REVISED EDITION 
 
 THE 
 
 AMERICAN 
 
 DESIGNED 
 
 FOR THE USE OF SCHOOLS AND ACADEMIES; 
 
 CONTAINING 
 
 AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS, WITH 
 CONCISE AND ORIGINAL METHODS OF SOLUTION, WHICH 
 SIMPLIFY MANY OF THE MOST IMPORTANT 
 RULES IN WRITTEN ARITHMETIC. 
 
 BY 
 
 JOHN F. STODDARD, A.M., 
 
 AUTHOR OF “THE JUVENILE MENTAL,” “THE PRACTICAL,” AND “THE 
 PHILOSOPHICAL ARITHMETIC,” “THE ELEMENTARY,” AND 
 “THE UNIVERSITY ALGEBRA,” “KEYS,” ETC. 
 
 NEW YORK: 
 
 S H ELDON 4Sc COMPANY. 
 
 » CINCINNATI : APPLEGATE A CO. CLEVELAND: INGHAM & BRAGG. 
 
 DETROIT: PUTNAM, SMITH A CO. CHICAGO: VV. B. KEEN. 
 
 AND ALL BOOKSELLERS. 
 
 * 
 
NORMAL MATHEMATICAL SERIES. 
 
 
 STODDARD’S JUVENILE MENTAL ARITHMETIC. 
 
 Price 13 cents. 
 
 STODDARD’S AMERICAN INTELLECTUAL ARITH¬ 
 METIC. Price 20 cents. 
 
 STODDARD’S PRACTICAL ARITHMETIC. Price 40cts. 
 
 STODDARD’S KEY TO THE INTELLECTUAL AND 
 PRACTICAL ARITHMETICS. Price 50 cents. 
 
 SCHUYLER’S HIGHER ARITHMETIC. Price 75 cents. 
 
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 BRA. Price 75 cents. 
 
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 STODDARD & HENKLE’S UNIVERSITY ALGEBRA 
 
 Price $1 50. 
 
 Entered, according to an Act of Congress, in the year 1849, by 
 JOHN F. STODDARD 
 
 In the Clerk’s Office of the District Court for the Southern District of 
 
 New York. 
 
 Entered, according to an Act of Congress, in the year 1860, by 
 SHELDON & COMPANY, 
 
 In the Clerk’s Office of the District Court for the Southern District of 
 
 New York. 
 
 Electrotyped by Smith & McDougal, No. 84 Beekman-st., N. Y. 
 
K Hohn 
 
 t 
 
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 \ 
 
 PREFACE. 
 
 Neither a desire of pecuniary gain, nor a wish to 
 appear as an author, prompted the presentation of 
 this work to the public. Having felt the necessity 
 of a more extended and systematic Intellectual 
 Arithmetic for the younger, as well as more ad¬ 
 vanced pupils, I prepared and used in manuscript, 
 in my own school, for a number of years, such a 
 series of questions as I deemed best adapted to 
 the purpose. After observing the superior mental 
 training derived from their use, and the ease with 
 which pupils thus trained comprehended the more 
 advanced branches of mathematics, I venture to 
 submit them to the public in the following pages, 
 hoping that they may prove as useful to other 
 schools as they have to my own. 
 
 The rule which I have observed in its preparation 
 is to tell but one thing at a time, and that in its 
 proper place. 
 
 It would be laborious to point out all the particu¬ 
 lars in which this work differs from others of a sim¬ 
 ilar character; I shall, therefore, give only a brief 
 exposition of its general plan, leaving the other 
 differences (which, doubtlessly, will be considered 
 of importance) to be found by those who study the 
 book. 
 
 Chapters First, Second , Third , and Fourth , treat 
 respectively of Addition, Subtraction, Multiplica- 
 
iv 
 
 PREPACE. 
 
 tion, and Division of simple numbers; each of 
 which is rendered familiar by an extensive col¬ 
 lection of practical questions. The last Lesson in 
 Chapter /Second , consists of questions,, which com¬ 
 bine Addition and Subtraction; the last Lesson in 
 Chapter Third , of questions combining Addition, 
 Subtraction, and Multiplication. Thus, an intimate 
 connection between Lessons and even Chapters is 
 kept up through the entire work, with the excep¬ 
 tion of Chapter Fifth, , which contains a few of the 
 most important tables of SV eights and Measures ; 
 each of which is illustrated with appropriate ques¬ 
 tions. 
 
 Chapter Sixth is devoted to the subject of 
 Fractions, and contains twenty lessons, hi which 
 many oiiginal combinations and concise solutions 
 occur. 
 
