will 5166 gallons fill ? 
 
 43. How many hogsheads can be filled from 19721 
 gallons : ?—and how many gallons will there be left? 
 
 44. Suppose aregiment of 512 men have 8192 pounds 
 of beef; how many pounds are there for each man? 
 
 45. if a dividend be 46 319, and the divisor 807, 
 what is the quotient ?— and what the remainder ? 
 
 ¥ 
 
116 WRITTEN ARITHMETIC. V. 
 
 » Section 4. | 
 ABBREVIATIONS. 
 
 When there are ciphers onthe right hand of a divisor, 
 
 cut them off, and omit them tn the operation; also cut off 
 
 and omit the same number of figures from the right hand 
 of the dividend. Finally, place the figures cut off from 
 the dividend, on the right of the remainder. 
 
 1. How many times 900 are there in 741 725? 
 900)7417125 _ We divide 7417 by 9; there 
 
 oe remains 1, to which we annex the 
 
 S24 125 95, making the true rem.. 125. 
 
 How many times 70 are there in 8 563612? 
 
 How many times 300 are there in 6374? 
 
 How many times 5000 are there in 46 578 ? 
 
 How many times 40 are there in 80603? 
 
 How many times 600 are there 675 700? 
 
 How many times 8000 are there in 16 000? 
 
 . Divide 65 237 by 50, and prove the operation. 
 
 . Divide 567 289 by 400, and prove the operation. 
 
 10. How many times 570 are there in 35871? 
 
 11. How many times 280 are there in 6423? 
 
 12. How many times 4200 are there in 91621? 
 
 13. How many times 9060 are there in 287 000? 
 
 When the divisor is 10, 100, 1000, §c., cut off as 
 many figures from the right hand of the dividend, as 
 
 a igh TBE cos 
 
 there are ciphers in the divisor; the other figures of the 
 dividend will be the quotient, and the gures cut off will 
 
 be the remainder. 
 
 14. How many times 10 are there in 240? 
 15. How many times 10 in 435; and how many over ? 
 16. How many times 100 are there in 4000? 
 
 17. How many times 100 in 748; and how many over? — 
 18. 100 cents are equal 1 dollar. How many 
 
 dollars are there in 5400 cents ? 
 
 19. In 642 cents, how many dollars are there; and | 
 
 how many cents over? 
 20. In 1937 cents, how many. dollars are thieds and 
 how many cents over? j 
 
 _ ee 
 
4. DIVISION. “117 
 
 When factors of the divisor can be found, (that is,. 
 when two numbers can be found, which, being multiplied 
 together, produce the divisor,) you may divide the divi- 
 dend by one of the factors, and the quotient thence arising 
 by the other: the last quotient will be the true one. a 
 
 21. Ina certain school there are 36 scholars, among 
 whom 540 quills are to be equally divided. How many 
 will’ iggcholar'réceive 2. oso) uy AQ oe 
 _.Let-us suppose the school to be divided into 4 classes, 
 
 allowing 9 scholars to be im each class. Then we will 
 find how many quills 1 class will receive, and from this 
 -number, findyhow many 1 scholar will receive. i 
 
 A) A 0 number of quills for the schddl. 
 
 9)135 number of quills for 1 class. 
 15 number of guills for 1 scholar. 
 
 Observe in the above example, that the divisors 4 and 
 9, are the factors of 36: and, if we had divided first by 
 the 9, and then by the 4,-our last quotient would have 
 been the same it now is. 
 
 22. Divide 11 376 by 72; using the factors of 72. 
 
 _ 23. If 1024 dollars be divided equally among 64 men, 
 how many dollars will } man receive ? 
 
 24. How many times is 42 contained in 1176? 
 
 25. If 27 yards of cloth cost 216 dollars, how many 
 dollars does 1 yard cost? phe 
 
 26. Suppose 1952 to be a dividend, and 32 the divi- 
 sor; what is the quotient? , 
 
 ad 
 
 To obiain the true remainder, where factors have been 
 used as divisors, multiply the last remainder by the firs: 
 divisor, and to the product add the first remainder. 
 
 97. Suppose 622 to be a dividend, and 35 the divi- 
 “sor; what is the quotient; and what the remainder? .. ~ 
 _. * 28..Suppose 99 to be a dividend, and 25 the divisor; 
 what is the quotient; and what the remainder ? a 
 29. Suppose 4862 to be a dividend, and 81 the divi- 
 
 sgor; what is the quotient; and what the remainder ? 
 ~ 30. Divide 1739 by 56. 
 
118 WRITTEN ARITHMETIC. Vv. 
 
 Questions to be answered Orally. 
 
 (1) When we say, ‘3 is contained in 20, 6 times, 
 and 2 over,’ which of these numbers have we for the 
 dividend ?— Which for the divisor >— Which for the 
 
 ‘| quotient ?— Which for the remainder ? (2) What 
 
 is meant by the dividend? (3) What is meant by 
 the divisor? (4) What is meant by the quotient? 
 (5) What is meant by the remainder? (6) Can the 
 remainder ever be equal to, or greater than the divi- 
 sor?—Why ? /(7) Suppose you have a number of 
 dollars to divide among a number of men; which num- 
 ber do you make the dividend ;— and which the divisor ? 
 —HIf there be a remainder, will it be so many dollars, 
 or so many men? (8) Recite the rule for division. 
 (9) How do you proceed when there are ciphers.on 
 the right hand of the divisor? , (10) How do you 
 divide by 10, 100, 1000, &c.? (11) How can you 
 divide by means of factors? (12) When you have 
 divided by the factors of the divisor, how do you find 
 the true remainder? © (13) How do you prove an 
 operation in division? 
 
 Perform the following examples by either of the fore- 
 going methods, which may be found convenient. 
 
 31. Suppose it takes 7 bushels of apples to make a 
 barrel of cider, how many barrels of cider can be made 
 from 945 bushels of apples ? 
 
 32. Suppose an acre of land properly cultivated, to 
 produce 38 bushels of corn; how ae acres must be 
 cultivated to produce 4902 bushels? 
 
 33. If 50 dollars will pay for an acre of land, how 
 many acres can be bought for 6900 dollars ? 
 
 34. How many days will a ship be in sailing from 
 New York to Liverpool; ‘allowing the distance to be . 
 3000 miles, and the ship to sail 100 miles a day ? 
 
 35. A vintner wishes to put 6615 gallons of wine into 
 hogsheads that will hold 63 gallons aplece y— how many. 
 hogsheads must he have ? 
 
4. . RETROSPECTIVE OBSERVATIONS. ae 
 
 36. If yo had 118 dollars, how many hats could you 
 pay for, at.5 dollars apiece; and what number of dollars 
 ee you have left? = 
 
 . Suppose a drover has 2130 dollars; how many 
 oxen can he pay’for, at 47 dollars ARE Es and how 
 many dollars will he have left? 
 
 38. In 668 360 yards of cloth, how many pieces, and 
 how many bales; there being 35 yards in each piece, 
 ang oF pieces in each bale? 
 
 If 4810 dollars be shared equally among 130 men, 
 ia much will each man redeive? ~ 
 
 40. A farmer planted 2072 trees in 14 equal. rows. 
 ’ How many did he plant if’a row? | 
 
 41..A gentleman wishes to spend 136 days im per- 
 forming a journey of. 3264 miles. How many miles 
 must he travel each day?.. 
 
 42. If'a man whose property is valued at 21148 dol- 
 lars be worth 17 times as much as his neighbor, how 
 much is his neighbor worth? 
 
 RETROSPECTIVE OBSERVATIONS. 
 
 In the course of the last four chapters, you have 
 practised four kinds of operations on numbers:: viz. 
 Addition, Subtraction, Multiplication, and Division. 
 These operations should be perfectly understood—the 
 effect of each should be distinctly perceived; for, it is 
 on their proper application, that the solution of all ques- 
 tions in arithmetic depends. 
 
 Addition is the operation by which two or more 
 numbers are united in one sum. 
 
 Subtraction is the operation by which the difference 
 between two numbers is found. 
 
 ‘Multiplication is the operation by which a icra is 
 produced, equal to as many times one given number, as 
 there are units in another given number. 
 
 Division is the operation by which we find how many 
 times one number contains another,— and, by which we 
 divide one given number into as many equal parts, as 
 there are units in another given number. 
 
 r, c 
 
 ¥ 
 
120 WRITTEN ARITHMETIC. | Ve 
 Questions to be answered Orally. 
 (1). How many kinds.of operations are practised | 
 on numbers?) (2) What are they called? (3). What 
 is Addition? (4) What is Subtraction? (5) What 
 is Multiplication? (6) Whatis Division? (7) Pro- 
 pose a question that you would solve by addition. 
 (8) Propose a question that you,would solve by sub- 
 traction. (9) Propose a question that you would 
 solve by multiplication. (10) Propose’a question 
 that you would solve by division. (11) How can a} 
 question in multiplication be solved by addition? | | 
 (12) How can a question in division be solved by. 
 subtraction? : 
 
 Section 5. 
 MISCELLANEOUS EXAMPLES. 
 
 1. The population of the world has been estimated 
 to be as follows. North America, twenty-six millions; 
 South America; twelve millions; Europe, two hundred 
 and twenty millions; Asia, five hundred millions; Africa, 
 thirty-eight millions; Australia, four millions. What is 
 the whole number? ie 
 
 .2. In 1830, the national debt of the United States 
 was 48 565406 dollars; in 1831 it was 39123191 dol- 
 lars. ._How much was paid in one year? 
 
 3. The national debt of England cannot be less than - 
 1900000 000 doliars, ° How many years would it take 
 to pay this debt, allowing ‘ten millions of dollars to be 
 paid annually? : | 
 
 4. What would be the expense of laying a rail-way 
 from Louisiana to Maine; the distance being 1800 miles, 
 and the rail-way costing 14000 dollars a mile?) 
 
 5. In how many days could a passage be effected 
 from Maine to Louisiana, on the proposed rail-way; 
 allowing a-car to run 25 miles an hour, day and night? 
 
 6. How many days would it take a man to ride on 
 horseback from Maine to Louisiana, riding 5 miles an 
 hour, and 10 hours a day? 
 
 * 
 
5. MISCELLANEOUS EXAMPLES. 121 
 
 7. Light passes from the sun to the earth—a distance 
 ‘of 95 millions of miles—in about 8 minutes. What 
 distance does light move in a minute? 
 
 8. The diameter of the earth is 7912 miles; and the 
 diameter of the sun is 112 times as great. What is the 
 diameter of the sun? 
 
 9. The income of the Bishop of Durham, in England, 
 is 106 560 dollars per annum. How many clergymen 
 would this support, on a salary of 800 dollars per annum? 
 
 ~10. Five men and three boys found a sum of money, 
 and divided it so that each man had 43 dollars and each 
 boy 26 dollars. What sum did they find? 
 
 11. Ifa trader buy 558 barrels of flour at 5 dollars a 
 barrel, and pay 14 dollars for storage, for how much 
 must he sell the flour, to gain 160 dollars? 
 
 12. Suppose 5 bushels of wheat to make a barrel of 
 flour, how many barrels of flour can be made from 12 
 bins of wheat, each bin containing 95 bushels? 
 
 13. In 12 times 95, how many times 5? 
 
 14. Ifa farmer sell 45 acres of land at 38 dollars an 
 acre, and divide the money equally among 4 sons and 1 
 daughter, what is each one’s share? 
 
 15. A man, who owned 520 acres of land, purchased 
 376 acres more, and then divided the whole into 8 equal 
 farms. How many acres did each farm contain? 
 
 16. In 520 plus 376, how many times 8? 
 
 17. If a man’s income be 1349 dollars a year, and 
 his expenses 3 dollars a day, how much will he Jay up 
 in a year; there being 365 days in a year? : 
 
 18. A merchant. gave 39 240 dollars for a cargo of 
 sugar, and after selling it, found he had gained 1671 
 dollars. For how much did he sell it? . 
 
 19..A merchant gave 18 dollars a hogshead for 24 
 hogsheads of molasses, and then sold the whole for 4000 
 dollars: did he gain or lose;—and how much? 
 
 20. A lot of land was divided into 8 farms, and each 
 farm contained 150 acres. How many acres were there 
 in the whole lot? 
 
 21. If a man’s expenses are 2 dol. a day, and his 
 income 17 dol. a week; what will he save in 7 weeks? | 
 
 L 
 
 ’ 
 
122 WRITTEN ARITHMETIC, Vi 
 
 22. Three men bought a ship: the first man paid 2274 
 dollars; the second paid 3 times as much as the first, 
 and the third paid as much as the first and second both. 
 What was the price of the ship? ) 
 
 23. A hogshead holds 63 gallons. How many gallons 
 of wine are there in 20 hogsheads; allowing that oat 
 hogshead wants 5 gallons of being full? 
 
 24. If a man earn 36 dollars a month, how many 
 months will it take him to earn 576 dollars? 
 
 25. If a man earn 40 dollars a month, and spend 13 
 dollars a month, how many months will it take him to 
 lay up 297 dollars? 
 
 26. A farmer having 20 barrels of pork, sold 9 barrels 
 at 22 dollars a barrel, and the remainder at 19 dollars a 
 barrel. What did he get for the whole? ; 
 
 27. If a trader, who has 152 barrels of flour, should 
 Jay out 1370 dollars in buying more flour, at 5 dollars a 
 barrel, how many barrels would he have? 
 
 28. A trader hired 650 dollars, and in 6 months a a 
 all but 92 dollars. How much did he pay? 
 
 29. What is the value of 139 yards of broad-cloth, ‘at 
 7 dollars per yard? 
 
 By the method of reasoning heretofore practised, we 
 should say in this solution, 139 yards are worth 139 
 times 7 dollars; and thus we should make 7 the multi- 
 plicand, and 139 the multiplier. But since it 1s more 
 convenient to make the smallernumber the multiplier, we 
 reason thus,—If the value of 1 yard were 1 dollar, the 
 value of 129 yards would be 139 dollars; since the value 
 of 1 yard is 7 dollars, the value of 139 yards is 7 times 
 139 dollars: and accordingly we make 139 the multiph- 
 cand, and 7 the multiplier. 
 
 30. A trader bought 240 sheep, at 4 dollars a head, 
 and paid for them in cows, at 20 dollars a head. How 
 many cows did he give? 
 
 31. If I pay 6 dollars an acre for the ploughing of 18 
 acres of land, and 100 dollars for having the whole 
 planted and hoed, what does the cultivation cost? 
 
 32. How many cows at 19 dollars a head, coll Pay 
 for 38 sheep at 4 dollars a head? 
 
‘he 
 
 5. MISCELLANEOUS a a 123 
 
 83. A farmer bought a field, val ed at 150 dols., for 
 which he gave 9 cows, valued at 14 dols. apiece, and 
 the rest in money. How much money did he pay? 
 
 34. What number must be added to 9 times 14, in 
 order that the sum shall be 150? 
 
 35. If a stage travel 13 miles in the same time that a 
 wagon travels 5 miles, how many miles will a stage 
 travel while the wagon Is travelling 65 miles? 
 
 36. Suppose that 9 bushels of wheat will fill a hogs- 
 head; how many hogsheads can be filled from a heap 
 containing 149 bushels; and how many bushels will be 
 left in the heap? 
 
 37. Charles and Joseph are studying arithmetic. 
 Charles is 322,examples in advance of Joseph, but 
 hele performs 55 examples in a day, and Charles, 
 41. In how many days will J. overtake ©.? 
 
 38. Two men started together and travelled on the 
 same road, at the rate of 7 miles an hour: but one of 
 them rested 1 hour in every 3 hours, and the other 
 rested-1 hour in every 4 hours. How far apart were 
 they, at the end of 12 hours? 
 
 389. A drover, having 599 dollars, wishes to buy all 
 
 the oxen he can pay for, at 34 dollars a head, and then 
 lay out the remainder of his money for ney. at 3 dollars 
 ahead. How many of each must he buy? 
 
 40. A, B, and © made upa purse of 500 dollars. A 
 put in 16 dollars, and B put in 3 times as much. How 
 “much did C put in? | 
 
 41. A merchant bought 64 tons of hemp at 215 dol- 
 lars a ton. How many ten-dollar pane notes did it take 
 to pay for the hemp: 
 
 42. A merchant paid 9600 itotlns for 43. tons of 
 hemp. At how much must he sell the hemp per ton, in 
 order to gain 247 dollars? 
 
 43. What number must be subtracted from 7342, in 
 order that the remainder shall be 456? 
 
 44. What number must be multiplied by 30, in order 
 that the product shall be 2130? 
 
 45. What number must be divided by 15, in order 
 that the quotient shall be 640? 
 
e 
 
 124 WRITTEN ARITHMETIC. Vv. 
 
 Section 6. 
 FEDERAL MONEY. 
 
 Federal money is the national currency of the United 
 States. Its several denominations are,— the MILL, the 
 CENT, the DOLLAR, and the EAGLE. 
 
 10 mills are equal in value to 1 cent. , 
 10 cents are equal to 1 dime. 
 
 10 dimes, or 100 cents, are equal to 1 dollar. 
 
 10 dollars are equal to 1 eagle. | 
 
 In commerce, we express eagles in dollars, and dimes 
 in cents. For example, instead of saying, 2 eagles and 
 5 dollars, we say, 25 dollars: and instead of saying, 3 
 dimes and 4 cents, we say, 34 cents. 
 
 1. How many cents are there in 86 dollars? (See 
 method of multiplying by 100, in page 106.) 
 
 2. How many cents in 7 dollars and 58 cents? 
 
 3. How many dollars are there in 3700 cents? (See 
 method of dividing by 100, in page 116.) 
 
 4. Howmany dols. and how many cts. over, in 534 cts.? 
 
 This character, $, placed before a number, shows the 
 number to express. dollars. For example, $12, is 12 
 dollars. When dollars and cents are expressed in one 
 sum, they are separated by'a point, thus, $4.16; to be 
 read, 4 dollars and 16 cents. Observe, there must be 
 two places of figures for cents: therefore, if the cents be 
 less than 10, a ‘cipher. must ‘be placed on the left hand 
 of the figure which expresses them. For example, 56 
 dollars and 9 cents is written thus, $56.09, 0 
 
 / 5, What is the woe sum of $34.25, $18.04, $142, 
 $176.81, and 58 cents? 
 
 34.25 In writing these numbers for addition, 
 18.04 . we place dollars under dollars, and cents 
 142 under cents. We then add up each col- 
 
 176.81 | umn, just as we add the columns of sim- 
 
 58 ple numbers. Finally, we point off two 
 ficures on the right of thé*sum for cents, 
 and the other figures are dollars. 
 
6. FEDERAL MONEY. 125, 
 
 6. What is the sum of $57.20, $6.02, and $81.16? 
 
 7. Add together $538, $1.52, $5.07, and 68 cents. 
 
 8. Add together 18 cents, $70.19, $56, and 7 cents. 
 
 9. Add together 36 dollars, 7 dollars and 45 cents, 
 
 * 86 cents, 130 dollars and 6 cents, and 340 dollars. 
 
 10. Add together 9 dollars, 1 dollar and 70 cents, 13 
 dollars and 7 cents, 50° cents, and 10 cents. 
 
 11. Add together 47 cents, 62 dollars, 9 dollars and 
 12 cents, 5 dollars agd 5 cents, and 3 dollars. 
 
 12. Add together 37 dollars, 4 dollars and 17 cents, 
 96 dollars and 1 cent, 99 cents, and 2 dollars. 
 
 13. What is the expense of one quarter’s schooling, 
 allowing $19 for board, $9 for tuition, $3.75 for books, 
 and 92 cents for stationary ? 
 
 14. A sailor paid $16.35 for a hogshead of molasses; 
 in New Orleans, and also. paid ¢3. 40 for the freight of 
 the molasses to Boston. For how much must he sell it 
 in Boston, in order to gain $4? 
 
 15. Subtract $4.35 from $6.48; taking cents from 
 cents, and dollars from dollars. 
 
 16. Subtract $7.18 from $48.50 
 
 17. Subtract $251.12 from $546.18. 
 
 18. Subtract $47.56 from $319. 
 
 319.00 In writing these sums of money for 
 
 47.56 subtraction, we supply the places of 
 
 sy, cents in the greater sum, by phere, 
 aia and then proceed to subtract. 
 
 When either of the sums of Federal money presented 
 for subtraction has no cents expressed, the places of cents 
 may be supplied by two ciphers. 
 
 19. Subtract $654 from $783.48. 
 
 20. Subtract $31.12 from $5390. 
 
 21. Subtract 42 cents from $51. 
 22. Subtract 7 cents from $1. ant 
 23. Subtract 5 cents from $754. An Bo sey 
 24. Subtract 4 cents from $4. PR sy ig 
 25. What is the difference between $3.06, and $9? 
 26. What is the difference between $6, and 7 cents? 
 