 Chapter Seventh consists of practical and in¬ 
 tricate questions of various kinds, which require for 
 their solution a thorough knowledge of the preceding 
 Chapters. This Chapter (which, it is believed, is 
 not contained in any similar work,) when thoroughly 
 understood, will be of incalculable benefit to those 
 who are studying, or intend to study Algebra. 
 
 Chapter Eighth includes Interest, Discount, and 
 per cent, of every description, in their various 
 modifications. The method of treating these sub¬ 
 jects is original; and renders the rules in Written 
 Ai ithmetics, under these heads (which are often 
 incomprehensible to pupils) perfectly intelligible by 
 reducing the whole to one continued train of rea¬ 
 soning. 
 
PEEFACE. 
 
 V 
 
 It is believed that this Chapter, if thoroughly 
 taught, can not fail to quicken, strengthen and de¬ 
 velop the reasoning powers ; bringing into exercise, 
 as it does, nearly every principle taught in the 
 twenty lessons of Chapter Sixth , and also, the 
 greater part of Chapter Seventh , it must of neces¬ 
 sity cause the pupil to acquire the habit of syste¬ 
 matically classifying his knowledge, that he may, 
 at any time, be able to call to his aid, such portions 
 of it as will assist him in illustrating or demonstra¬ 
 ting the 
 
 The mind is composed of a variety of faculties 
 which require for their development appropriate 
 and constant exercise. That Intellectual Arithme¬ 
 tic, when properly taught, is better calculated, than 
 any other study, to invigorate and develop these 
 faculties, to produce accurate and close discrimi¬ 
 nation, and, to enable the pupil to acquire a knowl¬ 
 edge of the Higher Mathematics with greater ease, 
 can not for a moment admit of a doubt. 
 
 J. F. STODDARD. 
 
 New York, August 1, 1860. 
 
 subject under consideration. 
 
SUGGESTIONS TO TEACHERS. 
 
 For the benefit of those whose experience is limited, I 
 make the following suggestions in regard to the most ap¬ 
 proved methods of teaching this important branch of study: 
 
 The lesson should be assigned previous to recitation, to 
 afford the pupils an opportunity for its examination: the 
 use of the book, by pupils, during class exercise, should be 
 entirely prohibited. 
 
 To concentrate the attention of the whole class, pupils 
 should be called upon promiscuously to solve the problems, 
 and not in rotation, as is too frequently the case. 
 
 No question should be read more than once, if done 
 slowly and distinctly; the student should be required to re¬ 
 produce and solve it without interruption, unless it be to 
 make a necessary criticism or correction. 
 
 Care should be taken that the pupils (during recitation) 
 assume an erect position, and that the language they use 
 be rigidly accurate as to construction and articulation. 
 
 Pupils, if not carefully guarded, will, in their hurried 
 solutions, pronounce many of the most simple words in¬ 
 correctly. For instance, the words: and , of, if for , with, 
 what, which, where, when , costs, quarts, how many, etc., are 
 not unfrequently pronounced : an, off, ef fur, withe, wat, 
 witch, ware, wen, coss, quais, hominy, etc. 
 
 By careful attention to all of these particulars, a lesson in 
 Intellectual Arithmetic is a practical lesson in elocution, 
 grammar, rhetoric, and logic, as well as a lesson in the 
 science of numbers. 
 
 It is respectfully suggested that the particular forms given 
 for the solution of questions be adhered to, unless better 
 ones should be devised by the teacher, J. F. S. 
 
ARITHMETIC. 
 
 CHAPTER I. 
 
 LESSON I. 
 
 1. 
 
 2 
 
 and 
 
 1 
 
 arc 
 
 liow 
 
 many ? 
 
 Solution. 
 
 —Two and one are 3. 
 
 
 
 2. 
 
 2 
 
 and 
 
 2 
 
 are 
 
 how 
 
 many ? 
 
 3. 
 
 2 
 
 and 
 
 3 
 
 are 
 
 how 
 
 many ? 
 
 4. 
 
 2 
 
 and 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 5. 
 
 2 
 
 and 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 6. 
 
 2 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 V. 
 
 .2 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 8. 
 
 2 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 9. 
 
 2 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 10. 
 
 3 
 
 and 
 
 2 
 
 are 
 
 how 
 
 many ? 
 
 11. 
 
 3 
 
 and 
 
 3 
 
 are 
 
 how 
 
 many ? 
 
 12. 
 
 3 
 
 and 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 13. 
 
 3 
 
 and 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 14. 
 
 3 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 15. 
 
 3 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 16. 
 
 3 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 17. 
 
 3 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 18. 
 
 4 
 
 and 
 
 3 
 
 are 
 
 how 
 
 many ? 
 
 19. 
 
 4 
 
 and 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 20. 
 
 4 
 
 and 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 21. 
 
 4 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 22. 
 
 4 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 23. 
 
 4 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 24. 
 
 4 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many 2 
 
8 
 
 ADDITION. 
 
 25. James killed 2 birds and John 1 ; bow many 
 did both kill ? 
 
 Solution.— If James killed 2 birds and John 1, they together 
 killed 2 birds and 1 bird, which are 3 birds. 
 
 26. I gave 2 cents to Henry, and 2 cents to Harvey ; 
 how many cents did both receive ? 
 
 21. Hiram had 2 cents, and his brother gave him 
 
 3 more; how many had he then ? 
 
 28. George gave me 2 apples, and Mary gave me 
 
 4 ; how many did both give me ? 
 
 29. A man had 2 cows, and he purchased 5 more ; 
 how many cows had he then ? 
 
 30. John’s father gave him 2 oranges, and his 
 mother gave him 6 ; how many did he receive in all ? 
 
 31. Philo bought 2 peaches, and his brother gave 
 him 1 ; how many had he then ? 
 
 32. Philip gave me 2 plums, and Myron gave mo 
 8 ; how many did they together give me ? 
 
 33. A farmer had 2 horses, and bought 9 more ; 
 how many had he then ? 
 
 34. William had 3 candies, and Moses gave him 2 
 more ; how many had he then l 
 
 35. John bought 3 apples, and I gave him 3; how 
 many had he then ? 
 
 36. Philip gave 3 cents for some nuts, and 4 cents 
 for some candies ; how many cents did he pay for both ? 
 
 3 1. I paid 3 cents for some wafers, and 5 cents for 
 a stamp; how much did both cost me ? 
 
 38. A merchant bought 3 barrels of sugar and 6 
 barrels of molasses ; how many barrels did he buy ? 
 
 39. Ralph is 3 years old, and Edward is 1 ; what is 
 the sum of their ages ? 
 
 40. A lemon cost 3 cents, and a pine-apple cost 8; 
 how much did both cost ? 
 
 41. James solved 3 questions in arithmetic, and 
 Oliver 9 ; how many did both solve ? 
 
 
ADDITION. 
 
 9 
 
 42. If it take 4 yards of cloth for a coat, and 3 for 
 a pair of j>ants, how many yards will it take for both ? 
 
 43. Samuel bought 4 marbles, and found 4 ; how 
 many had he then ? 
 
 44. Isaac bought 4 sheets of paper, and I gave him 
 5 ; how many had be then ? 
 
 45. A mau bought a peck of apples for 4 cents, and 
 a peck of pears for 6 cents; how much did the apples 
 and pears together cost ? 
 
 46. If Mary has 4 books, and her father should give 
 her 7, how many books would she then have ? 
 
 47. William has 4 marbles in his hand, and 8 in his 
 pocket; how many has he in all ? 
 
 48. Charles walked 4 miles, and rode 9 ; how far 
 did he go ? 
 
 49. In a certain class there are 5 boys, and 4 girls ; 
 how many pupils are there in the class ? 
 
 
 
 
 LESSON 
 
 II. 
 
 
 1. 
 
 5 
 
 and 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 2. 
 
 5 
 
 and 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 3. 
 
 5 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 4. 
 
 5 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 5. 
 
 5 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 6. 
 
 5 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 7 . 
 
 6 
 
 and 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 8. 
 
 6 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 9. 
 
 6 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 10. 
 
 6 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 11. 
 
 6 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 12. 
 
 7 
 
 and 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 13. 
 
 7 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 14. 
 
 7 
 
 and 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 15. 
 
 7 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 
10 
 
 addition. 
 
 16. 
 
 8 
 
 and 
 
 7 
 
 are 
 
 how 
 
 17. 
 
 8 
 
 and 
 
 8 
 
 are 
 
 how 
 
 18. 
 
 8 
 
 and 
 
 9 
 
 are 
 
 how 
 
 19. 
 
 8 
 
 and 
 
 5 
 
 are 
 
 how 
 
 20. 
 
 9 
 
 and 
 
 6 
 
 are 
 
 how 
 
 21. 
 
 9 
 
 and 
 
 8 
 
 are 
 
 how 
 
 22. 
 
 9 
 
 and 
 
 9 
 
 are 
 
 how 
 
 23. 
 
 9 
 
 and 
 
 10 
 
 are 
 
 how 
 
 24. 
 
 9 
 
 and 
 
 7 
 
 are 
 
 how 
 
 25. 
 