 L* 
 
126. WRITTEN ARITHMETIC. Vv. 
 
 27. A lady having $3, paid $1.15 for a yard of cam- 
 bric. How much money had she left ? 
 
 28. A farmer sold a barrel of pork for $21.50, taking 
 in payment a hogshead of salt at $5, and the rest in 
 money. How much money did he receive? 
 
 29. A trader began business with $648, and at the 
 end of 2 years, had $911.06. What did he gain? 
 
 30. A traveller having no money, sold his horse for 
 $92.75, and his gig for $78, and then paid $17 for pas- 
 sage home. How much money did he bring home? 
 
 31. A jockey gave $120 for a horse, and then ex- 
 changed for another horse, receiving $15.30 for differ- 
 ence of value, and then exchanged again, paying $28.50. 
 How much did the’last horse cost him? 
 
 32. How much is 18 times $4.72? ' 
 $4.72 is the same as 472 cents: there- 
 4.72 fore we multiply it as 472 cents, and the 
 18 product is 8496 cents. Now to change ~ 
 37 76 these cents todollars, we must divide them 
 ‘47 2 by 100: this we do, by pointing off two 
 484.96 figures for a remainder. The quotient is 
 ——— dollars, and the remainder is cents. 
 33. How much is 4 times $1.08 ? " 
 34. How much is 7 times $52. 31? 
 35. How many dollars are 8 times 75 cents? 
 36. How many dollars are 32 times 25 cents! ; 
 37. How much is 19 times 43 cents? 
 38. How much is 241. times. $654. 12? . 
 39. What is the value of 6 pounds of Hyson tea, at 
 $ 1.20 cents per pound ? 
 40. What is the value a 10 BES of flannel, at 64 
 cents per yard ? 
 41, What igithé value of 6° hats, at $6.47 ee 
 42. What will a laborer receive for 25 days’ work, 
 at $1.15 per day? 
 43. How much must be paid for 30 pounds of coffee, 
 when the price is 16 cents a pound? 
 44. How much must be paid for 12 drums of figs, 
 when the price is $1.55 a drum? 
 
6. FEDERAL MONEY. | 127 
 
 45. What is the value of 147 bushels of apples, at 8 
 cents per bushel ? 
 
 It is more convenient in this example, to make the 
 number of bushels the multiplicand and the number of 
 cents the multiplier. For method of reasoning, see re- 
 marks in section 5, under example 29. 
 
 46. If a man spend 28 cents a day, how much will 
 he spend in 365 days, or 1 year? 
 
 47. What is the cost of 430 pounds of SHORES at 
 20 cents per pound? 
 
 48. At 6 cents a pound, what is the value iH a quarter 
 of beef, weighing 214 pounds? 
 
 49. At $2.30, [230 cents] an acre, what is the value 
 of 4748 acres of wild land? 
 
 When the price of a single article is given in Federal 
 money, and the value of any number of that article is 
 required, either the price-may be multiplied by the num- 
 ber of articles, or the number of articles by the price; 
 the product will be the answer. 
 
 50. At $1.72 per pound, what is the value of 5 chests 
 of tea, each chest containing 64 pounds? ; 
 
 51. A trader gave $5.16 a barrel for 2170 barrels of 
 flour, and sold it so as to gain $100.50 on the, whole. f 
 For how much did he sell it ? 
 
 52. A man bought. 30 yards of cloth at 1.58 per 
 ‘ards and 30 yards at 86 cents per yard. How muéh 
 pages did the first piece cost, than the last ? 
 
 If I pay 22 cents a gallon for 72 hogsheads of 
 aes each hogshead. containing. 63 gallons, and then 
 sell the whole for $936, how much do I lose? 
 
 54. A man having $350, took.a journey of 700 miles, 
 paying 6 cents a mile for stage passage, and $14 for 
 board. How much money did he bring home ? 
 
 55. Ifa man earn $1.02 a day, and spend 36 cents a 
 day, how much will he lay up in 75, days? 
 
 56. If a man get $8.35 for every 6 days’ work, how 
 much will he get by working 510 days? 
 
 57. Suppose 42 casks to contain 46 gallons a mine 
 each; what is the value of the whole, at pl. AL pee? 
 
128 WRITTEN ARITHMETIC. Va 
 
 58. How many times 7 cents are there in $480.78? 
 7)430.78 We divide $430.78 as if the figures 
 stood to express the whole in cents. 
 
 61.84 he quotient is the number of times. 
 
 59. How many times 6 cents are there in $20.22? 
 
 60. How many times 15 cents are there in $11.10? 
 
 61. How many times 90 cents are there in $27.00? 
 
 62. How man¥ times $4.06, [406 cents | are there in 
 $190 146.04, [19014604 cna ? 
 
 63. How many lead pencils can you buy for $3.44, 
 when they are sold at 8 cents apiece? 
 
 64. How many pounds of butter, at 21 cents per 
 pound, can be bought for $3.57 ? 
 
 65. A laborer earned $53.75, by working at $1.25 a 
 
 day. How many days did he work ? 
 
 66. If 84 cents should be divided equally among 6 
 boys, what would each boy receive ? 
 
 67. If $28.71 [2871 cents] be divided equally among 
 9 men, what will each man receive? 
 
 68. If $205 58 be divided equally among 38 men, 
 what will each man receive ? 
 
 69. If $637 be divided equally among 24 men, what 
 will each man receive? 
 
 After dividing the number 
 
 24)637(26 of dollars by. the number of 
 ce men, it appears from the quo- 
 157 tient and remainder, that each 
 144 man can have $26, and still 
 1200 $13 will remain undivided. 
 
 een We change $13 to cents, 
 Tee by annexing two ciphers, and 
 
 100 then divide the cents by the 
 
 96 , number of men. From this 
 
 4 quotient and remainder yaa 
 
 i ears, that each man will have 
 Answer, $26.54. 54 Sent, and 4 cents will re- 
 
 Remainder, 4 cents. ya: undivided. 
 
 70. If $7640 be divided equally among 61 men, 
 what will each man receive ? 
 
6. FEDERAL MONEY. 129 
 
 71. 8 men received $ 230 for performing a piece of 
 work. What was each one’s share of the money ? 
 
 72. An insurance office, whose stock was owned in 
 1000 shares, divided among the stock-holders, piano. 
 How much was paid on one share? 
 
 73. The expense of a village school, for 6 months, 
 was $466.80; and it was. paid in equal shares by 40 
 gentlemen. What was each one’s share? 
 
 74. Add together $9.87, 50 cents, $705.30 and 
 $390: subtract from this sum, 606 dollars and 7 cents: 
 multiply the remainder by 45: divide the product by 37. 
 What is the quotient, and the remainder ? 
 
 75. A shoe-maker paid $1.58 apiece for 10 calf-skins, 
 and 22 cents a pound for 3 sides of sole leather, each 
 side weighing 35 pounds. From this stock he made 48 
 pairs of shoes, which he sold at $1.75 a pair. What 
 did he get for his work ? 
 
 76. Suppose a man, ate income is $400 a year, 
 should spend $3.90 a week, how much would he save 
 in 2 years; there being 52 weeks in 1 year? 
 
 77. Suppose wheat to be worth $1.05 per bushel, 
 and rye 70 cents per bushel: how many bushels of tye 
 must be given for 550 bushels of wheat ? 
 
 Questions to be answered Orally. 
 (1) What is Federal money? (2) State the 
 denominations of Federal money. (3) State. the 
 number of mills in a cent, the number of cents in a 
 dime, &c. (4) How many. cents make a dollar? 
 (5) By what short method do, you find the number of 
 cents in any number of dollars? (6) How do you 
 distinguish the number of dollars, that there are in 
 any number of cents? (7) In writing dollars ad 
 cents together, how many figures express the cents? 
 (S) When the cents to be written with dollars are 
 less than 10, what istobe done? (9) Suppose you 
 are dividing ‘dollars, and a remainder occurs, what is 
 to be done, in order to divide the remainder ? 
 
130 WRITTEN ARTE TTC. V. 
 Sorrow 7, | 
 TABLES OF COMPOUND NUMBERS. 
 _ ENGLISH MONEY is the national currency of England. 
 
 4 farthings (qr.) ....make 1 penny. d. 
 12) pence cits a: .+++make 1 shilling. S. 
 20 sshillings ........ make 1 pound. £. 
 
 TROY WEIGHT is used in weighing gold and silver. 
 24 grains (gr.)......make 1 pennyweight. dwt. 
 
 20 pennyweights ....make 1 ounce. 02." 
 
 12 ounces. 4 url make 1 pound. Ib. 
 
 AVOIRDUPOIS WEIGHT is the common weight, used in 
 weighing groceries, and all coarse commodities. 
 
 16 drams (dr.) ......make 1 ounce. OZ" 
 16: OUNCE Sis rs eo make | pound. Ib. 
 BS. OUNGS ee es ate make 1 quarter. qr. 
 
 4 Quartegs . sie: ...make 1 hundred-weight: cwt. 
 20 hundred-weight ...make 1 ton. fe 
 
 APOTHECARIES’ WEIGHT is used for the purpose of 
 compounding medicines, but not in selling them. 
 
 Gls. Brains (Pr. 64 v's make 1 scruple. 
 O\vegroples: nga, make 1 dram. Gb ay 
 Ge drains 4 tw ewes make 1 ounce. 5 
 12 ounces.........make 1 pound. ib 
 
 CLOTH MEASURE jis used in measuring cloth, lace, &e. 
 
 4 nails (na.).......make 1 quarter. qr. 
 Arnquarters oa. ..make 1 yard. yd. 
 Fy PURER DR siya ie, le te make 1 English ell. Fy. e. 
 5 \querters i... ...make 1 French ell. Fr. e. 
 3 quarters'........ make 1 Flemish ell. Fi. e. 
 DRY MEASURE Is used in measuring grain, salt, &c. 
 
 2 pints: (phy... . sc make Pguart’ "7 qt. 
 Be quarts els ss). make i peck) hs ee a 
 
 4 pecks . ++++++.+make 1 bushel. bu. 
 
7. COMPOUND NUMBERS. |. 131 
 
 Sod 
 
 WINE MEASURE is used by grocers and others, for 
 measuring wine, oil, molasses, and most other liquids. 
 
 4 gills (gi.)...-. seemaket pint, 7c pt. 
 Oe BRU feo aa tei 8 wien make 1 quart.  engt. 
 is UTES eH diate: gue make 1 gallon. gal. 
 ER Pe Ope ce) oe 8 a . make 1 barrel. mace 
 Ae LARS Ea A oleae ae make 1] tierce. . a 2aer 
 63° -gallons.......... make 1 hogshead. hhd. 
 84 gallons ....... -make 1 puncheon. pun. 
 TOG Mallon bey ks eee og make 1 pipe or but. «pp. 
 2 pipes, or 4 hhds. . . make 1 ton. | ed be 
 BEER MEASURE is used in measuring malt liquors. — 
 2. pitts (phi. as he make 1 quart. — He arts 
 A quarts ¢,-\/ eM ara make 1 gallon. — opal. 
 9 gallons ....: es aes ptm fein e002 Ca 
 a. firkins 37. yee make 1 kilderkin.) kil. 
 ®kilderkins' #7", make 1 barrel. bl. 
 LONG MEASURE is applied to length, distance, &c. 
 3 barley-corns ..... make 1 inch. ye We 
 12 "inches ois. t ep . make 1 foot. Ro oe at 
 Be FEU ces ten, Ce make 1 yard. yd. 
 54 yards or 165 feet ..make 1 rod or pole,» . 9 r. 
 ALS BOGS Es ba. oot abhi ate make 1 furlong. fur. 
 8 furlongs... 6.6.40 make 1 mile. ‘m. 
 ay PYANES i... 4th Cera make 1 league. i 
 92 furlongs... +... +s. make 1 geographical mile. _ 
 60. -geographical miles. make 1 degree. deg. 
 360 degrees....-...- the earth’s Se vinterence. 
 
 SQUARE MEASURE is used in hie ellos land, floor- 
 ing, boards, tiling, and all other surfaces ahidaver. 
 
 44° jnches i}. Ves make 1 foot. ft. 
 DLSSEe IEA al make l yard. “yd. 
 304 yards, or 272+ ft... make 1 rod or pole. st oT 
 ME" VES 262 igh oS «. make l-rood. See A 
 4 roods ....... Viale More. BESO AN O 
 640 acres... 0606s . make’ I made, , ays Sekt 
 
 as hates 
 HL stays FY | eye's 
 
132 WRITTEN ARITHMETIC. Vv. 
 
 CUBIC MEASURE is used in measuring solid bodies, 
 and in finding the capacity of rooms, boxes, &c. 
 
 71728 inchess.¥ ey fi o.% make 1 foot. ft. 
 40 feetofroundtimber. make 1 ton. sigh 
 
 . 50 feet of hewn timber . make 1 ton. Ty? 
 16 «cubic feet...... - make 1 footof wood. ft. w. 
 
 8 feetofwood...... make 1 cord of wood. Cz 
 
 TIME is naturally divided into days, by the revolution 
 ~ of the earth upon its axis; and into, years, by the revo- 
 lution of the earth round the sun. 
 
 60 seconds....,....make 1 minute. m. 
 GO aminuLes vy Bie sae .» make 1 hour. h. 
 24 -"hotire oor make 1 day. d. 
 GOB ORV Eh cist lais elie ee make 1 year. =. 
 
 The earth revolves round the sun once in 365 days, 
 5 hours, 48 minutes, and 48 seconds: this period is 
 therefore a Solar year. In order to keep pace with the 
 solar year in our reckoning, we makevevery fourth year 
 to contain 366 days, and eall it Leap year. 
 
 The year is divided into 12 months. The number | 
 of days in each month is commonly learned thus,— 
 
 ‘30 days hath September, ‘The 4th. 11th. 9th. and 6th., 
 April, June, and November ; Have 30 days to each affixed; 
 February hath 28 alone, And every other, 31, . 
 And all the rest have 31. Except the 2nd. month alone, 
 Leap year comes | year in 4; Which has but 28, in fine, ~ 
 
 Then February hathldaymore.’ |} 'Till leap year gives it 29,’ 
 
 Questions to be answered Orally. _ 
 
 (1) What is English money? (2) Recite the ta- 
 ble. (8) How many shillings are there in 2 pounds? 
 (4) How many pence in 2 shillings? (5) How ma- 
 ny pence in 8 farthings? (6) How many pence in 
 36 farthings? (7) How many farthings in 6d. 3qr. ? 
 
 (8) What is the use of Proy Weight? (9) Re- 
 cite the table. (10) How many ounces in 2 pounds? | 
 (11) How many penny-weights in 4 ounces? 
 
7 COMPOUND NUMBERS. 138 
 
 (12) What is the use of Avoirdupois Weight ? 
 (13) Recite the table. (14) How many ounces in4 
 pounds? (15) How many hundred-weight in 3 tons ? 
 (16) How many hundred-weight in 24 quarters? 
 
 (17) How is Apothecaries’ Weight used? -(18) 
 Recite the table. (19) How many scruples in 4 
 drams? (20) How many drams in 27 scruples?) 
 
 (21) What isthe use of Dry Measure? (22) Re- 
 .{ cite the table. (23) How many pecks in 12 bushels 
 -and 2 pecks? (24) How many bushels, and how 
 many pecks over in 35 pecks ? ta 
 
 (25) What is the use of Cloth Measure? (26) 
 Recite the table. (27) In 5 yards how many quar- 
 ters? (28) In 32 nails how many yards? (29) 
 How many English ells in 14 quarters ? 
 
 (30) To what is Wine Measure applied? (31) 
 Recite the table. (32) In 2 gallons of vinegar how | 
 many quarts >— how many pints ’—how many gills ? | 
 (33) In 32 gills how many gallons? 
 
 (34) What is measured by Beer Measure? (35) | 
 Recite the table. (36) How many gallons are there | 
 in 6 firkins? (37) How many kilderkins in 19 fir- | 
 kins? (38) How many firkins in 1 barrel ? 
 
 (39) What is Long Measure applied to? (40) 
 Recite the table. (41) What number of inches are | 
 there in | yard? (42) How many feet in 38 inches ? 
 (43) In 6 furlongs how many miles ? 
 
 (44) What is the use of Square Measure? (45) | 
 Recite the table. (46) How many square feet in 4 
 square yards? (47) How many rods in 2 roods? 
 (48) How many acres in 20 roods? 
 
 (49) What is the use of Cubic Measure? (50) | 
 Recite the table. (51) How many cubic feet are | 
 there in 3 feet of wood? (52) In 48 feet of wood, | 
 how many cords of wood? | 
 
 (53) How is time naturally divided? (54) Re- | 
 cite the table. (55) Whatisa Solar year? (56) | 
 How many months in a year? (57) Recite the 
 lines that tell the number of days in each month. 
 
134 WRITTEN ARITHMETIC. 
 
 Section 8. 
 REDUCTION OF COMPOUND NUMBERS. | 
 
 Reduction is the operation of changing any quantity 
 from its number in one denomination, to its number 
 in another denomination. For instance, if we change 
 an admeasurement from 2 feet to 24 inches, that is, if 
 we find how many inches there are in 2 feet, the opera- 
 tion is called reduction. Again, if we change 24 inches 
 to 2 feet, this operation is also called reduction. 
 
 ENGLISH MONEY. 
 
 1. How many farthings 
 in £13 8s. 4d. 2qr. 
 
 BONE OE. We 
 13 8 4 2 
 
 20 
 
 268 shillings. 
 L2G ii 
 
 oor 
 
 3220 pence. 
 4 
 
 Ans. 12882 farthings. 
 
 In this example, we con- 
 sider, that there are 20 
 times as many shillings as 
 pounds in any sum; there- 
 fore we multiply the 13 
 pounds by 20, and add the 
 8 shillings to the product. 
 Then, since there are 12 
 times as many pence as 
 there are shillings, we mul- 
 tiply the shillings by 12 and 
 add the 4 pence to the pro- 
 duct. Lastly, since there 
 are 4 times as many farth- 
 ings as pence, we multiply 
 the pence by 4, and add 2 
 farthings to the product. 
 
 e 
 
 2. How many pounds in 
 12882 farthings ? 
 
 qr. 
 4)12882 
 12)3220 Qgqr. 
 2|0)26/8 4d. 
 £13 8s. 
 
 £ s. d. qr. 
 Ans. 13 8 4 2 
 
 This example is the re- 
 verse of the first example. 
 We here consider, that ev- 
 ery 4 farthings make 1 pen- 
 ny; therefore, we find by 
 division how many times 4 
 there are in the number of 
 farthings: the quotient is 
 pence, and the remainder is 
 farthings. Then, since ev- 
 ery 12 pence is 1 shilling, 
 we divide the pence by 12; 
 the quotient is shillings, 
 and the remainder pence. 
 Lastly, since every 20 shil- 
 lings make 1 pound, we di- 
 vide the shillmgs by 20. 
 
 f 
 
8, COMPOUND NUMBERS. . 135 
 
 RULE FOR REDUCTION. When a greater denomina- 
 tion is to be reduced to a smaller, multiply the greater 
 denomination, by that number which is required of the 
 smaller, to make ONE of the greater; adding to the 
 product so many of the smaller denomination as are ez- 
 pressed in the given sum. Perform a like operation on 
 this product, and on each succeeding product. 
 
 When a smaller denomination is to be reduced to a 
 greater, divide the smaller.denomination by that number 
 which is required of the smaller, to make ONE of the nest 
 
 greater: the quotient will be of the greater denomination, | 
 
 and the remainder will be of the same denomination with 
 the dividend. Performa like operation on'this quotient, 
 and on each succeeding quotient. | 
 
 3. How many farthings are there in 18s. 7d. 3qr.? 
 
 4. How many pounds are there in 9207 farthings ? 
 
 5. How many pence are there in £5 Os. 1ld.? 
 
 6. How many shillings are there in 647 farthings ? 
 
 7. How many times § pence are there in £3 5s.? 
 
 TROY WEIGHT. a 
 8. How many grains in| 9. How many pounds in 
 
 15lb. lloz. 18dwt? 92112 grains ? 
 Ib. oz. dwt. 2|0) 
 Leuer (13 24)92112(38318 
 12 Te SO 13 
 191 201 
 20 192 12)191(15 
 3838 91 12 
 24 72 71 
 15352 192 60 
 7676. 192 11 
 
 Ans. 92112 grains. 
 ) Ans. 15\b. 1loz. 18dwt. 
 
 10. How many penny-weights in 9]b. 130z. 16dwt. ? 
 11. How many pounds of silver in 829 penny-weights? 
 12. How many grains in 100z. 19dwt. 12gr. ? 
 
 13. How many pounds in 23641 grains ? 
 
ry 
 J 
 
 136 WRITTEN ARITHMETIC. Ne 
 
 AVOIRDUPOIS WEIGHT. 
 
 14. How many pounds are there in J ton? 
 
 15. How many drams are there in 7 tons, 3 quarters, 
 97 pounds, 5 ounces, and 13 drams ? 
 
 16. How many tons are there in 31122 pounds? 
 
 17. What will 3 hundred-weight, 3 quarters, and 17 
 pounds of indigo cost, at $2.67 per pound? 
 
 18. A wealthy farmer wishes to put down 3T. 18cwt. 
 qr. 8lb. of butter, in firkins, containing 50 pounds 
 apiece. How many firkins will it require: ‘ 
 
 APOTHECARIES’ WEIGHT. 
 
 19. How many scruples are there in 1 pound? 
 
 20. How many pounds are thére in 1395 drams ? 
 
 21.,In 3ib 95 03 1D 10gr. of epecacuanba, how 
 many doses are there; each dose containing 30gr. ? 
 
 22. If it take 1 ounce of salts for a dose, what will 
 75 pounds amount to, at 4 cents a dose? 
 
 23. If it take 10 grains of calomel and 1 scruple of 
 Be for a dose, how many doses are there in lib 13 
 
 5; of such a mixture ? 
 CLOTH MEASURE. 
 
 24. How many nails are there in 1 English ell? 
 
 25 How many yards are there in 16240 nails? 
 
 26. In 320 yards, and 3 quarters, how many quarters ? 
 How many Flemish ells ? 
 
 27. How many more nails are there in 75 English 
 ells, than there are in 93 yards? 
 
 _ 28. A shop-keeper sold cloth enough in one day to 
 gain £6 1s. 8d., at a profit of 2 farthings on every 
 yard. How much did he sell? 
 
 DRY MEASURE. 
 
 29. How many pints are there in 1 bushel ? 
 
 30. How many pints are there in 58 bushels, 3 pecks, 
 7 He ale? and 1 pint? 
 
 . How many bushels are there in 8240 quarts ? 
 f “ee If 3 bushels and 2 pecks of corn will fill a barrel, 
 what quantity of corn will 20 barrels hold? 
 
 83. Suppose it takes 3 pecks of salt to preserve a 
 harrel of pork, how much salt would be necessary to 
 serve < barrels of pork ? 
 
8, COMPOUND NUMBERS. | 137 
 
 WINE MEASURE. 
 
 34. How many gills are there in 1 hogshead ? 
 
 35. How many hogsheads are there in 9084 pints ? 
 
 36. If 3 tierces of molasses be sold at 12 cents a 
 quart, what will the whole amount to? 
 
 37. What would 2 pipes of Madeira wine amount t to, 
 at 67 cents per quart? 
 
 38. Acertain toper drank 1 gill of rum every forenoon, 
 and 1 in the afternoon, for 6 years; in consequence of 
 which, he died. How many hogsheads did he drink ? ° 
 
 BEER MEASURE. 
 
 39. In 2 barrels and 1 firkin, how many pints? 
 
 40. In 6538 quarts, how many kilderkins ? 
 
 41. How many bottles, holding 6 gills apiece, will be 
 required, to bottle 6 barrels of porter? 
 
 42. A man retailed 4 barrels of ale, and received for 
 it $69.12. At what price did he sell it a pint ?. 
 
 43. Suppose a retailer to sell 3 quarts of porter every 
 day for 1 year, excepting 52 Sabbaths, how many bar- 
 rels would he sell in the year? ‘ 
 
 LONG MEASURE. 
 
 44. In 35 yards, 2 feet, 10 inches, how many inches ? 
 
 45. In 29578 barley-corns, how many yards? 
 
 46. In 16 leagues and 2 miles, how many rods? 
 
 47. How many geographical miles would a ship. sail, 
 in going round the globe? 
 
 48. In 2541 inches of wire, how many yards? 
 
 49. Suppose 7 inches of wire to make | link of a 
 chain, and 4 links to measure 1 foot; how many yards 
 of wire would make a chain 8 feet long ? 
 
 SQUARE MEASURE. 
 
 To find the number of square inches, feet, or rods, in 
 any surface which has four sides, and four equal angles, 
 [corners,| multiply the length dill breadth together. | 
 
 50. How many square “inches are there in a slate, 
 that is 13 inches long, and 8 inches wide ? 
 
 51. How many square rods are there in a field 28 
 rods long, and 16 rods wide? How many acres? 
 
 52. How many square yards of carpeting will cover a 
 floor 36 feet long, and 18 feet wide? 
 
 mu *. 
 
138 WRITTEN ARITHMETIC. V. 
 
 CUBIC MEASURE. 
 
 A cube may be illustrated by a solid block, having 6 
 equal sides. Let us suppose we have before us a num- 
 ber of small blocks, representing cubic inches. If we 
 lay 144 of these blocks together upon the table, they 
 will cover a square foot. Then, if we cover this layer 
 of blocks with another layer, and thus continue till we 
 have piled up 12 layers, the pile will contain 12 times 
 144 cubic inches, or 1 cubic foot. Therefore, to find 
 the cubical contents of any thing, multiply its length, and 
 breadth, and depth together. 
 
 53. How many cubic inches are there in a brick, 
 that is 8 inches long, 4 inches wide, and 2 inches thick ? 
 
 54. How many cubic feet in a box, that is 25 inches 
 
 long, 20 inches broad, and 11 inches deep? , 
 
 55. How many cubic inches in | ton of hewn timber ? 
 
 56. How many cubic feet in a pile of wood 15 feet 
 long, 4 feet wide, and 5 feet high? How many feet of 
 wood? -How many cords ? | 
 
 57. How many cubic feet in a cord of wood ? 
 
 TIME. 
 
 58. How many seconds are there in a common year ? 
 How many in a leap year? How many in a solar year ? 
 
 59. How many minutes are there in 57 days? 
 
 60. If your pulse beat 73 times in a minute, how 
 many times will they beat in the month of January ? 
 
 61. How many years and days, from the Ist day of 
 January, 1830, to the Ist day of October, 1834 ? 
 
 . Questions to be answered Orally. 
 
 (1) What is meant by reduction? (2) How do 
 you reduce shillings to pence? (3) How do you 
 reduce pence to shillings? (4) How do you reduce 
 Avoirdupois ounces to pounds?—-Why? (5) How 
 do you reduce pounds to ounces?— Why? (6) 
 How do you reduce yards to nails? (7) How do 
 you reduce nails to yards? (8) Recite the general 
 rule for reduction. — 
 
9, COMPOUND NUMBERS. 139 
 
 Section 9. 
 COMPOUND ADDITION. 
 
 ENGLISH MONEY. 
 1. What is the whole sum of £13 7s. 10d. Qqr., £4 
 12s. Od. Iqr., £60 Os. 11d. 3qr., 19s. Od. 2qr., £116, 
 £7 10s. 10d., 1s. 8d. 3qr., and £76? 
 
 The sum of the column of 
 
 ys: | de dr. 
 B37. .1 ho farthings is 11; equal to 2d. 3qr. 
 oe) aie oie. 1 We write the 3qr. and add the 
 60° O88bl 3 2d. to the column of pence. 
 Oi) i The sum of the pence is 41; 
 LYV6,. 0; a. equal to 3s. 5d. We write the 
 10 °TO. 0 5d. and add the 3s. to the column 
 fe ae 2 of shillings. The sum of the 
 *64..00 000 shillings is 52; equal to £2 12s. 
 278 12.5 3 We write the 12s.'and add the 
 
 £2 to the column of pounds. 
 
 RULE FOR COMPOUND ADDITION. Write the num- 
 bers so that each denomination shall stand in a@ separate 
 column. Add the numbers of the lowest denomination 
 together, and divide their sum by that number which is 
 required of this denomination to make 1 of the neat high- 
 er: write the remainder under the column added, and 
 carry the quotient to the next’column. Thus proceed 
 with every denomination. 
 
 2. What is the sum of £4 18s. 9d., £100 7s. Od. 
 Igr., 16s. 4d., 3s. 6d. 2qr., £20, and £9 7s. 4d.? 
 
 3. What is the sum of 11s. Od. 3qr., £33 2s. 6d., 
 8s. 7d. lqr., £450, £9 17s: 8d. Sqr., and £37 9s.? ° 
 
 4. A man in London paid for a hat, £1 18s. 6d.; for 
 a coat, £9 8s. 4d., foravest, £1 10s.; for pantaloons, 
 £8; for boots, £1 2s. What did the suit cost? 
 
 TROY WEIGHT. ’ 
 
 5. Add together these quantities of silver. 4Ib. 9oz. 
 16dwt., 100z. ldwt. 22¢r., and 3lb. 40z. Odwt. 6gr. 
 
 6. Add together lloz. 15dwt. 18¢r., 2lb. 100z. 18dwt. 
 23gr., Mlb. Ooz. 17dwt. 3gr., and 50z. 12dwt. 
 
140 WRITTEN ARITHMETIC. Vv. 
 
 AVOIRDUPOIS WEIGHT. 
 
 7. Add together 14T. 10cwt. 2qr. 23lb. 40z., 27T. 
 4cwt. 2qr. 24]b. 140z., and 3qr. Olb. 150z. Lidr. 
 
 8. Add together 16cwt. Iqr. 11lb. 60z. 16cwt. 2Qqr. 
 20lb., 57, Ocwt. Sqr. 5lb. 13oz. Qdr., and 2T. 
 
 APOTHECARIES’ WEIGHT. 
 
 9. What is the weight of a mixture containing 5 ib 
 103 53 1D 8er., 63 29, 55 1D 18gr., and 2th 43? 
 
 10. What is the weight of a mixture containing 1 ib 
 33 15 2D, 73 55.15 ldgr., and 4th 03 63? 
 
 CLOTH MEASURE. 
 
 11. Add together 19yd. 2qr. Sna., 14yd. 2Qqr. Ina., 
 32yd. Oqr. Ina., 2qr. 2na., and 57yd. 3qr. 2na. 
 
 12. Add together 15E.e. 4qr. 2na., 6E.e. Sqr. Ina., 
 ch e. dqr. Sna., 230K.e., and 4E.e. 4qr. 
 
 DRY MEASURE. 
 
 13. Add together 25bu. 2pk. 5qt., 240bu. Opk. 6qt., 
 316bu. 3pk. 7qt. Ipt., and 650bu. Qpk. 5qt. 
 
 14. Add together 635bu. Opk. 3qt., 247bu. Spk. Oqt. 
 Ipt., 2bu. 3pk. 6qt., 56bu., and 31bu. Opk. 2qt. 
 
 WINE MEASURE. 
 
 15. How many hogsheads are 12hhd. 42gal. 3qt. 
 Ipt., 548hhd. 62gal. Sqt., and Shhd. Qgal. lqt. ? 
 
 16. How many tons are 117. Ip. 116gal. Sqt., Ip. 
 48¢al., 5T. lp. S6gal. 3qt., 102gal., and 4T. ? . 
 
 BEER MEASURE. : 
 
 17. Add together 5bl. 1kil. lfir. 8gal. Sqt., fir. 5gal. 
 Qqt. Ipt., 16bl. Okil. Ofir. 4gal., and 25bl. Lkil. 
 
 18. Add together Ifir. 7gal. 3qt., 24bl. Okil. Ifir. 
 Ggal. 2qt. Ipt., and 20bl. 1kil. fir. 4gal. 
 
 LONG MEASURE. , 
 
 19. How many yards are 45yd. 2ft. 11in., 13yd. oft. 
 Qin., 1ft. 10in., and 20yd. 1ft. Sin. 2b.c. ? 
 
 20. How many miles are 10m. Ofur. 36rd., 58m. 
 7fur. 13rd., 3Srd., 16m. 4fur. 21rd., and 6fur. ? 
 SQUARE MEASURE. 
 
 “21. How many yards are 36yd. 7{t, 126in., 3yd. 6ft., 
 130in., 7lyd. Sft. 140in., and Loyd. 4ft. Qin. ? 
 
 92. How many acres are 384A. 3R. 32rd., 86A. OR. 
 2ird., 381A. 2R., and 46A. IR. 25rd. ? 
 
 a 
 
10. COMPOUND NUMBERS. 141 
 
 CUBIC MEASURE. 
 
 23. How much hewn timber is 7T. 45ft. 1712in., 
 ST. 39ft. 1698 in., and 10T. 29ft. 800in. ? 
 
 24. How many cords of wood are 9C. 7ft.w. 15c.ft., 
 4C. 6ft.w. 12c.ft., and 14C. 7ft.w. 11c.ft. ? 
 
 TIME. 
 
 25. Add together 2¥. 250d. 18h. 51m. 15s., 1Y. 
 18d. 7h. Om. 55s., and 240d. Oh. 37m. 29s. 
 
 26. Add together 4Y. 141d. 10h. Om. 5s., 12Y. 
 194d. 20h. 49m., and 2Y. 280d. Oh. 55m. 38s. 
 
 Section 10. 
 COMPOUND SUBTRACTION. 
 
 ENGLISH MONEY. 
 
 1. An English merchant gave £9176 16s. Sd. Iqr. 
 for a ship’s cargo, and then sold the same cargo for 
 £9607 4s. 5d. Sqr. How much did he gain? 
 
 To subtract the Sd., we unite 
 £ ss. d. qr. ‘1 of the 4s. with the 5d., mak- 
 
 9607 4 5 3 ing 17d., and take 8 from 17. 
 
 9179 Ae Sit Then, having used 1 of the 4s., 
 
 430 7 9 2 we unite £1 with 3s., making 
 
 Ty ae eg 23s., and take 16 from 23. 
 
 RULE FOR COMPOUND SUBTRACTION. Write the 
 several denominations of the smaller quantity under the 
 same denominations of the greater quantity: then, begin 
 with the lowest denomination, and perform subtraction 
 on each denomination separately. Whenever a number © 
 expressing a denomination e the upper line 1s smaller 
 than the number under it, increase the upper number by 
 as many as make 1 of the-neat higher denomination, and 
 consider the number of the neat higher denomination in 
 
 the wpper line, to be 1 less than it stands. 
 
 % 
 
 Bo 
 2. Subtract £4 11s. 6d. from £61 14s. 5d. 
 .3. If an English servant receive £1 per month, and 
 spend 13s. 4d. 3qr. per month, what does he lay up? 
 4. Subtract £75 18s. 7d, Iqr. from £856 14s. 9d, 
 
 » f 
 
142 WRITTEN ARITHMETIC. Vv. 
 
 TROY WEIGHT. 
 5. Subtract 1]b.0 oz. 19dwt. from 2 Ib. 1loz. 9dwt. 
 6. A silver-smith having 4 |b. 30z. of silver, worked 
 up lloz. 14dwt. of it. How much had he left? 
 AVOIRDUPOIS WEIGHT. Wi 
 7. From 8T. 12cwt. lqr. 17]b. take 7ewt. 3qr. 2 lb. 
 8S. A farmer laid in 68T. of hay, and used 557. 
 14cwt. in wintering his stock. How much had he left? 
 APOTHECARIES’ WEIGHT. 
 9. From 1b 83 53 take 73 735 2D 16er. 
 10. A mixture weighing 33 2D, contains 8D of jalap, 
 and the rest is rhubarb. How much rhubarb? 
 CLOTH MEASURE. 
 11. Subtract 3qr. 2na. from 46yd. Igqr. Ina. 
 12. If 7yd. 2qr. 2na. be cut from a piece of cloth 
 containing 46yd. Igr. 3na., how much will be left ? 
 DRY MEASURE. 
 13. Subtract 4bu. Ipk. 7qt. 1pt. from 87bu. 
 14. A farmer raised 100bu. of corn, and sold 46bu. 
 opk. of it. How much had he remaining ? 
 : WINE MEASURE. 
 15. From 2hhd. 15gal. take Lhhd. 20gal. Sqt. 
 16. If from a tierce of molasses 7gal. 2qt. Ipt. leak 
 out, how much will remain in the tierce? 
 BEER MEASURE. 
 17. From 4bl. 1kil. If. take Ifir. 7gal. 3qt. 
 18. A brewer having 26b]. 1kil. of beer, sold 12bl. 
 Okil. lfir. How much had he remaining? 
 LONG MEASURE. | 
 19. Subtract 4yd. 2ft. Gin. from Syd. ft. 10in. | 
 20. John rode 16m. dfur.fand Henry rode 20m. 1fur. 
 Srd. How much further did H. ride, than J.? 
 : A SQUARE MEASURE. ~ 
 21. A farmer owning 94A. of land, sold off a piece, 
 48 rods long, and 20 rods wide. How many acres had 
 he remaining? (See Square Measure, page 137.) 
 CUBIC MEASURE. 
 22. Ifa piece of timber 9 feet long, 2 feet wide, and 
 1 foot thick, be taken from 2T. 14ft. of hewn timber, 
 how much will be left? (See page 138.) 
 
 \ 
 
 \ 
 
 \ 
 
11. COMPOUND NUMBERS. 143 
 
 TIME. 
 23. Subtract SY. 45d. 6h. 50m. from 5Y. 14d. 12h. 
 24. A ship went to India and returned, in 321d. 7h. 
 How much less than a year was she in the voyage? 
 
 Section ll. 
 COMPOUND MULTIPLICATION. 
 
 ENGLISH MONEY. 
 1. What is the value of 8 yards of English broad- 
 cloth, at £2 Os. 5d. 3qr. per yard? 
 . £ sy chqeage. 8 times 3qr. are 24qr., equal to 
 2 O53 6d. 8 times 5d. are 40d., and 6 
 a we carry are 46d., equal to 3s. 
 6.3 10.0 10d. 8 times Os. is Os., but we 
 seo E LEO carry 3s. 8 times £2 are £16. 
 
 RULE FOR COMPOUND MULTIPLICATION. . Begin 
 with the lowest denomination, and multiply each denomi- 
 nation separately; divide each product by the number 
 which is required of its own denomination to make 1 of 
 the next higher; write the remainder under the denomt- 
 nation multiplied, and carry the quotient to the product 
 of the next higher denomination. 
 
 2..Multiply £529 13s. 10d. 3qr: by 5. 
 
 3. What is the value of 7 tons of hemp, at £50 183 
 10d. per ton. 
 
 4. Multiply £7529 18s. Od. lqr. by 6. 
 . §. Multiply £250 16s. 11d. by 24. 
 
 In examples like this, it 1s most convenient to multi- 
 ply by factors of the multiplier. 
 
 6. Multiply £57 8s. 10d. 2qr. by 45. 
 
 7. What cost 34 cows, at £3 9s. 6d. apiece? 
 
 Here find the price of 32 cows by the factors of 32, 
 and to the product add the price of 2 cows. 
 
 8. Multiply £1746 14s. 10d. 2qr. by 46. 
 
 9. What is the value of 29 yards of Irish linen, at 
 7s. Od. Qqr. per yard. 
 
 10. Multiply 18s. 4d. by 83. 
 
144 WRITTEN ARITHMETIC. Ve. 
 
 TROY WEIGHT. 
 11. Multiply 141b. O0z. Sdwt. llgr. by 7. 
 12. What is the weight of 11 Federal dollars; the 
 weight of 1 dollar being 17dwt. Ser. ? 
 AVOIRDUPOIS WEIGHT. 
 13. Multiply 7T. 12cwt. Iqr. 14]b. by 8. 
 14. What is the weight of 25 hogsheads of fish; each 
 hogshead containing Bewt. 3qr. 151b.? 
 CLOTH. MEASURE. 
 15. Multiply 29yd. 2qt. 3na. by 9 
 16. How many yards of broad-cloth are there in 35 
 pieces; each piece containing 47yd. Igr. 2na? 
 DRY MEASURE. 
 17. Multiply 33bu. 3pk. 6qt. Ipt. by 5. 
 18. How many bushels of corn are there in 18 bags; 
 - each bag containing 2bu. 2pk. 5qt. Ipt. ? 
 WINE MEASURE. | 
 19. Multiply lp. lhhd. 52gal. 2qt. Ipt. by 4 
 20. How many hogsheads of wine are there in 13 
 casks; each cask containing 49gal. 3qt. ? 
 BEER MEASURE. 
 21. Multiply 6b]. 1kil. Ofir. 6gal. Qqt. Ipt. by 7. 
 22. If 1 man drink 2gal. 3qt. Ipt. of beer in a week, 
 how much will 38 men drink in a week ? 
 LONG MEASURE. 
 ae Multiply 5lea. 2m. 6fur. 36rd. by 8. 
 24. If a man travel 55m. 5fur. 17rd. a day, for 18 
 ie how many miles will he have travelled. 
 SQUARE MEASURE. 
 25. Multiply 36A. 3R. 27rd. by 6. 
 26. How many square yards are there in 14 rolls of 
 carpeting; each roll containing 52yd. 3qr. 
 CUBIC MEASURE, 
 2%. Multiply 1T. 34ft. 1200in. of round tale by 3. 
 28. There are 4 piles of wood; each containing 8C. 
 6ft.w. 12c.ft. How much wood is there in all. 
 TIME. 
 29. Multiply 4¥. 255d. 16h. by 9. 
 30. Ifa ship alter her latitude 1 degree i in sailing 16h. 
 40m., in what time will she alter it 15 degrees ? 
 
12. COMPOUND NUMBERS. 145 
 
 Section 12. 
 COMPOUND DIVISION. 
 
 1. If £2047 13s. 9d. be divided equally among 6 
 men, how much will each man receive? 
 | We divide the pounds, and 
 Te s gig swe thereremains £1. This £1 
 6)2047 13 9 we reduce to shillings, and 
 Cig OME ae ee, 2. unite it with the 13s. making 
 S41 5 7 2q%- 335. \Wedividethe 338., re- 
 duce the remainder to pence, 
 and proceed as before. 
 2. If 19s. 11d. 3qr. be divided equally among 3 men, 
 how much will each man receive?’ 
 3. Divide £16 14s..10d. 3qr. equally among 5 men. 
 4. Divide £3 Os. 8d. equally among 7 men. 
 5. Divide £59 18s. 4d. equally among 25 men. 
 This operation is in lon 
 pes He ie hs division. We first divide 
 50 the pounds: the quotient is 
 rir £2, and the remainder, £9. | 
 
 9 We then reduce the £9 to 
 _29 shillings, adding in the 18s., 
 25)198(7s. | and divide this sum [198s.] 
 tho as before: the quotient is 
 “93 : 7s. and the remainder, 23s. 
 12 We then reduce the 23s. to 
 ——- pence, adding in the 4d., and 
 25)280(11d. divide this sum as. before. 
 25 5d. remain undivided. Ob- 
 
 dw 90 serve, that, in every instance, 
 25 | the quotient and remainder 
 
 are of the same denomination 
 with the dividend. 
 
 RULE FOR COMPOUND DIVISION. Divide each 
 denomination separately, beginning with the highest. 
 Whenever a remainder occurs, reduce it to the next low- 
 er denomination, add it to the number expressed in the 
 lower denomination, and divide it therewith. 
 
 N 
 
 5d. remaining. 
 
146 WRITTEN ARITHMETIC. Vv. 
 
 6. Divide £460 5s. 10d. equally among 37 men. 
 
 7. If 15cwt. 3qr. 18lb. of flour be packed equally in 
 9 barrels, how much will each barrel contain ? 
 
 8. If it take 15 yards of cloth to make 6 coats, how 
 much does it take to make 1 coat? 
 
 9. If an army consume 492bu. Opk. 6qt. of wheat 
 in 42 days, how much does it consume in 1 day? , 
 
 10. Divide 3qt. Ipt. of wine equally among 7 men. 
 
 11. If 30hhd. 13gal. 2qt. of cider will fill 18 casks 
 of equal size, how much does each cask hold? 
 
 12. Divide 58m. 2fur. 32rd. into 8 equal distances. 
 
 13. Suppose a man is to travel 339m. 4fur. 20rd. in 
 6 days; what distance must he travel each day ? | 
 
 14. If a field containing 22A. 2R. 12rd. be divided 
 into 4 equal lots, what will each lot contain? — 
 
 15. Suppose a township, containing 17715 acres of 
 land, should be divided into 80 equal farms, how many 
 acres would each farm contain ? . 
 
 16. Suppose a rail-way car to perform 4 trips in 5d. 
 16h. 9m., in what time does it perform 1 trip? 
 
 Questions to be answered Orally. 
 (1) Which of these numbers is a compound num- 
 ber,— £356, or £2 18s.?. (2) Why is it called a 
 compound number? (3) Recite the rule for addi- 
 tion of compound numbers. (4) Suppose the sum 
 of a column of numbers expressing furlongs to be 37; 
 what must be written under the column, and what 
 must be carried to the next column ?— Why? (5) 
 Recite the rule for subtraction of compound num- 
 ‘| bers. (6) Recite the rule for multiplication of 
 compound numbers. (7) Recite the rule for divi- 
 sion of compound numbers. 
 
I. FRACTIONS, 143 
 
 CHAP. VI. 
 FRACTIONS. 
 
 Fractions have been exemplified in page 44, and the 
 mode of expressing them has been defined in page 74. 
 
 A proper fraction expresses a quantity, less than a unit. 
 Therefore, the numerator of a proper fraction, must be 
 less than the denominator: for example, 7. 
 _~ An improper fraction expresses a quantity, equal to a 
 unit, or greater than a unit: therefore its numerator must 
 equal, or exceed its denominator: thus, 3. 4. 
 
 A compound fraction is a fraction of a fraction—a 
 
 part of a part of a unit: for example, of 4. 
 
 NOTE. ‘The written operations required in the several sec- 
 tions of this chapter, correspond with the mental operations 
 involved in sections of the same number, in chapter VI, Oral 
 Arithmetic. Learners will be enabled to perceive the written 
 process to be adopted, by recurring to the oral examples. 
 
 BEC araN 1. 
 1. What is the sum of 3; and + and #3? 
 * These Badeibng have a common denom- 
 5 tnator; that is, they all have the same de- 
 ’s . nominator. We add the numerators only, 
 —* and under the sum of the numerators, place 
 12 the common denominator. 
 
 2. What is the sum of 2 andy and 3 and 3? 
 
 3. How much is 39 and “4 is and ~2 {> and 3% ‘and qe? 
 
 4. Aman paid 5% of a dollar for breakfast, 7% 
 dollar for dinner, and ze of a dollar for supper. “What 
 part of a dollar did be spend ¢ 
 
 5. How much is + and 3 and 3 and and 4 
 
 6. A merchant sold 4 2 of a ship to one man, a Ts 
 another. What part i the ship did ah sell ? 
 
 7. Add together 7 and 7 ra and 43 and 7% and 32? 
 
 8. How much is 2 and } + andy and 3 wy 
 
 9. How much is 744 and +45 and i 0, and +3; ? 
 
 a 
 
148 WRITTEN ARITHMETIC. VI. 
 
 Section 2. 
 
 Write upon the slate, the several fractions required 
 in the followmg examples. 
 
 1. If you divide a bushel.of corn into 8 equal parts, 
 and then put 6 of the parts into a sack, what fraction of 
 a yy 4 will there be in the sack ? 
 
 . If an acre of land be divided into 20 equal lots, 
 a 14 of the lots be enclosed by a fence, what fraction 
 of an acre will there be in the enclosure ? 
 
 3. Suppose any thing to be divided into 45 equal 
 parts; what fraction will express 26 of the parts? 
 
 4. Suppose 1 dollar to be divided into 100 equal 
 parts; what fraction will express one of the parts? 2 of 
 the parts? 6 parts? 25 parts? 99 parts? 
 
 3 SecTION 3. 
 1. If = be subtracted from 44, what will remain ? 
 
 Both of these numerators express fif- 
 teenths; therefore we merely subtract one 
 " numerator from the other, and under the | 
 5 Yremainder, place the denominator. 
 
 If 34 be subtracted from 3%, what will remain? 
 What i is the difference between 2 and 3? 
 If 44 be subtracted from 4 5 what will eens 
 What is the difference between! Ss, and 4 
 A farmer divided a ton of hay into 20 pes parts, 
 and gave 14 parts to his cows, and the rest to his sheep. 
 What fraction of a ton did the sheep get? 
 
 7. Subtract $ from 1,— that is, subtract $ from the 
 number of eighths that there are in a whole one. 
 
 8. Subtract 54 from a whole 1. 
 
 9. What is the difference between 4, ise and 1? 
 
 10. Subtract 24% from a whole 1. 
 
 11. A merchant owning a ship, sold 13 of her to one 
 man, +; to another, and 3 to another "What part of 
 the ship did he still own : > 
 
 12. A boy having 1 dollar, paid away +55 Of it, and 
 lost 5- What fraction of a dollar had he left? 
 
 13. Subtract 244 from a whole 1. 
 
 Tela le 
 
 x 
 3 
 5 
 
 a 
 
 a 
 
2.3. 4. 5. RELATIONS OF! NUMBERS. 149 
 
 RELATIONS OF NUMBERS. 
 
 Section 4, 
 
 We frequently have occasion to view one*number as 
 a certain part of another number; and thus we notice 
 the relation that exists between the two numbers. In 
 order to state what part one number is, of another, we 
 make the number wh Ach: is the part a numerator, and the 
 other number a denominator. 
 
 State the fractions, which answer to the sollerips eX- 
 amples, upon the slate. 
 
 1. What part of 5 cents is 1 cent? is 3 cant? 
 
 2.) What part of 101s 1? is'2? is BP’ isiO? 
 
 3. What part of £1 or 20 shillings, is 1 shilling ? is 
 6 shillings? is 14 shillings : P 
 
 4. What part of 35°is i? is8? mis 112 is 34? 
 
 5, paps part of pl or 100 cents, is l-cent? is 2 
 cents? is9 cents? is 46 cents? is 94 cents? 
 
 _ 6. What part of 6 pence is 1 Se ful is 5 pence? 
 
 7. What part of 1 shilling is 1 penny? is 7 pence? 
 
 . 8. What part of l‘peck is 1 quart? is 7 quarts? 
 
 9. bie i part of 1 hogshead is 1 gallon? is 18 gals. ? 
 
 ok If Ay of a hogshead of wme be worth BI, what 
 is 23 of a thd worth? What j is Ihhd. worth? 
 
 11. What part of lyearis 1 day? is10 days? is 40 
 days? is 100 days? is 275 days? 
 
 12. If aman spend $1, in +45 of a year, how much 
 will he spend in 3'4 of a year? in 42% ofa year? 
 How much will he spend in 1 year? +R 
 
 13. What ei of 2016 is 1? is 842 is 759? 
 
 SECTION 9. 
 1. Suppose 4 of a ‘iy to be worth $4703; eh Is 
 the whole ship worth ? 
 : 4703 is 5 of what number? 
 . If dof an acre of land produce 71 bushels of po- 
 oid how many bushels will 1 acre produce ? 
 4. 7list 5 of what number? 
 5. 875 is $ of what number? — 
 6. 1900 is 4 of what number ? 
 n* 
 
150 WRITTEN ARITHMETIC. VI, 
 
 7. If 230 men will lay } of a mile of rail-way a week, 
 how many men will it take to lay 1 mile in a week? 
 
 8. 230 is 4 of what number ? 
 
 9. 44 is + of what number ? 
 
 10. 6902 is 3 of what number ? 
 
 11. If ;4 of a pound of silver be worth $1.09, what 
 is 1 pound of silver worth? | - 
 
 12. If a ship sail 17 miles in 3; of a day, what dis- 
 tance would she sail in the whole day? . 
 
 13. 204 is + of what number? | 
 
 14. If 4, of a pipe of wine be worth $1.15, what is 
 the whole pipe of wine worth? 
 
 15. Suppose 3 of the sugar in a hogshead to weigh 
 lcwt. 2qt. 12lb.; what does the whole weigh? 
 
 Section 6. 
 
 1. If 1 acre of land will produce 126 bushels of po- 
 tatoes, how-many bushels will 3 of an acre produce? 
 
 2. What is 4 of 126? — | 
 
 3. Suppose 38406 needles can be made from a bar 
 of steel; how many can be made from 4 of the bar? 
 
 4. What is 4 of 38406? | | 
 
 5. If 1 dollar will pay for 316 quills, what number o 
 quills will + of a dollar pay for? ; 
 
 6. If you eat 1095 meals in 1 year, what number of 
 meals do you eat in + of a year? 
 
 7. What number of cubic inches are there in 4 of a 
 cubic foot? (See Cubic Measure, page 132.) 
 
 8. If 1 week’s board cost $3.64; what does 7 of a 
 week’s board cost ? 
 
 9. Suppose a packet ship to be worth $17841.50; 
 what is ={; of her worth? © 
 
 10. A man, having $205.12, paid.44 of his money 
 for a piece of land. What was the price of the land ? 
 
 11. A man gave $2568 for a house, and then paid 34 
 
 part as much for having it repaired. For how much 
 must he sell the house, in order to lose nothing? 
 
 12. What is 7'; of 1800? . 
 
 13 Suppose a piece of cloth to contain 60yd. 2qr.; 
 how much cloth is there in 3 of the piece? 
 
6.7. 8. RELATIONS OF NUMBERS. 151 
 
 Section. 7. 
 
 1. Suppose that 12 men are to pay. debt of $420, 
 in equal shares; what must 1 man pay? 
 
 Solution. 1 man is 12 of 12 men; therefore 1 man 
 ie pay 75 of $420. 54, of 420 is— 
 
 . If a prize of #3936 be divided equally among 8 
 ie what part of the money will 1 man receive? How 
 many dollars will 1 man receive? 
 
 3. 27 men own 864 acres of land to i What 
 part of 864 acres does 1 man own? What number of 
 acres does 1 man own? 
 
 4. If $135.45 will pay for 1hhd. af wine, what part 
 of the money would pay for 1 gallon? What would be 
 the ite of 1 gallon? 
 
 If 170 acres of land produce 6630 bushels of corn, 
 es part of 6630 bushels does 1 acre produce f How 
 many bushels does 1 acre produce ? 
 
 6. If 6 yards of broad-cloth be worth £11 11s. 9d., 
 what part of the money is 1 yard worth? What is the 
 value of 1 yard, in pounds, shillings, &c. ? 
 
 7. A black-smith paid ¢63 for 15 tons of coal. What 
 did the coal cost him per ton? 
 
 Section 8. 
 
 1. A man purchased a farm for $5642, and paid 4 of 
 the price in cash, and gave his note for the remainder. 
 How many dollars did he pay down? 
 
 Direction. First find 7 of $5642, by dividing this 
 sum by the denominator of the fraction; then find 4- 
 sevenths, by aap the quotient by the numerator. 
 
 =A What is 3 of 1905 
 
 If an acre of land will produce 14870 ears of corn, 
 ioe many ears will ¢ of an acre produce ? 
 
 4. What is 2 of 19064? 
 
 5. Suppose : an acre of land to be worth $48.16; what 
 is the value of $ of an acre of the same land ? 
 
 6. If 1 dollar will pay for 270 quills, what number of 
 we will 3 of a dollar pay for ? 
 
 If 72 gallons of wine leak’ from a pipe in 1 day; 
 ee many gallons leak out in gy of a day? © 
 
152 WRITTEN ARITHMETIC. 2 ais 
 
 8. Suppose a hogshead of sugar to be worth £20 4s. 
 8d.; what is the value of Z g of the sugar ? 
 9. What is 42 of 4720? 
 
 In the several foregoing examples in this section, the 
 learner has probably divided the given number by the 
 denominator of the fraction, and multiplied the quotient 
 by the numerator. It is, however, sometimes more 
 convenient, to multiply the given number by the nume- 
 rator, and divide the product by the denominator. 
 
 10. What is 4 of 32? (Here are the two methods.) | 
 
 First Method. ae Second Method. 
 4)32 32 
 8 is 1 of 32. 3 
 Mom 4)96 Pe times 32. 
 24 is8 times 3 z of 32, 24 istof3 times 32, 
 which is } of 32. ry which is $ of 32. 
 
 We may see why these two methods of operation 
 prodtice the same result, in the following illustration. 
 Here is 3 of 32 units arranged in one line, and 4 of 3 
 times 32 units arranged in three lines. ‘The number of 
 units [@] in the two arrangements is the same. iP 
 
 ©66996900 029900008 6890809882 OO0O00000. 
 
 @0908929 00000000 00000099 90900000 
 @0@O6S06090@ OO000000 QOO0C000D DO000000 
 @6080008 00000009 909000900 09900000 
 
 11. Find = 13 of 60156, by each of the above methods. 
 
 12. Find 57; of 40549, by the second method. 
 
 13. A laborer worked 4 of a year, at 92 cents per 
 day. What did his wages ‘amount to? 
 
 14. In 45 of a Aa 95 of wine, how many gallons? 
 
 15. Whatiis 8, of $1491? 
 
 After rausletplly hip by 6 and dividing by 100,. reduce 
 the remainder to cents, and divide the cents. : 
 
 16. A borrowed of B, $758, promising to pay it in 
 “one year; and, in addition thereto, he agreed to pay a 
 sum, equal to ;&5 of the sum borrowed, for the use of 
 the money. How much must B receive? 
 
 17. What is z8>5 of $ 28? 
 
9. 10. RELATIONS OF NUMBERS. 153 
 
 Section 9. 
 
 1. If $686.56 should be divided equally among 8 
 men, what part of the money,—and what number of 
 dollars and cents, would 3 men receive ? 
 
 2. Suppose that $33 will pay for 198 yards of cloth; 
 what part of 198 yee eed how many yards can be 
 pou for $14? 
 
 If 15 acres of land produce 283bu. Opk. 4qt. of 
 silat: what part of this quantity,—and how bh bush- 
 els will 9 acres produce ? 
 
 4. If 540 barrels of flour will supply an army for 30 
 days, how many bushels will supply it for 19 days? | 
 
 Solution. 19 ek are 4; of 30 days; therefore the 
 army will consume 4? of 540 barrels, 
 
 5. -If a mansean build 256 rods of fence, in 60 days, 
 how. many rods can he build in 45 days ? 
 
 6. If 72.tons of hemp cost $13680, what will 20 tons 
 . cost, at the same rate? 
 
 7. Ifittake a man 31 days to travel 1178 miles, how 
 maeRy miles can he travel in 25 days? 
 
 . If 24 English watches are worth £108 18s. .» what 
 is ‘te value of 7 watches of the same kind ? 
 
 Sreerron 10. 
 
 1. If 16 men can fell 208 trees in a day, how many 
 ‘trees can 35 men fell in ee same time ? 
 
 2. What is 35 times =& of 208°? 
 
 3. If 10 barrels of flour cost $59.30, how much will 
 33 barrels cost, at the saine price per barrel? 
 
 4. What is 33 times 3); of $59.30? 
 
 5. If 64 soldiers eat 443 pounds of beef in a week, 
 how many pounds will 250 soldiers eat in a week? 
 
 £ What is 250 times ~; of 448? 
 
 If 12 gallons of linseed oil be sold for $13.44, 
 
 ae should be the price of 52 gallons of linseed oil ? 
 
 8. What is 52 times 31; of $13.44? 
 
 9. If a man earn 491. 70.in7 months, how much can 
 he earn in 2 years? 
 
 10. If 48 pounds of feathers can be bought for $16, 
 how many pounds can be bought for $25? 
 
154 WRITTEN ARITHMETIC. VI. 
 
 Section ll. 
 
 1. If 2 of an acre of land will produce 28 bushels of 
 potatoes, how many bushels will 4 of an acre produge 4 
 How pany bushels will 1 acre produce? 
 
 2. If 3 of a hogshead of sugar be worth ¢ 22.50, what 
 is ¢ of it worth? What is the whole worth ? 
 
 3. $22.50 is ¢ of what sum of money ? 
 
 4, Suppose a ° ship to sail 105 ipiles in 7 of a day; 
 what distance will the ship sail in 5 of a day ? What 
 distance will she sail in the whole day ? 
 
 5. 105° is +3 of what number? 
 
 6. If 34 of a chest of tea be worth $23, what is 7) 
 of it worth? What is the whole of it worth? 
 
 hy $23 is q7 of what sum of money? 
 
 If $ of a bag of coffee be worth $38.46, what is 
 ae whole bag of coffee worth? 
 
 9. Suppose a rail-way car to run 198 miles, in 35 of 
 a day; what distance will it run in 1 day ? 
 
 10. If 192. men will perform ¢ of a certain piece of 
 work in a week, what number of men will it take, to 
 perform the whole of the work in a week ? 
 
 11. 192 is $ of what number ? 
 
 12. A man purchased a farm, and after he had aid 
 
 x5 Of the price, he still owed $1288. What must have 
 been the price of the farm? 
 
 13. A trader purchased a pipe of wine, and after + of 
 it had leaked out, be sold the ig at $1. 15 per 
 gallon. How much did it amount to? 
 
 Questions to be answered Orally. 
 
 (1) What is meant by a common denominator of 
 two or more fractions? (2) How do you add frac- 
 tions, that have a common denominator? (3) How 
 do you subtract one fraction from another; the two 
 fractions having a common: denominator? (4) 
 When a certain fractional part of a number is known, 
 how do you find the whole of the number? (5) 
 When the whole of a number is known, how go you 
 find any certain fractional part of it? 
 
Ii. 12, 18. RELATIONS OF NUMBERS. 155 
 
 Section 12. 
 REVIEW. 
 
 1. (§ 1.) If youshould pay 745 of a dollar for a quire 
 of paper, 7% of a dollar for a slate, and ;4°, for a book, 
 what fraction of a dollar would you spend ? 
 
 2. (§2.) If a ton of hay be rolled up in 20 equal 
 heaps, what fraction of a ton will 14 heaps be? 
 
 3. (§ 3.) Suppose a young man to lay out +$ of his 
 money for a farm; what part of his money has he left ? 
 
 4. (§4.) Suppose a school to be allowed 15 minutes 
 for recéss; what fraction of an hour is the recess ? 
 
 5. (§ 5.) 5 of an ounce, or Idwt. of pure gold, is 
 sufficient to gild a silver wire, 65 miles in length. What 
 length of wire may be gilded with 1 ounce ? 
 
 6. ($ 6.) If a man’s income be $198:a year, how 
 much is his income for =; of a year, or 1 month? 
 
 7. (§7.) If $14 will pay for 70 books, what part of 
 70 books,— and how many books, will $1 buy ° 
 
 8. (§ 8.) If a man’s income be $803 a year, how 
 much is his income for 349; of a year, or 30 days? | 
 
 9. (§9.) Suppose $93.66 to be paid for 14 yards 
 of broad-cloth; what part of the money does 6 yards _ 
 cost? How many dollars do 6 yards cost? 
 
 10..(§ 10.) If 11 barrels of flour are worth $59.07, 
 what is the value of 25 barrels, at the same rate ? ! 
 
 11. (§11.) If 18 shillings be given for ;° of a hun- 
 dredweight of fish, what must be given for 1 cwt. ? 
 
 FRACTIONS AND RELATIONS. 
 
 Section 13. 
 
 1. Suppose you can read 12 pages in an hour; how 
 many hours will it take you to read 160 pages ? 
 
 12)160(13+4; We find, by division, it will take 
 12 13 hours, and still 4 pages remain 
 “ao to be read. Now, since it takes 
 36 qs of an hour to read 1 page, it 
 — will take 4 of an hour to read 4 
 
 4 pages. Ans. 13-4; hours. 
 
156 WRITTEN ARITHMETIC. no Vik 
 
 Any REMAINDER, which appears after the operation of 
 division, is the numerator of a fraction, the divisor being 
 the denominator; and this fraction forms a part of the 
 quotient. Therefore, place the remainder and the divi- 
 sor, as a fraction, to the right of the quotient. 
 
 2. At $2 per yard, how many yards of cloth can be 
 bought for $49; that 1s, how many whole yards, and 
 what part of another yard can be bought? | 
 
 3. How many times 2 are there in “49? 
 
 4. How much flour can be bought for $639, at $5 
 per barrel; that is, how many barrels, and what part of 
 another barrel can be bought ? 
 
 5. In 639, how many times 5;—that is, how many 
 fives, and what part of another 5, in 639? 
 
 6. How much salt can be bought for 87 shillings, at 
 4 shillings per bushel? 
 
 ‘f Suppose a rail-way car to run 16 miles an ie BE 
 in how many hours will it run 350 miles? 
 
 8. How many times 12 are there in 1049? 
 
 9. How many times 39 are there in 76800? 
 
 10. In 438 shillings, how many pounds are there ? 
 
 Observe that 1s. is 3, of £1; therefore the ‘remain- 
 der in this example, may be expressed as a fraction. 
 
 11. How many yards of cloth can be bought for 549 
 shillings, at £1 per yard? © 
 
 12. Suppose a ton of hay to be equal in value to 34 | 
 
 bushels of oats; how euge tons of hay must be given 
 for 450 bushels of oats ? 
 13. How many times 17 are there in 23 times 31? 
 14. How much rice, at $4 per cwt., must be given 
 for 6201b. of cheese, at 10 cents: per Peas 
 SECTION 14:5 a 
 
 og 
 
 CHANGE OF WHOLE NUMBERS TO FRACTIONS. 
 
 1. How many thirds are there in 14? | 
 
 14 | In 1 there are 3- -thirds; 
 3 therefore, there are 3 times 
 — , asmany thirds as wholeones, 
 ~ 42-thirds. Ans. %. in any whole number. 
 
14. 15. FRACTIONS AND RELATIONS, 157 
 
 RULE. To change a whole number to an improper 
 fraction, multiply the whole number by the pik a 
 pe the product will be the numerator. 
 
 . If you cut 17 sheets of paper into half-sheets, BON 
 thi? halves will there be ? 
 3. How many fifths of a dollar are there 4 16? 
 4. In 31 pounds, how many sixths of a pound ? 
 5. In 73 yards, how roa eighths of a yard? 
 6. Change 641 to ninths. Change 641 to tenths. 
 7. If astage run 1 mile in 3 of an hour; how many 
 miles would it run in 126 hours ?- 
 8. How many fourths are there in ‘154 ry 
 152 In this me Ta we add the 
 ee 3-fourths to the fourths produc- 
 pr oaint ed by the multiplication of 15 
 63-fourths. by 4, and thus obtain, &. 
 Note. ° A whole number and a fraction expressed to- 
 gether, thus, 154, is called a mized number. 
 
 9. How many eighth of a mile in 574 ‘miles ? 
 10. Change ae i7 7 to an improper fraction. 
 Change Ads a an improper fraction. 
 . If. sofa dollar will pay for 1 gallon of beer, how 
 
 ‘ cae fer can be bought for $64? 
 
 13. If 4 of a dollar will pay for 3 yards of ribbon, 
 
 ~ how many "yards can be bought for $62? 
 
 aS 
 
 Section 15. 
 CHANGE OF FRACTIONS TO WHOLE NUMBERS. 
 1. How many whole ones are there in 4? 
 
 3)42-thirds. - Since 2 make a abate 1, there 
 te ery are as many whole ones in 4 
 14 wholes. as there are times 3 in 42g, 
 
 RULE. To change an improper fraction to a whole 
 number, divide the numerator by the denominator, and 
 the quotient will be the whole number. 
 
 2. How many whole sheets of paper must be cut into 
 halves, to make 49 of a sheet ? 
 
 0 
 
158 WRITTEN ARITHMETIC. VI. 
 
 3. In 245 of a dollar, how many dollars ? 
 4. How. many pounds are there in +32 of a pound? 
 e In 1216 of a yard, how many yards are there ? 
 . If a stage run 1 mile in 5 of an hour, how many 
 Hoe would it be in running 126 miles? 
 7. Change 33? to’a whole number. | 
 8. Suppose 8 pounds of sugar can be bought for $15 
 ~ how many pounds will 242° of a dollar pay for ? 
 9. Change ° toa mixed number ? 
 5)87 We divide the 87-fifths by 5, and 
 ——  _ obtain 17 whole ones: then, there are 
 17$  2-fifths over, making 172. 
 10. Change 242 to a mixed number. 
 11. How iy dollars are there in 537 of a dollar ? 
 _ 12. How many gallons in 4 of a gallon : ? 
 13. If + of a dollar will pay for 1 pound of coffee, 
 how many ° dollars will 312 pounds of coffee cost? 
 14. If 1 pound of butter cost 2 of a dollar, what. would 
 be the price of 491 pounds, at the same rate? 
 
 é Secriox 16. 
 1. Add together 7, 42,44, 43, 4 and + 
 The sum of these fractions will be an iaaeee frac- 
 tion, and it must be changed a a mixed number. 
 2. What is the sum of 49157, 75-8 and 836, ? 
 
 Ai 8, In this example, we add together - 
 | 758 the elevenths, and find their sum to 
 836-6 be 44; whichis equal to 2,4. The 
 ——-} zz we write down, and carry the 2 to 
 140445 ih | 
 11 the column of units. 
 
 3. What is the sum of 4192, 182, 12§, 85737, 9+, 
 251%, 141$, and 254? 
 4. Add together 336 fs, 1412, 970118, 28, 15839 
 12404, 3 ory 100 35, and 4 o5° 
 5. Subtract 18762 from 22583 3, 
 22582 We cannot its 3 from 3 2, therefore, 
 18765. We join 1 unit with the 2 3, making ¥7, 
 2 and take 3 from . We then proceed 
 3815 to take 6. units from 7 units. 
 
16. 17. 18. FRACTIONS AND RELATIONS. 159 
 
 6. Subtract 460314 from 717064. 
 
 7. Subtract 6092} from 542006723. 
 
 ’ 8. If 172 yards of cloth be cut from a piece contain- 
 ing 49 yards, how much will be left ? 
 
 9. A retailer put,into a firkin, 283% pounds of butter 
 at one time, 19+% pounds at another, and 357% pounds 
 at another, and then sold out 2547 pounds. How many 
 pounds still remained in the firkin ? 
 
 Section 17. 
 3 
 
 1. Suppose a rail-road car to run 3 of a mile in 1 
 minute; what distance will it run in 47 minutes ? 
 
 2. How many whole ones in 47 times 2? 
 
 3. If 2 of a yard of broad-cloth will make 1 jacket, 
 how many yards will it take to make 18 jackets? 
 
 4. How many whole ones in 18 times $? 
 
 5. If 4 of a pound of gunpowder tea cost 1 dollar, 
 how many pounds can be bought for 50 dollars ? 
 
 6. How many whole ones in 50 times 4? 
 
 * 
 
 Section 18. 
 1. ‘What is the product of 864, multiplied by 9? 
 864 _ We multiply + by 9 thus, 9 times 7 
 9” is 475 equal to 57. Then we write 
 ——— this + under the 4, and carry the 5 to 
 7797 the product of the 6 units. 
 2. What is the product of 413, multiplied by 7? 
 3. What is the value of a field, which contams 5 
 acres, allowing it to be worth 544 dollars per acre? 
 4. How much is 4 times 3542? 
 5. How much is 9 times 14731 44? 
 6. How much is 28 times 544? 
 
 544 Here we are obliged to multiply by 
 28 8 units and 2 tens separately, and we 
 432 cannot well bring in the product of the 
 108 fraction by the 2 tens. Therefore, 
 1g2 we first multiply the whole numbers, 
 
 YM ae , wet | 
 15302 and then find 28 times 3, ina separate 
 3 operation, which is not here written. 
 
160 WRITTEN ARITHMETIC. VI. 
 
 7. How much is 92 times 2051-4 
 
 8. How much iis 100 times 1447 om 
 
 9. How many gallons of wine are iHeph in 31 at 
 each cask containing 547% gallons ? 
 
 10. A merchant paid $75 74% apiece, for 47 mules. 
 What did the whole amount to? ru 
 
 11. If a steam-boat run 23642 miles in 1 day, what’ 
 distance will it ran m 16 days? ; 
 
 12. How much is 15 times a9! ° 
 
 13. What cost 75 books, at ¥55 of a dollar apiece ? 
 
 14. If a horse eat 43 of a bushel of oats a day, how 
 many bushels will he eat in 365 dave? ay. # 
 
 | Section 19. | 
 1, If 4 of achest of tea be worth $6.874, what is 
 the whole chest worth? 
 2. If 4 of a dollar will pay for travelling 973 miles 
 on a turnpike road, how far can you go for $1? 
 3. 7902 is 45 of what number ? 
 
 4. Ift ofa kite line be 25% yards in length, what is . 
 
 the whold oe of the line? 
 
 5. 305+. is 3 of what number ? fe 
 
 6. If a “man can eam 123 cents in $ of a day, what 
 sum of money can he earn in 1 day? 
 
 7. If of a yard. of gold wire be worth 42 of a dollar, 
 what is the value of 1 yard of the wire: Sl 
 
 SECTION 20. 
 
 1. A boy having $2, gave 1 of his money for a knife. 
 
 Wan fraction of I dollar did the knife cost ? 
 2. + of 2 is equal to what part of 1? 
 
 3. 6 men divided 5 barrels of flour equally among 
 them, each man taking 4 of the flour in each barrel. 
 Vb fraction of a barrel did each man get? 
 
 4. 1 of 5 is equal to what part of 1? 
 
 5. If you should take ;4 of a bushel of corn from each 
 of 10,bushels, what fraction of 1 bushel would you obtain ? 
 
 6. What part of 1 is 16 of 10? 
 
 7. What part of lis 35 of 2? is 25 of 83 is 35 of 4? 
 ye is 3, of 33? | 
 
 » 
 
q 
 
 19. 20.21. FRACTIONS AND RELATIONS. « 161 
 
 8. A tenant raised 28 bushels of corn, and gave his 
 landlord 4 of it. What improper fraction of a bushel, 
 [how many thirds of a bushel,] did the landlord receive ? 
 How many bushels did the landlord receive ? 
 
 9. 4 of 28 is equal to what improper fraction? Then 
 4 of 28 is equal to how many whole ones? 
 
 10. 4 of 42 is equal to what improper fraction? Then 
 + of 42 is equal to what mixed number ? 
 
 11. =; of 29 is equal to what improper fraction ? 
 Then +! of 29 is equal to what mixed number ? 
 
 12. If $721 should be divided equally among 6 men, 
 how many sixths of a dollar would each man have? 
 How many dollars would each man have? 
 
 Section 2]. 
 
 1. Suppose a hogshead of brown sugar to be worth 
 $115; what is the value of 4 of the sugar? 
 
 2. What is 4 of 115? 
 
 3. 5 men from Connecticut, bought. 793 acres of land 
 in Michigan, and divided it into 5 equal farms. How 
 many acres were there in each farm ? 
 
 To find ¢ of 793 acres, we divide 793 by 5. The 
 quotient is 158 acres, and there is a remainder of 3 acres. 
 To divide these 3 acres, we take + of each acre for each 
 farm. tof 3 acres is 2 of 1 acre. 
 
 4. What is of 1315? of 5380? F of 8201? 
 
 5. Suppose 12 men to share equally in a prize of 
 $551.20; what is each man’s share? 
 
 6. What is 7; of 55120? =, of 967? =; of 700° 
 
 7. The Young Ladies’? Class Book, which consists 
 of 408 pages of select reading lessons, has been read 
 through by 25 scholars; each reading an equal portion. 
 How many pages did 1 scholar read ? 
 
 8. + of £1 [+ of 20s.] is how many shillings, and 
 what fraction of a shilling? 
 
 9. Find 4 of £7 in shillings— that is, reduce £7 to 
 shillings, and find 3 of the number of shillings. 
 
 10. 4 of 5 shillings is how many pence? 
 
 11.. How many grains in 7; of 6 pennyweights ? 
 
 12. 4 of 3 ounces is how many drams? *y 
 
 o* 
 
5° | 
 
 162 WRITTEN ARITHMETIC. VI. | 
 
 13. 11 men divided 9 hogsheads of molasses equally | 
 among them. How many gallons had each man ? 
 14. 16 of 7 furlongs is how many rods? | 
 15. 7 of 6 square feet is how many Square inches ? | 
 _ 16. How many seconds are there in q'z of 10 hours ? 
 4 17. Atrader sold 4 of a hogshead of wine at a7 cents — 
 for every 4 of a gallon. What did it amount to? 
 
 Section 22. 
 
 1. If 34 barrels of flour be made from 147 bushels of 
 wheat, how much wheat will make 9 barrels of flour ? 
 
 2. What is 9 times 3 of 147° 
 
 3. If 8 yards of paper ean cost $38, what will 13 
 yards cost, at the same rate t 
 
 4. What i is 18 times 4. of 38? 7 times 75 of 654? 
 5 times zz of 270? 21 times yy of 40975? 
 
 5. If it cost $1.25 to ride 20 miles in a stage, how 
 much will it cost to ride 32 miles? 
 
 6. If $16 will pay for 85 pounds of butter, how many 
 pounds will $25 pay for? 
 
 7. If 12 cords of wood cost B75, what will be the » 
 cost of 19 cords, at the same rate? 
 
 8. Suppose 2lcwt. of flour to be worth the same as 
 65 bushels of salt; how many bushels of salt must be 
 ee in exchange for 18 cwt. of flour? 
 
 If 8 barrels will hold 19 bu. one: 4qt. of corn, how 
 ek corn can be put into 15 barrels ? 
 
 Section 23. 
 
 1. When writing paper is sold at $5. 42 per ream, 
 
 what is the price of } of a ream? 
 2. If 1 of aream of paper is worth $1.352, what is 
 
 4 of a ream worth? 
 
 3. Suppose a hogshead of sugar to be worth $93; 
 what is 7, of it worth? 
 
 4. If 3 7 of a hogshead of sugar is worth $13. 287 
 what is $ of it worth ? 
 
 5. What is } of 3765? What is 8 S of 3765 : r 
 
 6. How many gallons are there in 4 of a pipe of wine? 
 How many gallons in 7 of a pipe? 
 
 a 
 “n 
 \ ze 
 er \ 
 
Ss ¢ Oe heer oe! 7 
 paddled YO ieee Vig 
 92, 23. PERCENTAGE. 63 
 
 In the following examples, it will be most convenient 
 to multiply by the numerator of the fraction, before 
 dividing by the denominator. See Second Method of 
 operation, exemplified in page 152. 
 
 7. The highest point of the Andes, is 21440 feet: & 
 Mont Blanc, of the Alps, is 4 as high. What is he : 
 height of Mont Blanc ? 
 
 8. Virginia contains 66000 square miles: Rhode 
 Island is only 7% as large. How many square miles are 
 there in Rho e sland? 
 
 9. If a man’s income be $1000 per year, what i is his 
 income for 9 months, or = of a year? 
 
 10. Suppose a man by constant industry can earn 
 $1.50 per day; what will he earn in 10 days, allowing, , 
 him to rest 7 of the time? 
 
 11. How much must be paid for 55 of a ton of Russia 
 hemp, when the price is $210 per ton? 
 
 12. A man having 4 miles to go, rode % of the way, 
 and walked the remainder. How many rods did he walk ? 
 
 13. Suppose 45000 pounds of iron to be sufficient to 
 lay the track on 1 mile of rail-way; how many pounds 
 of iron are-required to lay the track on 14 mile? 
 
 14. How much is 4500 plus ¢ of 4500? 
 
 15. Suppose a rail-way car to run 350 miles a day; 
 what distance will it run in 5? days? 
 
 16. How much is 5% times 350?— That is,— how 
 much is 5 times 350 and 2 of another time 350? 
 
 17. How much is 6% times 91? 84 times 146? 
 
 32 times 244? 124 times 379? 1675 ~ times 978? 
 
 PERCENTAGE. 
 
 The term, per cent., is an abbreviation of per centum, 
 and signifies, by the hundred. 1 per cent. of any num- 
 ber, is TO9 of that number; 2 per cent. Is 7553, 3 per- 
 cent. is 7353 4 per cent. is 7653 and so on. 
 
 18. What.is 5 per cent. of 360 dollars : p 
 
 360 Since 5 per cent. is 735, we multiply 
 
 by 5, and divide by 100. To divide 
 
 Ree by. 100, we merely point off two figures 
 $18.00 from the right, as taught in page 116.. 
 
a) ae Ay et SAN “a 
 \ ) Pd %, ny * ae of v ¢ 5 * 5 
 1647, WRITTEN ARITHMETIC. VE: 
 
 19. What is 1 percent. of 100? 2 percent. of 100? 
 20. What is 2 per cent. or +35 of 350 dollars ? 
 21. A merchant, who has $3875 deposited in the . 
 bank, wishes to draw out 4 per cent. of his deposit. 
 “How many dollars must he draw? 
 22. What is 6 per cent. or 48; of 4250 dollars? © 
 ,/ 23. What is 6 per cent. of $92.50, or 9250 cents? 
 24. What is 4 per cent. of $132.75? 
 
 » 25. A merchant having 2513 gallons of wine on hand, 
 Jost 1 per cent. of the whole, by leekage from the casks. 
 How many gallons did he lose? | 
 
 26. Find 6 per cent. of 128 dollars. 
 
 128 After multiplying and dividing, our 
 Lr 6 quotient is $75%%. Now, since 45 of a 
 phy dollar is 1 cent, ;°%,-of a dollar is 68 
 
 $7.68 cents: therefore the answer is $7.68. 
 
 27. Find 7 per cent. of 2517 dollars. 
 
 28. Find 18 per cent. of 20 dollars. | 
 
 29. What is 4 per cent. of $70.14, or 7014 cents ? 
 
 In this example, after multiplying by 4, and dividing 
 by 100, there is a remainder of 56. And since the 
 ‘juotient is cents, this remainder is +5 of a cent. 
 
 30. What is 9 per cent. of $470.46¢ | 
 
 31. What is 55 per cent. of $964.07? | 
 
 32. A and B have $500 apiece. If A should give B 
 6 per cent. of his cash, what would each then have? 
 
 33. What is $ of 1 per cent. of 62 dollars? 
 
 34. What is 44 per cent. of 62 dollars ? 
 
 35. What is 3 per cent. of 246 dollars ? 
 
 36. What is 54 per cent. of 246 dollars ? . 
 
 37. A merchant paid $491 for a quantity of salt: for 
 how- much must he sell it, to gain 9 per cent. ? 
 
 38. A trader paid $230 for a piece of cloth, contain- 
 ing 46 yards, and sold it so as to lose 4 per cent. 
 At how much did he sell it per yard? 
 
 39. If I pay $525 for 90 barrels of flour, at. what 
 price per barrel must I sell it, to gain 7 per cent.? 
 
 40. Suppose a merchant to pay $85 per ton for 6 
 tons of iron; at what price must he sell it per hundred- - 
 weight, in order to gain 12 per cent.? 
 
23. INTEREST. 165 
 
 41. A merchant failed in business, | and was able to 
 pay his creditors only 65 per cent. of their demands. 
 What did he pay.on a demand of $534 ? | 
 
 INTEREST. 
 
 Interest i is money. paid for the use of money that has 
 been owed. For instance, suppose that A lends B $100 
 _ for one year, and at the end of the year, B pays, not 
 
 only the $100, but also pays $6 for the use of the $100: 
 in this case, & 6 is*the interest. 
 
 The money for which interest is paid, is called the 
 Principal. The sum per cent. paid for one year’s in- 
 terest, is called the Rate. The principal and interest 
 added together, are called the Amount. 
 
 RULE FOR COMPUTING INTEREST. JJMWultiply the 
 principal by the rate per cent., and divide the product 
 by 100: the quotient will be the interest for 1 year. 
 
 42. What is the interest of $100, for 1 year, at 5 i 
 cent.? What is the amount? 
 
 43. What is the interest of $1 or 100 cents, for 7 
 year, at 5 per cent.? What is the amount ? 
 
 44, What is the interest of $354, at 6 per cent. for 
 1 year’ for 2 years? for 3 years? for 4 years? 
 What is the amount for 4 years? 
 
 45. What is the interest of $40.50, for 4 years, at 6 
 per cent.? What is the amount? 
 
 46. What is the interest of $18, for 3 years, at 7 
 per cent.? What is the amount? 
 
 47. What will $8410 amount to in 15 years; the rate 
 of interest being 4’ per cent.? 
 
 48. What is ‘the ingevoet of $6470, for 3 years, at 55 
 per cent.?: Whatis the amount? — 
 
 When interest is to be computed for any number of 
 months,— First find the interest Jor, 1, year then take +} 
 of a year’s interest for 1 month; 7 or + for 2 fonths; 
 z= Or g, for 3 months; and so on. 
 
 49. What is the interest of $35, for one month, at 6 
 per cent. per annum? What is the amount? 
 
166 WRITTEN ARITHMETIC. VL 
 
 50. What is the interest of $21, for 2 months, at 7 
 “per cent. per annum ? 
 
 51. What is the interest a $4291, for 3 months, at 
 5 per cent. per annum ? 
 
 52. At.4 per cent. per annum, what is the interest of 
 $ 122.75 for 4 months? for 5 months? for 6 months? 
 for 7 months? for 8 months? for 9 months? for 10 
 months? What is the amount for 11 months ? 
 
 53. What is the interest of $14. 50, for 1 yet and 1 
 month, at 6 per cent.? 
 
 54. What is the interest of $19. 25, for 3 years and’ 
 
 2 months, at 8 per cent.? 
 
 55. What is the amount of $458, for.2 years and 3 
 months, at 7 per cent.? 
 
 56. What is the amount of $8.75 for 5 years and 4 
 months, at 4 per cent.? 
 
 57. What is the amount of $91. 50, for 2.years and 7 
 months, at 8 per cent.? — 
 
 58. What is the interest. of $81, from February 7, 
 1832, to August 7, 1835, at 6 per.cent.? 
 
 59. Suppose a promissory note of $145, to be dated, 
 January 15, 1831; what will be the amount of that note, 
 October 15, 1834; the rate being 6 per cent.? 
 
 60. A owed B $96, on interest at 6 per cent. At 
 the end of 2 years, A paid the interest then due, and $25 
 
 of the principal: at the end of 3 years and 11 months, — 
 
 he paid the whole debt. What was each payment? 
 
 When interest is to be computed for any number i 
 days,— Furst find the interest for 1 ‘pede then take 3 
 of a month’s interest Jor 1 day; #5 Or 35 Jor 2 fei 
 35 OF 1p for 3 days; +; or + for 4 Deupsi go or & for 5 
 days; 5 or = for 6 days; and 50 On. 
 
 In the following operations, in this section, all fractions 
 of a cent may be disregarded: this being the common 
 practice in business. , 
 
 61. What is the interest of $231, for 7 days, at 6 
 per cent. per annum? 
 
 Direction. . First find the interest for A year; then for 
 tg of a year or 1 month; and then for 34 of a month. 
 
33, INTEREST. 167 
 
 62. What is the interest of $75, for 10 days, at 6 
 per cent. per annum ? 
 
 63. What is the interest of $254 for 21 days, at 6 
 per cent. per annum ? 
 
 64. What isthe interest of $110, for 5 months, and 
 8 days, at 6 per cent. per annum? 
 
 65. What is the interest of $34 for 1 year, 3 months, 
 and 25 days, at 6 per cent. per annum? 
 
 66. What is, the interest of $91.18, for 3 years, 2 
 months, and 13 days, at 6 per cent. per annum? 
 
 Several other methods are practised by merchants, 
 in computing interest; among which, are the following. 
 
 When the rate ts 5 per cent.—Divide the principal by 
 20, and the quotient is the interest for 1 year. 
 
 67. What is the interest of $4207, for 2 years, at 5 
 per cent. per annum ? 
 
 68. What is the interest of #01. 17, for 4 years, at 
 5 per cent. per annum? 
 
 When the rate is 6 per cent. — Multiply the principal 
 by half the number of months in the time, divide the 
 product by 100, and the quotient is the interest. 
 
 69. What is the interest of $119, for 16 months, at 
 6 per cent. per annum f 
 
 70. What is the interest of $96.48, for 10 months, at 
 6 per cent. per annum ? 
 
 71. What is the amount of $27.56, on interest 6 
 months, at 6 per cent. per annum? 
 
 72. What is the interest of $133.24, for 11 months, 
 at 6 per cent. per annum ? 
 
 To find the interest for pays, the rate being 6 per 
 cent.—Multiply the principal in ‘dollars by the “number 
 of days, divide the product by 6, and cut off one figure 
 from the right of the quotient. The rest ofthe quotient 
 » figures express NEARLY the interest, in cents. 
 
 73. What is the interest of $249, for 75 days, at 6 
 per cent. per annum ? 
 
 74. What is the interest of $5824, for 21 days, at 6 
 per cent. per annum ? 
 
“468 © WRITTEN ARITHMETIC. VI. 
 
 75. What difference will it make to the man who pays 
 interest on $100 for 1 year, whether it be computed by 
 ee or, according to true rule in page 165: ? 
 
 DISCOUNT. 
 zsh § is an abatement of a certain part of'a debt, 
 
 when the debt is paid before it becomes due. For in- 
 
 stance, suppose that A is bound to pay B $106, in one 
 
 year from the present time; but B, wanting the money | 
 
 now, agrees to receive $100 for the debt, on condition 
 of present payment: in this case, $100 is the present 
 worth of the debt, and $6 the discount. 
 
 The present worth of any debt due at a future period, 
 is that sum of money, which, if put at interest, would 
 amount to the debt, by the time the debt becomes due. 
 Ahgeatore, when the rate of interest is 5 per voy , that 
 is, 7gq Of the principal, then the discount is z>5 of the 
 principal; when the rate of interest is 6 per cent, , that 
 is, +£5 of the principal, then the discount is +8~ of the 
 principal; and so on. 
 
 RULE FOR COMPUTING DISCOUNT. Multiply the 
 principal by the rate of interest; then divide the product 
 by a number, which is to be found by adding 100 and 
 the rate together. The quotient will be the discount. 
 
 76. What is the discount on $48.51, due in 3 years; 
 the rate of interest being 5 per cont per annum, and 
 consequently the discount being +25 per annum? 
 
 77. What is the discount on $247, due in 1 aa 
 the rate of interest being 6 per cent. ? 
 
 78. What is the present worth of $150, due inl 
 year, the rate of interest being 6 per cent. ? 
 
 Find the discount, and subtract it from the*debt. 
 
 79. What is the present worth of $1640, due in 2 
 years, the rate of interest being 5 per cent. ? 
 
 80. What is the difference between the discount on 
 $100 for 1 year, and the interest of $100 for 1 year; 
 the rate of interest being 6 per cent.? — 
 
 81. Find the present worth of $75, due in 2 years 
 and 9 months, [27 years], interest being 6 per cent. ? 
 
24. 25. 26. FRACTIONS. 169 
 
 Section 24. 
 
 1. Suppose { of a piece of broad-cloth to be worth 
 i 87; what is 4 of the piece worth ? What is the 
 whole piece worth: ; 
 
 rid 11887 is 2 of what number? — 
 
 . If the interest of $100 be ae 50 for +5 of a year, 
 wit’ is the interest of $100 for zz of a year? Then 
 what would be the interest for 1 year? 
 
 4. If 33 of an acre of land produce: 133 bushels of 
 potatoes, “how many bushels does y' of an acre produce ? 
 How many Rushels would 1 acre produce? 
 
 pt 9071 is #; of what number? 
 
 - If a man earn $190 a year by working 5 of the 
 (ce how much could he +i by working constantly ? 
 7. $14 is 8 per cent. or 75 of what sum of money? 
 
 Section 25. 
 CHANGE OF THE TERMS OF FRACTIONS. 
 
 The numerator and denominator of a fraction, are 
 called the two terms of a fraction.. These terms may be 
 changed, and the fraction may ‘still express the same 
 quantity. For instance, the terms 2 and 3, in the frac- 
 tion ¥, may be changed to 4 and 6, and the fraction will 
 becomes 4, which is still equal to 3. 
 
 1. 2 is equal to how. many twenty-fourths ? 
 
 Dixdchion B-eighths are equal to 24-twenty-fourths; 
 therefore, find 3 of 24, and this number will be the re- 
 quired) numerator of 57- 
 _» 2. 2 is equal to how many fourteenths ? 
 
 3. Change 4 2 to eighteenths and add + 1 to it. 
 4. Dis equal to how many forty-fifths ° 
 5. ppeneeyy ;{ to fortieths, and then take 3} from it. 
 
 Section 26. 
 
 REDUCTION OF FRACTIONS TO LOWER TERMS. 
 When a number can be found, that will divide both 
 terms of a fraction, without a remainder, the two quo- 
 tients arising from the division, will express the fraction 
 reduced to lower terms. For example, both terms. of 
 Pp. 
 
170 WRITTEN ARITHMETIC. | Vi 
 
 the fraction 3% can be divided by 3, and the reduced 
 fraction will be 3. . Again, both terms of 7 can be divid- 
 ed by 2, and the reduced fraction will be} 4. Thus any 
 fraction may be reduced to its lowest terms, by repeat- 
 edly dividing the terms, until no number will divide 
 
 them both without a remainder. 
 
 1. Reduce each of the following fractions to its low- 
 
 3. 6 RL poet, 6 Fe es hihi 
 est terms. §- 9: is* I2* 5: 1e* 37° 24° 
 
 2. Reduce each of the following fractions to its low- 
 10 20 100 600 10 
 
 est terms. 55+ go: 300° 800° 106° 90: T200- 
 
 Only once dividing the terms of a fraction, will reduce © 
 it to its lowest terms, if we use the greatest common di- 
 visor, that is, the greatest number that will divide both 
 
 terms without a remainder. 
 
 ‘TO FIND THE GREATEST COMMON DIVISOR of two 
 numbers,— Divide the greater number by the smaller, 
 then divide the divisor by the remainder; and thus con- 
 tinue dividing the last divisor by the last remainder, till 
 nothing remains. The divisor used last of all, will be 
 the greatest common divisor. 
 
 3. Find the greatest common divisor of 91 and 117. 
 
 91)117(1 This operation is perform- 
 91 ed according to the direction 
 26)9 1(3 above, and 13 is found to be 
 
 78 the greatest common divisor; 
 
 — or the greatest number b 
 baa which oF tnd 117 can be de 
 <n vided without a remainder. — 
 4. Find the greatest common divisor of 15 and 235. 
 5. Reduce 72 to its lowest terms, by using the great- 
 est common divisor of the two terms. 
 6. Reduce to their lowest terms, $72, 33%, and 333 
 
 Section 27. ‘ 
 
 COMPOUND FRACTIONS. 
 
 A compound fraction arises from dividing a unit into 
 a certain number of equal parts, and then dividing one 
 of these parts into other equal parts. 
 
27. “FRACTIONS. 171 
 
 TO REDUCE A COMPOUND FRACTION TO A SIMPLE 
 FRACTION,— Multiply all the numerators together for a 
 new numerator, and allthe denominators for a new denom- 
 inator: then reduce the new fraction to its lowest terms. / 
 
 1. Reduce 2 of 5 to a simple fraction. 
 
 2. 4 of a water melon was divided equally among 6 
 boys. What fraction of the melon did 1 boy receive? 
 
 3. Reduce % of ¢ to a simple fraction. 
 
 4. 2 of an acre of land was divided into’4 equal lots. 
 What fraction of an acre did 2 lots contain? 
 
 5. Reduee = of 4 to a simple fraction. 
 
 6. 2 of +& is equal to what part of 1? 
 
 fi Weanca' q7 of 7 to a simple fraction. 
 
 8. 1 penny is what. part of 1s.? what part of £1? 
 
 9. 7 pence is what stm pa fraction of £1? 
 
 pap Restion 7 pence is 75 of 1 shilling, and 1 shilling 
 as yo Of £1. Therefore, 7 pence is 75 of 35 of £1. 
 
 10. Reduce 1 Brains to the fraction of an, ounce; 
 that is, reduce 42 of =, to a simple fraction. 
 
 11. Reduce 3 nails tothe fraction of a yard. 
 
 12. Reduce 4 inches to the fraction of a yard. 
 
 13. Reduce 25 seconds to the fraction of an hour. 
 
 14. Rogues of z of $ toa simple fraction. 
 
 15. 3 of $ of 2 to is equal to what part of 1? 
 
 16. Reduce -f qs of 3% of.4 to a simple fraction. 
 
 When the lower lagen of a compound number 
 are to be reduced to the fraction of a higher denomina- 
 tion,— First, reduce the given quantity to the lowest de- - 
 nomination mentioned, and this number will be the 
 numerator: then reduce a unit of the higher denomina- 
 tion, to the same denomination with the numerator, and 
 this number will be the denominator. 
 
 17. Reduce 14s. 10d. 2qr. to the fraction of £1. 
 14s. 10d. 2qr. . £1 is 20s. The denomin- 
 
 12 12 ator and numer- 
 Te ator here found, 
 Se a 240d. make Git: this 
 
 os fraction, wien re- 
 Num. 714 qr. Denom. 960 qr." duced, is 442. 
 
 Y 
 
é . 
 
 172 WRITTEN ARITHMETIC. VI. 
 
 18. Reduce 2s. 7d. 1qr. to the fraction of £1. 
 
 19. Reduce 11d. 3qr. to the fraction of a pound. 
 
 20. Reduce 15s. Od. 3qr. to the fraction of a pound. 
 
 21. Reduce 10d. 1qr. to the fraction of a shilling. 
 
 22. Reduce 2s. 9d. 3%qr. to the fraction of a pound. 
 
 Direction. Find the number of fifths of a farthing in 
 2s. 9d. 3%qr., for a numerator; then find the number of 
 fifths of a farthing in £1, for a denominator. 
 
 23. Reduce 84 pence to the fraction of a pound. 
 
 24. Reduce 5qt. Ipt. tothe fraction of a bushel. 
 
 25. Reduce 9gal. Sqt. Ipt. to the fraction of Ibhd. 
 
 26. Reduce 6 rods 3yd. 2ft. to the fraction of a mile. 
 
 27. Reduce 35-4, seconds to the fraction of a day. 
 
 When the fraction of a higher denomination is to be 
 reduced to its value in whole numbers of lower denomi- 
 nation,— Multiply the numerator by that number of the 
 next lower denomination which is required to make a unit 
 of the higher, and divide the product ‘by the denominator; 
 the quotient will be a whole number of the lower denomi- 
 nation, and the remainder will be the numerator of a frac- 
 tion. Proceed with this fraction as before, and so on. 
 
 28. Reduce # of £1 to its value in shillings &c. 
 
 2 _..... Since ? of £1 is the same as 7 of 
 20 20 shillings, we find 7.of 20 shillings, 
 7)40 | in shillings and the fraction of a shil- 
 saw ling;— itis 54shillings. Then, since 
 ae 3 of 1 shilling is the same as 7 of 12 
 2 pence, we find ? of 12 pence;— it is 
 7)60 84 pence. Then, since 4 of 1 pen- 
 
 4 ny is the same as 4 of 4 farthings, 
 4 we find 4 of 4 farthings;—it is 24 
 
 aa farthings. Thus by finding one de- 
 
 nomination ata time, we finally ob- 
 
 27 tan, 5s.'\8d.. 27 axe re 
 
 29. Reduce 2 of £1 to its value in shillings &c. 
 
 30. 4 of £1 1s how many shillings, pence, &c.? 
 
 31. In 2 of a shilling, how many pence, &c.? 
 
 32. Change £15 4 to pounds, shillings, pence, &c. 
 
 .83. Reduce fof 1ewt. to quarters, pounds, &c. 
 
2Q8, FRACTIONS. 173 
 
 34. Change 9,6 pounds, to pounds, ounces, and drams. 
 
 35. Reduce 3 of a mile to furlongs, rods, feet, &c. 
 
 36. In 107 acres, how many acres, roods, rods, &c. 
 
 37. How many dimes, cents, and mills, in 34, of #1 ? 
 
 38. In 73 of a dollar, how many cents and mills ? 
 
 39. Suppose sugar to be $12 per hundredweight; 
 what quantity can be purchased for $113? 
 
 Section 28. 
 COMMON DENOMINATORS. 
 
 When two or more fractions have the same number 
 for a denominator, this number is called their Common 
 Denominator. Fractions having different denominators, 
 must be reduced to a common denominator, before ad- 
 dition or subtraction can be performed on them. 
 
 RULE FOR REDUCING FRACTIONS TO A COMMON 
 DENOMINATOR. Multiply each numerator into all the 
 denominators except its own, foranewnumerator. Then 
 multiply all the denominators together for a common de- 
 nominator, and place it under each new numerator. 
 
 1. Reduce 3, $, and §, to a common denominator. 
 
 9) 4 6 mete, 
 9 8 8 9. 
 45 32 48 % 
 7 7 9 KG 
 i 224 432 
 “30a 504 50 504 
 Reduce 2, 34, and } to a common denominator. 
 Reduce 44 and =& to a common denominator. 
 Reduce 4, 4, and 42 to a common denominator. 
 i 
 
 30 
 Reduce 4, +, 2, and } to a common denominator. 
 
 4 
 
 i 
 
 How much is 2 and 4 added together ? 
 How much is +4 and 38 added together ? 
 
 8. How much is § and 2 and +3, added together ? 
 
 9. If <4 be taken from 2, how much will remain ? 
 10. If 2 be taken from +4, how much will remain ? 
 11. Which is greater, 3 or 74 ’—how much greater ? 
 
 AT co Ww 
 
174 WRITTEN ARITHMETIC. VL 
 
 Section 29. 
 
 1. A farmer raised 1422 bushels of corn in one field, 
 and 237-75 bushels in another. How many bushels did 
 he raise " both fields ? 
 
 The learner may reduce the fraction in his answer, to 
 its lowest terms, in this, and all future examples. 
 
 2. A farm is divided into three lots;— the first lot con- 
 taining 464 acres, the second 50§ acres, and the third 
 62%, acres. How many acres are there in the farm ? 
 
 3. Add together 4414 and 654 and 2556+ 
 
 4. If 6% be taken from 8§ how much will remain? 
 
 5.) Subtract 4372 from 16592. 
 
 6. If 62 gallons of wine should leak from a cask con- 
 taining 53% gallons, how many gallons would remain? 
 
 7. Add together 623% and 11375; and then subtract 
 from the sum 4502. 
 
 8. Three soldiers shared a loaf of bread as follows:— 
 the first took 7 of it, the second took + of it, and the 
 third took the. remainder. . What fractional part of the 
 loaf did the third soldier receive ? 
 
 9. A trader having 25 barrels of flour, sold 84 barrels 
 to one man, and 944 barrels to another. What ‘quantity 
 of flour had he then remaining? ' 
 
 Section 30. 
 ic Suppose I have 16 dollars; to how many men can 
 I give 3 of a dollar apiece § ‘ot ty 
 
 2. How many times is 3 contained in 16? 
 
 3. How many pairs of gloves can I buy for 18 dollars, 
 the price being } of.a dollar a pair? 
 
 4. Divide 18 by 4; that is, reduce 18 to fourths, and 
 find how many times 3-fourths is contained therein. — 
 
 5. Divide 46 by 2; that is, find how many times the 
 fraction 2 is contained in 46. 
 
 6. If a man walk 1 mile in 7 of an hour, what dis- 
 tance will he walk in 4 hours P 
 
 ' ‘7. How many times is 33; contained in 4? 
 
 8. How many times is 2 2 contained 4 in? 
 
 Direction. Reduce 2 and Z to a common denomina- 
 tor, and then divide one numerator by the other. 
 
29. 30. 31. FRACTIONS. 175 
 
 9. How many times is ;% contained in 44? 
 
 10. How many barrels of flour can be bought for 38 
 dollars, at 4% dollars per barrel? 
 
 11. How many times is 25 contained in 917? 
 
 12., How many times is 62 contained in 424? 
 
 Direction. Reduce the two fractions to a common 
 denominator; then reduce the mixed numbers to impro- 
 per fractions, and divide one numerator by the other. 
 
 13. If a barrel of cider will last a man 34 months, 
 how many barrels will he drink in 102 months ? 
 
 Section 3l. 
 REVIEW. 
 
 1. (§ 13.) Suppose a man to earn 95 cents per day; 
 how many days would it take him to earn $43.16? ». 
 
 2. (§ 14.) How many pounds of sugar can be bought 
 for $142, when the price is } of a dollar a pound? 
 
 3. (§15.) If 1 yard of silk cord cost 34 of a dollar, 
 what is the price of 75 yards, at the same rate? 
 
 4. ($ 16.) If 142 yards of cloth be cut from a piece 
 containing 524 yards, how much will be left ? 
 
 5. (§17.) If a pound of shot cost 3 of a dollar, 
 what will be the cost of 17 pounds, at the same rate ? 
 
 6. (§ 18.) How much corn will grow on 140 acres 
 of land; allowing each acre to produce 342 bushels? 
 
 7. (§ 19.) If a man’s expenses be $46.2455 for q5 
 of a year, what will be his expenses for 1 year? ¥ 
 
 8. (§ 20.) 4+ of 71 is equal to what improper frac- 
 tion? Then 4 of 71 is equal to what mixed number ? 
 
 9. (§ 21.) Suppose 42 men to share equally in a 
 prize of $1000; what is the share of one man? 
 
 10. (§ 22.) Ifa man can cut 46 cords of wood in 14 
 days, how many cords can he cut in 60 days? 
 
 11. (§ 23.) Suppose a man can build a mile of wall 
 in 310 days; in what time can he build 7 of a mile ? 
 
 , 12. (§ 24.) A man bought a quantity of flour, for 
 
 domestic use, and in 36 days he found that 74 of it was 
 consumed. How long would the whole last? 
 
 * 
 oS 
 
176 WRITTEN ARITHMETIC. VI. 
 
 13. (§ 25.) is equal to how many ninths? how 
 many thirty-sixths? how many seyenty-fifths ? 
 
 14. (§ 26.) Reduce the two fractions, 27 and #8, to 
 their lowest terms, and then add them together. 
 
 15. (§ 27.) Suppose a farm to contain 98,3, acres of 
 land; how many acres are there in 2 of the farm? 
 
 16. (§ 28.) Add together, +2, and = and 43; then 
 _ subtract 3° from the sum;— what is the remainder ? 
 
 17. (§ 29.) If 4 and 3% of a number be subtracted 
 from itself, what part of that number is the remainder ? 
 
 18. (§ 30.) If the mail-stage run 93, miles in 1 hour, 
 how many hours will it be in running 1757 miles? 
 
 RETROSPECTIVE OBSERVATIONS. 
 
 A fraction is rendered greater by increasing the nu- 
 merator, and smaller by increasing the denominator. 
 
 To multiply a fraction by a whole number,— Either 
 multiply the numerator, or diwide the denominator. 
 
 - To divide a fraction by a whole number,— Either di- 
 vide the numerator, or multiply the denominator. 
 
 When a number is multiplied by 1, the product is 
 equal to the multiplicand. Therefore, when a number 
 is multiplied by a fraction, which is less than 1, the pro- 
 duct must be less than the multiplicand. 
 
 To multiply a whole number by a fracttion,— Multiply 
 by the numerator, and divide by the denominator. 
 
 Dividing a number by 1, gives a quotient equal to the 
 dividend. Therefore, dividing a number by a proper 
 fraction, must give a quotient greater than the dividend, 
 ‘because, the fraction being less than 1, is contained a 
 greater number of times in the dividend. 
 
 To divide a whole number by a fraction,—Multiply 
 by the denominator, and divide by the numerator. 
 
 To multiply a fraction by a fraction,—Multiply nu- 
 merator by numerator, and denominator by denominator. 
 
 To dwide a fraction by a fraction,—Multiply the nu- 
 merator of the dividend by the denominator of the divisor, 
 Jor a numerator; and multiply the denominator of the die~ 
 idend by the numerator of the divisor, for a denominator. 
 
 * 
 
32. MISCELLANEOUS EXAMPLES. 177 
 
 19. Multiply the fraction, 7 a 355 by 38. 
 20. Divide the fraction, =3;, by 145. 
 21. Multiply $706 by the fraction, 
 22. Divide 611 by the fraction, 455 
 23. Multiply the fraction, 2037 Mi the acho, tr 
 
 24. Divide the fraction, ,, by the fraction, 4$ 
 
 25. What is the product of 6084 multiplied by" 8.2? 
 26. What is the quotient of 457 2" divided by 33° 
 
 SEcTION 32. 
 MISCELLANEOUS EXAMPLES. 
 
 1. Suppose a man can perform a journey in 14 days 
 and 3 hours, travelling 9 hours a day; in what time can 
 he Bie Mies the journey, travelling 11 hours a day? 
 
 . A trader gave $75 for 56 gallons of wine, and lost 
 11 pads ok by leakage.” At how much per gallon must 
 he sell the remainder, to get the whole cost? 
 
 3. Suppose a retailer to pay $165 for a ton of sugar, 
 at what price must he sell it per pound, in order to gain 
 10 per cent. on the cost? 
 
 4. What quantity of salt, worth 62 cents per bushel, 
 must be given in exchange for 258 pounds of pork, 
 worth 9 gents per pound?» 
 
 5. What is the profit on 400 hogsheads of molasses, 
 purchased in New Orleans at 125 cents per gallon, [63 
 gal. in each hhd.], freighted to New York at $ 3.50 per 
 hhd., and sold at 24 cents per gallon; Sgal. 2qt. having 
 leaked from each hhd. on the passage? 
 
 6. Ifa pint of rum a day will kill a man in a year and 
 a half, how many men would a cargo of 600 hogsheads 
 oh in the same time? 
 
 If 11 young men can become fools by drinking 6 
 bottles of wine, at $3 a bottle, what would it cost a 
 dinner party of 25, to become fools in like manner? 
 
 8. If a man’s expenses be $1.40 a day, and his in- 
 come $700 a year, what will he lay up in 7 years? 
 
 9. A and B are laborers—A earns % 19.50 a month, 
 and B earns $16.25; but A gives B -% of his earnings. 
 What will each lay up in 14 months? 
 
 10. Find the difference betiaey of 91, and 3 of 91. 
 
 203. 
 464 
 
32. MISCELLANEOUS EXAMPLES. 179 
 
 On the opposite page, 30 cities and towns are exhib- 
 ited in their respective situations, relative to each other; 
 and the number of miles, by foe road from town to 
 town, is noted in figures. 
 
 11. Find the distance from Walliigion’ through the 
 intermediate towns, to Augusta, Me....... from Washing- 
 ton to Detroit....... from Washington to St. Louis....... 
 from Washington to Natchez.......from Washington to 
 New Orleans....... from New Orleans to Augusta, Me. 
 
 12. Suppose a citizen in each of the places on the 
 opposite page, to start for Washington, and travel 7 
 miles an hour, 10 hours in each day; how long will a, 
 one be in performing his journey ? 
 
 13. How long would it take you to walk from your 
 school-room to Washington; allowing that you could 
 walk 34 miles an hour, 7 hours in each day ? 
 
 14. Two men started at the same time— one of them 
 from New Orleans, and the other from Augusta, Me.— 
 and travelled towards each other, with equal speed. 
 Between what two towns, and what distance from each 
 of these towns did they meet ? 
 
 15. Mr. A. went from Portland to Baltimore, travel- 
 ling 5 miles an hour, and 10 hours a day, Mr. B. per- 
 formed the same journey; but started 1 day later, and 
 travelled 7 miles an hour. Where did B. pass A.? 
 
 16. Divide $1000 among A, B, and C, giving B 
 twice as much as A, and € twice as much as B. 
 
 17. Gunpowder is composed of 5 parts sulphur, 7 
 parts charcoal, and 38 parts nitre. How ey pounds 
 of each ingredient, in 100 pounds of powder ? 
 
 18. A and B purchased a cow for $16. A paid $9 
 of the price, and B paid $7. They sold the cow for 
 $21. What was each one’s share of the gain ? 
 
 Solution. Since A paid yz of the price, and B 34, 
 A must have 7% of the gain, and B iz 
 
 19. C and D traded in partnership; C owned $450 
 of the stock in trade, and D $290. They gained $146. 
 What was each one’s share of the gain? 
 
 20. Suppose $1000 stock in trade to gain ee 
 ,what is the gain on $351 of that stock? 
 
< 
 
 A 
 180 WRITTEN ARITHMETIC. VI. 
 
 21. E and F purchased 245 acres of land, for $2600. 
 E paid $1200 of the money, and F paid the remainder. 
 How much land should each one have? 
 
 22. The national debt of England is not less than 
 $1900000000. Allowing 5 percent. interest to be paid 
 on this sum, how many families would it support, each 
 family spending $400 per annum? 
 
 23. If a man can dig a trench in 15 days, and a boy 
 can dig the same trench in 18 days, in what time can 
 they both dig it? (See example 20, Oral sec.) 
 
 24. How many days will it take 17 men to perform a 
 piece of work, that 1 man can perform in 95 days? 
 
 25. How many days will it take 30 men to perform a 
 piece of work, that 4 men can perform in 50 days? 
 
 26. How many days will it take 25 men to perform a 
 piece of work, that 6 men can perform in 40 days? 
 
 27. If 15 yards of carpeting, which is one yard wide, | 
 will cover the floor of a room, how many yardyof car- 
 peting, 3-quarters wide will cover the same floor? 
 
 Direction. Find the number of square quarters con- 
 tained in 15 yards of the wider carpeting; then divide 
 this number, by the number of square quarters contained 
 in one yard of the narrower carpeting. 
 
 28. Suppose 34 yards, of broad-cloth 5-quarters 
 wide, to. be made into a cloak; how. many yards of silk 
 3-quarters wide, will it take to line the cloak? 
 
 29. How many yards of carpeting that is 5-quarters 
 wide, will cover the floor of a room which is 194 feet 
 in length, and 15 feet.in width? 
 
 30. How many bricks will it take to build a wall, 1 
 foot thick, 5 feet high, and 24 feet long; each brick be- 
 ing 8 inches long, 4 inches wide, and 2 inches thick? 
 
 31. If aman can hoe 44 of an acre of corn in a day, 
 and a boy + of an acre, how much can they both hoe in 
 aday? In what time can they both hoe 9 acres? 
 
 32. There is a cistern, having 3 pipes; the first pipe 
 will discharge the cistern in 4 hours, the second. in 5 
 hours, the third in 6 hours. What part of the contents 
 of the cistern would all the pipes together let off in 1 hour. 
 ' In what time would they all discharge the cistern? 
 
32. MISCELLANEOUS EXAMPLES. 181 
 
 33. What is the height of a steeple, whose shadow is 
 148 feet 4 inches, when a shadow 5 feet 4 inches long 
 is projected from a post 6 feet 4 inches high? _ 
 
 34. A trader failed in business, owing $11000, and 
 having only $5000 to divide among his creditors. How 
 much'did he pay on a debt of $95.20? 
 
 35. A fox has 50 rods the start of a greyhound, but 
 the hound runs 15 rods while the fox runs 93. How 
 many rods must the hound run to catch the fox ? 
 
 36. A cubic foot of air weighs 1g ounce. How many 
 pounds of air does a room contain, which is 16 feet long, 
 14 feet wide, and 10 feet high? 
 
 37. What number must that be, which, bene m- 
 creased by its half, and its third, becomes 88 ? 
 
 38. Aand B hired a pasture for $30. A tured in 3 
 cows, and B turned in 12 sheep. Allowing 5 sheep to 
 be equal to 1 cow, what must each pay? |” a 
 
 39. Suppose London to contain 1250 000 inhabitants, 
 New York 203000, Philadelphia 167000, Baltimore. 
 80 000, and Boston 61 000; how many times greater is 
 Tediou than each‘of the other cities ? 
 
 EXPLANATION OF CHARACTERS. 
 
 -+ This character placed between numbers, shows 
 that they are to be added together; thus, 6-++4 is 10. 
 
 — This character between numbers, shows that the 
 number on the right hand is to be subtracted from the 
 number on the left hand; thus, 9—3 is 6. 
 
 < This character shows, that numbers are to be 
 multiplied together; thus, 4X5 is 20. 
 
 + This character shows, that the number on the left 
 hand is to be divided by the number on the right hand; 
 thus, 28+4 1s 7 
 
 = This character shows, that the number on the right 
 is equal to the number on the left; thus, 4--S8—=12. 
 8—3=5. TX3—21. 3274-8. 
 
 40. 1426026 + 706241 + 360515 = how much? 
 
 41. 5147-+ 28650-++ 643—426= how much ? 
 
 42. 40673-+62—40275 x 58 =how much? 
 
 43. 872-+9516—1430 X16+12=how much? ‘ 
 Q 
 
For instance, in the number 1.111, the As 
 
 1 next to the right of the unit is l-tenth, Ge 
 that is, 715 of a units the 1 next to the right 22% Z 
 of the 1-tenth is 34, of atenth, or l-hun- 3843 
 . dredth of a unit; the a next to the right pees 
 of the 1 -hundredth, IS 75 of a hundredth, 1.111 
 
 182 WRITTEN ARITHMETIC. VI. 
 
 DECIMAL FRACTIONS. 
 Section 33. 
 
 A decimal fraction is a fraction whose denominator is 
 10, or 100, or 1000, &c. ‘The denominator of a deci- 
 mal fraction is never written: the numerator is written 
 with a point prefixed to it, and the denominator is un- 
 derstood to be a 1, with as many ciphers annexed, a8 
 there are figures ic the numerator. Thus, .3 is 33; 
 wool ig. tao3 .316 1 18 to003 0164 is ptt - 
 
 1. Write upon the slate, the decimals expressing the 
 
 460, i708 0) $642 9 60m5, 
 following fractions. to: ieee anita econ 100000° 
 
 When a whole number and a decimal are written to- 
 gether, the 3 point Is pinged between them. Thus, 
 24.6 is 24455 5.71 1s 54553 48.364 is 48335. 
 
 2. Write the following mixed numbers, expressing the 
 fractions decimally. 38%. 516;%.. a 5? 2445 35- 
 
 It is observable in our system of writing whole num- 
 bers, that any figure, wherever it may stand, expresses 
 a quantity 4; as great as it would express, if it were 
 written one place further to the lett. For instance, in 
 
 - the number 1111, the 1 hundred i is =/; of a thousand; the 
 
 1 tenis 4 of a hundred, or 745 of a thousand; the 1 
 unit is 75 of a ten, or 7,55 of a thousand. In decimals, 
 this system is continued below the place of units. 
 
 or 1-thousandth of a unit. 
 
 Ciphers placed on the right hand of decimal figures, 
 do not alter the value of the decimal; because, the fig- 
 ures still remain unchanged in their distance from the 
 unit’s place. For instance, .5, .50, and .500 are of 
 equal value,—they are each equal to 3. But every 
 cipher that is placed on the left of a decimal, renders 
 its value ten times smaller, by removing the figures one 
 
33. DECIMALS. 183 
 
 place further from the unit’s place. Thus, if we prefix 
 one cipher to .5, it becomes .05 [425]; if we prefix two 
 ciphers, it becomes .005 [+;%9]5 if we prefix three ci- 
 phers, it becomes .0005 [35255]; and so on. 
 
 3. Write upon the slate, decimals expressing the fol: 
 
 ieutedn ts 4 " 3 ie mary 
 
 lowing fractions. 799+ to0d+ Todo + TOOTTG * TOTODNN- 
 To read a decimal fraction,—Enumerate and read 
 
 the figures, as if they were whole numbers, and conclude 
 
 by pronouncing the name of the lowest denomination. 
 
 4. Copy upon the slate, the several numbers standing 
 in the following columns, and then read them. 
 
 -06 .065 -0007 24.02 
 -00S -409 -06264 5.763084 
 O13 .207862 - 10809 160.052 
 0514 5004 .6500171 712.3005 
 
 5. Write in i the following mixed numbers. 
 9550 46 7 [000 1270000 60 r900 
 Stoo0 . Tro000 «= 200 1955 8 1000000 
 Sio00 =» S5ta55 lipoo0 © 8 xs000000 
 
 ADDITION OF DECIMALS. 
 6. Add the following numbers into one sum. 63.75 
 
 and 524.0764 and .23 and 261.803. 
 
 63.75 In arranging decimals for addition, 
 524.0764 we place tenths under tenths, hun- 
 23 dredths under hundredths, &c. We 
 261.803 then begin with the lowest denomi- 
 849.8594 ‘Ration, and proceed to add the col- 
 
 cag. ait eral umns as in whole numbers. 
 
 7. What is the sum of 2.164, 870.31, 756, 9. 18, 
 157.0008, 26.104, and .3728° 
 
 8. What is the sum of 2706, 58.2, .2065, 6.441, 75, 
 14.2, and 990.752? 
 
 In Federal Money, the dollar is the unit; that is, dol- 
 Jars are whole numbers; dimes are tenths, cents are 
 hundredths, and mills are thousandths. See page 124. 
 
 9. Add together $24.6, $9.07, $5.009. and 5 cents. 
 
184 WRITTEN ARITHMETIC. VI. 
 
 10. Write the following sums of money in the form 
 of decimals, and add them together. $46 and 9 cents, 
 14 cents, $7 and 8 mills, 6 dimes, 8 dimes and 7 mills. 
 
 SUBTRACTION OF DECIMALS. 
 11. Subtract 52.6087 from 406.91. 
 
 406.91 After placing tenths under tenths, 
 52.6087 &c., we subtract as in whole num- 
 De honwe» . bers.) The blank places over the 7 
 web ened a and 8, are viewed as ciphers. 
 12. Subtract 943.076 from 8270.54. 
 13. Subtract 1084.72 from 5603:0626. 
 14. Subtract 146.1706 from 16094. 
 15. Find the difference between .8 and .08,. by sub- 
 tracting the smaller decimal from the greater. 
 16. Find the difference between .45 and .31067, by 
 subtracting the smaller decimal from the greater. 
 _ 17. What is the difference between 1 and .046 ? 
 18. Write 4 dollars and 8 mills in decimal form, and 
 subtract therefrom, 6 dimes and 5 mills. 
 19. Subtract 7 cents and 3 mills from 10 dollars. 
 
 MULTIPLICATION OF “DECIMALS. 
 Multiplying by any fraction, is taking a certain part 
 of the multiplicand for the product; consequently, mul- 
 tiplying one fraction by another, must produce a fraction 
 smaller than either of the factors. For example, 3% 
 multiplied by =§; 1s 44%, or, decimally, .9 multiplied by 
 .8 is .72. Hence you may observe, that the number of 
 decimal figures in any product, must be equal to the 
 
 number of decimal figures in both the factors. 
 
 20. Multiply 531 by .52. 65.7 by .43. 7.06 by .24. 
 .439 by .38 .149 by .26. 
 
 031 65.7 7,00 | 9.) 439 149 
 
 -02 43 24 .38 .26 
 
 1062 1971 2824 3512 894 
 2655 2628 1412 1317 298 
 
 i ee” 
 
 rn 
 
33. ss DECIMALS. 185 
 
 RULE FOR MULTIPLICATION OF DECIMALS. JWVul- 
 tiply as in whole numbers ; and in the product, point off 
 as many figures for decimals, as there are decimal places 
 in both factors. If the number of figures in the product 
 be less than the number of decimal places in both factors, 
 prefix ciphers to supply the deficiency. 
 
 21. Multiply 1608 by .4,—that is, find .4 of 1608. 
 
 22. Multiply .45 of a dollar by 8. 
 
 23. How much is 36 times .495 of a dollar ? 
 
 24. What cost 18 yards of cloth, at $ 4.072 per yd.? 
 
 25. What cost 28.7 yards of cloth, at $9 per yd.? 
 
 26. What cost 9.3 acres of land, at $8.41 per acre? 
 
 27. If 1 yard of silk cord cost 7 mills, [.007], what 
 is the price of .9 of a yard? 
 
 28. What is 6 per cent. or .06 of 340.4? 
 
 29. Multiply 42.863 by 70.28. 
 
 30. Multiply 2046 by .932. 
 
 31. Multiply .7253 by .0423. 
 
 32. Multiply 6.5431 by .402. ! 
 
 33. What is the product of .04 multiplied by .07 ? 
 
 34. What is the product of .005 by .009 ? 
 
 35. Multiply 7 and 5-hundredths by 6-thousandths. 
 
 DIVISION OF DECIMALS. 
 
 RULE FOR DIVISION OF DECIMALS. Divide as in 
 whole numbers ; and in the quotient, point off as many 
 figures for decimals, as the decimal places in the dividend 
 exceed those in the divisor; that is, make the decimal 
 places in the divisor and quotient counted together, equal 
 to the decimal places in the dividend. 
 
 If there be not figures enough in the quotient to point 
 off, prefix ciphers to supply the deficiency. 
 
 When there are more decimal places in the divisor, 
 than in the dividend, render the places equal, by annez- 
 ing ciphers to the dividend, before dividing. _ 
 
 After dividing all the figures in the dividend, if there 
 bea remainder, ciphers may be annexed to it, and the 
 division continued. The ciphers thus annexed, must be 
 counted with the decimal places of the dividend. 
 
186 WRITTEN ARITHMETIC. VI 
 
 36. Divide 64.395 by 40.5. Divide 5.8674 by 127. 
 40.5)64.395(1.59 127)5.8674(.0462 
 
 405 508 
 
 2389 787 
 
 2025 Be 2 
 3645 | 254 
 3645 254 
 
 37. Divide 2033.1 by .324. Divide 1383.2 by 60.8. 
 .324)2033.100(6275 60.8)1383.2(22.75 
 ae 
 
 1944 16 
 891 | 1672 
 648, 1216 
 2430 , 4560 
 2268 | 4256 
 
 1620 » 3040 
 1620 3040 
 
 38. How many times is .27 contained in 1.224? 
 | The sign of addition, or 
 .27)1.224(4.533-+ more, here shows, that the true 
 
 108 quotient is more than the pre- 
 1445) ceding figures express. We : 
 135 might continually annex ci- | 
 
 phers to this remainder, and 
 
 20 carry on the division, but we 
 bata should never arrive at a com- 
 90 plete quotient. For the pur- 
 Si poses of business, it is seldom 
 oy necessary to extend the quo- 
 
 tient below thousandths. 
 39. How many times is 1.23 contained in 3021.741 ? 
 40. How many times is 1243.4 contained in 5.387148? 
 41. How many times is .204 contained in 77112? 
 42. How many times is 4.2 contained in 194.334? 
 43. How many times is 30.02 contained in 94.657 ? | 
 44. How many times is .44 contained in .1606? | 
 45. What is the quotient of 42.65 divided by 36? | 
 46. What is the quotient of .8 divided by 8? | | 
 
33, DECIMALS. 187 
 
 CHANGE OF COMMON FRACTIONS TO DECIMALS. 
 
 RULE. Annex ciphers to the numerator, and divide 
 it by the denominator: the quotient will be the decimal. 
 
 47.. Change 75 to a decimal. 
 
 By annexing four ciphers, we 
 12)70000 — obtain four decimal figures. We 
 .5833-- might, however, annex more ci- 
 phers, and carry the decimal lower. 
 48. Change 4 to a decimal. 
 49. Change the following fr actions to ther hip gis he 
 decimals. 3. a 3, 43 p+ 3: 
 50. Change 3% of a sar to a decimal; Hae is, find 
 how many cents and mills there are in { 2: of a dollar. 
 51. Change $487 to a decimal expression: 
 52. Change £31653 to a decimal expression. 
 
 When the lower denominations of a compound number 
 are to be reduced to the decimal of a higher denomina- 
 tion,— First reduce the given quantity to @ common 
 fraction, (as taught in Sec. 27 ,) then change the common 
 fraction to a decimal. 
 
 53. Reduce 7s. 6d. to the decimal of a £. 
 
 54. Reduce 15 shillings to the decimal of a £. 
 
 55. Reduce 6d. Sqr. to the decimal of a shilling. 
 
 56. Reduce 2s. 11d. 3qr. to the decimal of a £. 
 
 57. Reduce 1 farthing to the decimal of a shilling. 
 
 58. Reduce £18 Qs. 7d. to a decimal expression. 
 
 59. Reduce 14dwt. 18gr. to the decimal of an oz. Troy. 
 
 60. Reduce 4qt. Ipt. to the decimal of a bushel. 
 
 61. Reduce 3qt. Ipt. 2g]. to the decimal of a gallon. 
 
 62. Reduce 10r. 3yd. 2ft. to the decimal of a mile ? 
 
 63. Express 29yd. 2qr. 3na. of cloth pet oath & and 
 find its cost, at $’7.625 per yard. 
 
 To reduce the decimal of a higher denomination to its 
 value in whole numbers of lower denomination,— Multi- 
 ply the decimal by that number of the next lower denom- 
 ination which makes a unit of the higher, and the product 
 will be of the lower denomination. Proceed in like 
 manner with the decimal in each succeeding product. 
 
188 WRITTEN ARITHMETIC. Pian i, 
 
 64. Reduce .6526 of a £ to its value in shillings, &e. 
 
 6526 We multiply the decimal of a £ 
 . 20 by 20, to find the shillings, because, 
 13.0520 there are 20 times more shillings 
 12 than pounds in any sum, whether the 
 sum be a whole number or a decimal. 
 The same reasoning also applies, in 
 aa ra finding the pence, and the farthings. 
 2.4960 Answer, 13s. Od. 2qr.-+- 
 65. Reduce .4039 of a £ to its value in shillings, &c. 
 66. Reduce .857 of a shilling to pence and farthings. 
 67. Reduce .76 of a ton to cwt. qr. lb. &c. 
 68. In .2094 of a day, how many hours, minutes, &c.? 
 69. In .57 of an acre, how many roods, rods, &c.? 
 70. Reduce £15.2908 to its proper expression in 
 pounds, shillings, pence, and farthings. | 
 
 EXCHANGE OF CURRENCIES. 
 
 In New England, Virginia, Kentucky, and Tennessee, 
 
 4 of a dollar is called a shilling. 
 
 ° In New York and North Carolina, 3 of a dollar is 
 called a shilling. 
 
 In Pennsylvania, New Jersey, Delaware, and Mary- 
 land, + of a dollar is called a shilling. 
 
 In South Carolina and Georgia, 3 of a dollar is call- 
 
 ed a shilling. 
 
 71. How many cents and mills, that is, what decimal 
 of a dollar, na New-England shillmg? in 2 Mian ce 
 in 3 shillings? in 4 shillings? in 5 shillings ? 
 
 72. How many cents and mills ina New-York shil- 
 ling? in 2s.? inds.? in4s.? in 5ds.? in6s.? in7s.? 
 
 73. How many cents and mills in a Pennsylvania shil- 
 ling? in 2s.? in 3s.2? in 4s.? in 5s.? in 6s.? 
 
 74. How many’cents and mills in a Georgia shilling ? 
 in 2s.? in 3s.? in 4s.? 
 
 To change shillings, pence, and farthings to Federal 
 money,— Reduce the pence and farthings to the decimal 
 of a shilling, and multiply the whole sum by that frac- 
 tion of a dollar which 1s equal to one shilling. 
 
33. DECIMALS, 189 
 
 75. Change 14s. 6d. 3qr., of the currency of New- 
 England, to Federal money. 
 
 76. Change 12s. Sd. Iqr., of the currency of New- | 
 York, to Federal money. 
 
 77. Change 16s. 5d., of the currency of Pennsylva- 
 nia, to Federal money. 
 
 78. Change 18s. 8d. 2qr., of the currency © of Georgia, 
 to Federal money. 
 
 79. What is the value, in Federal money, of 8 New- 
 England shillings? 8 New-York shillings? 8 Penn- 
 sylvania shillings ? 8 Georgia shillings ? 
 
 PERCENTAGE AND INTEREST BY DECIMALS. 
 
 Percentage and Interest have already been explained 
 in pages 163, and 165. Since PER cENT. indicates hun- 
 dredihs, it is properly expressed in the first and second 
 decimal places, taken together. Thus, 6 per cent. is 
 -06; 12 per cent..is .12. A fraction of 1 per cent. is 
 expressed in decimals lower than hundredths. Thus, 
 5 per cent. is .005; 4-per cent. is .0025; 64 per cent. 
 is 065; 124 per cent. is .1275. 
 
 Multiplying by a decimal, produces such a part of the 
 multiplicand, as the decimal indicates. Therefore,— 
 
 To find the percentage on any sum,— Multiply the 
 sum by the decimal which denotes the rate per cent. 
 
 80. An auctioneer sold a bale of goods for $648:85, 
 on which he received a commission of 24 per cent. 
 What did his commission amount to ? 3 
 
 81. Suppose an insurance office to charge 12 per 
 cent. for a fire risk; what will it cost to insure a house, 
 which is valued at $4500? 
 
 82. Suppose the shares in a rail-road stock, to cost 
 originally $100 apiece; what is the value of 15 shares, 
 
 -. after the stock bas risen 124 per cent.? 
 
 83. A smith bought 75 tons of iron, at $95 per ton; 
 and for cash, obtained a discount [abatement] of 54 per 
 cent. How much did he pay ? 
 
 84. What is the amount of $85.62, at 6 per cent. 
 interest, for 3 years, 5 months, and 17 days: ? 
 
190 WRITTEN ARITHMETIC. VI. 
 
 85. What is the interest of $225, from September 
 21, 1831, to February 7, 1834, at 6 per cent.? 
 
 A part of a debt is sometimes paid, and the remainder 
 still continues at interest. In such case, it 1s usual to 
 compute the interest to the time of the partial payment, 
 subtract the payment from the amount, and consider the 
 remainder as the future principal. 
 
 86. A note of $58.25 has been standing 18 months 
 at 6 per cent.; but, 5 months after the date, $14 eae 
 paid and endorsed. What is the amount of the note ? 
 
 87. A note of $120, at 6 per cent., is dated, July 5, 
 1830; and on the back of it is this endorsement, fine 
 24, 1831, Received, $56. What amount is required to 
 pay this note, on the 21st. of March, 1833? 
 
 88. Suppose a note of $432.50, at 6 per cent., to be 
 dated January 10, 1832, on the back of which, is this 
 endorsement,— October 7, 1833, Received, 200; — 
 what is the amount of this note, May 9, 1834? 
 
 Interest is sometimes computed for each year sepa- 
 rately, and the amount of each year is taken for the 
 principal of the succeeding year. The interest thus 
 obtained, is called Compound interest. 
 
 89. Suppose a note of $1528, to be dated August 
 12, 1827, and to remain at 6 per cent. compound inter- 
 est, until April 9, 1835; what is the amount? 
 
 90. A man owing $2534, due in 4 years, without in- 
 terest, wishes to advance payment. What difference 
 will it make to him, whether 6 per cent. interest for the 
 time be allowed as discount, or, the discount be com- 
 puted according to the just rule, in page 168? 
 
 THE END OF PART SECOND. . 
 
\ 
 
 N 
 
 \@ PS Ga 
 INDEX. 
 ORAL ARITHMETIC. 
 
 3 din 
 
 NiniegBtni.s .<.vsqack.s nos vadu Wp Actin sie ps cabal Ke vata’ %: 
 PROTUORE Rs. \.. sadans cous oes cgale.s cube mine t a i Sey ald Se BN 
 Subtraction J sy alate isc a stan Sees date hs oa ath Oo ee Oem 
 Correspondent Exs. in Addition and a apniaak en eee a 4 i 
 PARIGRHCAION ois dea odinn to ricity her 'eer hee BSS paeae a0 5 : 
 Division Ge Ma. daly WN. hela tole PEG SEE» ce ee : ae eee | 
 Correspondent Exs. in ‘Maltiplication and Division ... peeve 34 
 Commected Operations s:.4s sss. ses22as +a +c oe’ hs duties 0S 
 PD POCMONS: Cate i wiab's Su, cblle's!a don Sas sien dsb eccaeh ase slestan dae 44 
 Relationsfof Nupabers 4... 00 vee os cee Lene. oR 48 
 Fractions and Relations, .: 9.5502 ¥s...550 08.0% ‘6 Ries ee pes 
 Notation OPM paghioate sok icp v's yioin'ein th hi;siajuls oa gield ones 74 | 
 WRITTEN ARITHMETIC : 
 mNutneration foo 00. cUshee cies foes As ese uaee oes Se a 
 AAAItION es. east Saas va bo Gah sede nade sae pone Onaee 93 | 
 Subtraction) +... Mt PP LPM sea teeta cass eeeea san ste SE 
 ° pone ee Phy res BEC BT Pisies ipo Mies UL | 
 ‘» Abbreviati BR inSNFultp ition i mess Fo ae -, O03 
 ‘Atal poe. nee % : : Leeds igs vn eats ae el no fae «. 108 
 * Abbreviations in Diision ............0.c0eeeeee a0. ae, 0G 
 Mederal Money ics ss oes v's hae Obie dagine VaiekV omice s wes -. 124 
 /Gompound Nunabersiveg. 1. 705s ee eee bb ks % Sa ¢ 130 
 FYACtONS) ins us get es ib ae Cav wicks tat abe see alsa agent 147 
 Melations of Numberaiisn i we ee ees 4 viele vecayleapes 149 | 
 Fractionsand Relagions sy o.40¢)'s de ciias «sis ove days hele neha 155 
 Change of Whole Numbers to Fractions ............... .. 156 
 Change of Fractions to Whole Numbers ........ Sans tawt 157 
 Percentage .....ssceccceccsccceccececeserccsereecesverees 163 
 REEVES oo .. oases 6 Rte ee DS ERS valg » suri amet Gk 
 CONE iho REG cua Ke VRS wah Potion os Paha hth di diee Tas ... 168 
 Change of the Terms of Fractions .......... Pr uoees wees 169) 
 Reduction of Fractions to Lower Terms..............-.+ 169 
 Combeund Fractions \.)03 7. ea cossbanetcdebeesedscenecend a 
 Common Denominators ...........-. i dled awn old guid aule trae 173 
 Diecamal TACOS h : abate beha Casideieids os sividinws oohigules 1 
 Change of Common Fractions to Decimals .............. 18 
 _ Exchange of Currencies ...... Pig arrestee Sheets ase Le 
 Percentage and Interest by PICCUDBIA. cin vvaabapne hen ves a 
 
 \ 1 4 
 r 
 
 1 
 
Pag ' Boston, Mey 24, 16 
 
 _né'sulyctibers, In ructere ithe public schools in the city of Boston, avail 
 chemselyés of the earli t gpportunity to express their approbation of Part Sec- 
 “ond, of the North Ameritan Arithmetic, by Frederick Emerson. The oral 
 es written exercises being arranged in corresponding chapters and sections, 
 
 may be taught separately or connectedly : this they deem a very great excel- 
 ence. ‘The principles are laid down in progressive order, and are illustrated 
 Ye the inductive method. Fractional Arithmetic is skilfully explained—and 
 will no longer puzzle the learner. ‘The work is evidently written with great care 
 nd ability. The undersigned, therefore, confidently hope its merits will be as 
 Ily and freely appreciated by the enlightened friends of education, as were 
 
 f Part First. Fe MACKINTOSH, Jr. CHA ESFOX, ASANDREWS, 
 ALKER, ABEL. WHEELER, SAMUEI) BARRETT, 
 CONA NT ROG) PARKER, JAMES ©ROBINSON, 
 DAVID ‘BTOWER, re) TIS@PIERCE, BARNUM®FIELD, 
 
 f 
 
 4 : 
 {Conclusion of 4 letter to ‘the Publishers.] The NortTH AMERICAN 
 RITHMETIC is nov a mere repetition of other publications on the subject. It 
 
 Js an original —original in its plan,—original in its execution,—origi- 
 nal j j arran tat and questions,—original in every thing, excepting the 
 \e halt induce ethod. I think the author has been peculiarly happy in 
 the Sagi and pave of his treatise,—in the arrangement of oral and written 
 
 exercises in cqresponding chapters,—and, especially, i in his mode of treating 
 Neral am acquainted with no school-book that I could with more con- 
 idenc® reow Aen to the notice of teachers, and others interested in the sub-. 
 i of elementary education, ,  E. BAILEY... 4% 
 ' [Principal of the Young Ladies’ High School, Boston.) 
 
 ee ey New York, Oct. 6, 1832. z 
 I. consid eLBthorsan *s North “American secouuglaiorg First *and @art ” 
 » Secendjwi a the Key,*as perfectiagSchookbookifa Savy ver @xamined.® 
 Nabo on this brafghwof dnstructionghas#soav ell@and@ruly gt Picaghaubjcc 
 ‘one is'plainjand . and the chaaclieee: which distmguish it as a school- 
 book, are those that should prevail in every introduétory work offered for the 
 
 ¥ 
 
 use o of youth. SAMUEL W. SETON. 
 : . [ Visiter for the Public School Society, New York.) 
 ~ ue ier, Philadelphia, Jan. 13, 1883. 
 
 ‘ [Conclusion of a letter to the Author.) It gives me great satisfaction 
 to observe the gradual introduction into our treatises for children, of the 
 “method of induction, so effectual in its developement of their intellectual re- 
 sources, arid so superior to the dogmatic method formerly in use. Until aaa 
 
 _ \in a few years, the plan which you have adopted was unknown aang 
 
 ‘4 lit 36 not pérhapssemar kable, that a bigotedgattachment to things faaatha famil ioe and ceed 
 
 “a want of power and inclination to investigate the philosophical prineip ie 
 
 which the,mind is to be cultivated, should “have conspired to renin Sling 
 
 ) tional’ sygteu slow in its advances. The addition which you have ma 
 Wthe, classqgf works above mentioned, will, I trust, be eminently useful im = 
 \ dering the study of Arithmetic, both easy and profitable. Your combi nation 
 ‘of intel lectual and written exercises must commend itself to every teack 
 
 \ Yours truly, WALTER R. JOHN rhs . 
 
 a [Principal of the Philadelphia Hig naa 
 
 , See notices on the cover. Want of room prevents the insertion of any 
 ~ other testimonials; among which, are, letters from the following sources 
 
  Spwarp TURNER, Professor of Math. and Nat. Phil. in eens, Coleg. 5 
 JOHN ADAMS, Principal of the Phillips Academy, Andover. ay ; ee ; 
 GEORGE W. KEELY, Professor of Mathematics in Waterville cate ani ‘ 
 AL CASWELL, Professor of Mathematics in Brown University. tee 
 ‘AMOS EATON, Senior Professor in the Rensselaer School. Pi i 
 JAMES HAMILTON, Prof. Math., Nat. Phil. § Astronomy in Nakane a 
 
TSO AA et as RRS ad Ria A ox cote" an nee BY» Feapopeal mae 3 a3] 
 
 ‘ H AMERICA Co 
 EMERSON’S SEC NARITHMETIC: 
 
 | ” 
 To Mr. Frederick Emerson. Si: 
 
 and Second Parts of your North Amc... 3 07 12 01 
 
 highly pleased with the plan of the work, afaune. 7104559 
 
 its execution thus far. It unites simplicity with fulness, ‘any 
 
 will thus be sare to interest fhe beginner, whilst it farnishes, af 
 
 “Se same time, an ample guide to the more advanced pupil. 
 
 aespectfall, and truly yours, ALBERT HOPKINS. 
 [Professor of Mathematics.and Natural Philosophy 
 tw Williamstown College.) 
 
 Unicn College, Schenectady, Feb. &th, 1833. 
 Mr. F. Emerson. Sir,—! have received the First and Second 
 Parts of the North American Arithmetic, - od examined then ~ 
 with pleasure. The relationg.of numbers are happily tlastratec 
 by the relations of sensible objects. ‘This renders the work 
 more ent rtaining and instrueitve, espeefilly at that. ~e to which 
 arithmetic is better adapsedtham anany of those st:dies which 
 for wani of a system like this are too often mtroduced. Here 
 the student will acquire not merely rules to «-uide his hand, but 
 principles to enlighten his un:’erstanding. He is not furnished 
 with. a mere mill for grindin, aumbers into a certain result 
 under cover. «Wishing yor. continued success, : 
 I am, si, respeetfully, your ob’t ser’t, B. F. JOSLIN. 
 [Professor of Mathematics and Natural Philosophy 
 in Union College.) .. eo 
 = 
 
 Burlington, 15th Febrnary, 1833. 
 [Conclusion of a Letter to the Author.) I should think it hardly 
 possible that a child could be faithfully conducted through these 
 two works, [First and Second Parts’, without-being vastly better 
 acquainted with the subject than children formerly were. Being'™ 
 judiciously compelled in rome.measure to invent their own rules, 
 they-can scarcely fail of beine:: le to assign a proper reason for 
 the process, as -vell as to yr: / ct it fox “uture ase: Indeed, fF 
 i Me , vue particiuar in waich, for the use ef vera 
 a8, they could be improved. Yours respectfulle@eevgay 
 , ; JAMES DEAN. 
 [Pref ssor of Mathematics and Natural Philosophy, 
 in the University of Vermeont.] 
 
 Athens, C ic, Febrnuiy the Ist, 1833. 
 Mr. Emerson. Dear Sir—I have carefully and attentively 
 examined the ‘First and Seeotd Parts’’ of ‘‘ The North Amers 
 ican Avithmetic ;” and can say, with pleasure, that the work 
 meets my cordial approbaticr: You have, perhaps, rendere? 
 Arithmetiy as highly interestine to the youthful :nind)as thi 
 nature of the subject. will admit. Your method of: illustrating 
 the fundamental pfinciples of ¥rections is clear, forcible, an 
 peculiarly happy in its adaptation to the minds of youth. 
 Iam, yours, &c. WILLIAM WALE. 
 [Professor of Mathematics, in the Ohio University.] 
 
 VERSiTy =a 
 513 OF ILL) 
 Non? INPT.21639 Nols URBANA