 9 
 
 and 
 
 11 
 
 are 
 
 how 
 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 
 . **.”• IXXIS answered o questions correctly and 4 
 incorrectly; how many questions was she asked ? 
 
 21. A beggar met two boys ; one gave him 5 cents, 
 and the other gave him G cents; how many cents did 
 they together give him ? 
 
 28. A man bought a hat for 5 dollars, and a pair of 
 boots for 6 dollars; how much was the cost of both ? 
 
 29. There are 9 boys on one bench, and 8 on an¬ 
 other ; how many are there on both ? 
 
 30. Maria gave her teacher 5 pinks and 7 roses* 
 how many flowers did she give him ? 
 
 31. Tlariy caught 5 squirrels, and Henry cauo-ht 8 * 
 how many did both catch ? 
 
 32. If we learn 5 pages this week, and 9 next; how 
 many will we learn in the two weeks ? 
 
 33. Frank sold a melon for 6 cents, and an orange 
 lor 5 cents; how many cents did he receive for both ? 
 
 34. John bought 6 whips, and Joseph gave him 6 * 
 how many had he then ? 
 
 35. George had 6 chestnuts, and Richard gave him 
 7 ; how many had he then ? 
 
 36. Henry bought 6 candies, and Sarah bought 8 * 
 how many were bought by both ? 
 
 37. Rebecca has G oranges, and Catharine has 9 * 
 how many oranges have both ? 
 
 38. A boy bought 7 apples, and his father gave 
 him 6 ; how many had he then ? 
 
ADDITION. 
 
 11 
 
 39. Minerva bought 7 yards of ribbon, and her mother 
 gave her 7 ; how many yards did she then have ? 
 
 40. There were 7 boys sitting on one bench, and 8 
 on another ; how many were there on both ? 
 
 41. There were 7 boys at play, and 9 other boys 
 joined them ; how many were there in all ? 
 
 42. If I have 8 cents in one hand, and 7 cents in the 
 other, how many have I in both ? 
 
 43. If Mary has 8 peaches, and Margaret has 9, 
 how many have both ? 
 
 44. Sally gave 9 cents for some thread, and 7 cents 
 for some needles ; how much did the needles and thread 
 cost her ? 
 
 45. Charles has 9 marbles, and Albert has 5 ; how 
 many marbles have Charles and Albert ? 
 
 * 46. 9 birds were in a tree, and 6 were on the ground; 
 
 how many were there in all ? 
 
 47. Sarah gave 9 cents for some cinnamon, and 
 7 cents for some raisins; how many cents did these 
 cost her ? 
 
 48. George shot 9 pigeons, and James shot 8 ; how 
 many did both shoot? 
 
 49. Russel caught 7 fish, and Robert caught 5 ; how 
 many did both catch ? 
 
 50. In one field there are 8 horses, and in another 
 there are 9 ; how many are there in both ? 
 
 - - 
 
 LESSON III. 
 
 1. How many are 10 and 2? 10 and 3 ? 10 and 4 ? 
 
 10 and 5 ? 10 and 6 ? 10 and 7 ? 10 and 9 ? 10 and 8? 
 10 and 10 ? 
 
 2. How many are 2 and 2 ? 2 and 12 ? 2 and 22 ? 
 2 and 32 ? 2 and 42 ? 2 and 52 ? 2 and 62 ? 2 and 
 72 ? 2 and 82 ? 2 and 92 ? 
 
12 
 
 ADDITION. 
 
 3. How many are 3 and 3 ? 3 and 13 ? 3 and 23 ? 
 3 and 33 ? 3 and 43 ? 3 and 53 ? 3 and 63 ? 3 and *73? 
 
 3 and 83 ? 3 and 93 ? 96 and 4 ? 
 
 4. How many are 4 and 4 ? 4 and 14 ? 4 and 24 ? 
 
 4 and 34 ? 4 and 44 ? 4 and 54 ? 4 and 64 ? 4 and 74 ? 
 
 4 and 84 ? 4 and 94 ? 98 and 2 ? 
 
 5. How many are 5 and 5 ? 5 and 15 ? 5 and 25 ? 
 
 5 and 35 ? 5 and 45 ? 5 and 55 ? 5 and 65 ? 5 and 75 ? 
 
 5 and 85 ? 5 and 95 ? 
 
 6. How many are 6 and 6 ? 6 and 16 ? 6 and 26? 
 
 6 and 36 ? 6 and 46 ? 6 and 56 ? 6 and 66 ? 6 and 76 ? 
 
 6 and 86 ? 6 and 96 ? 
 
 7. How many are 7 and 7 ? 7 and 17 ? 7 and 27 ? 
 
 7 and 37 ? 7 and 47 ? 7 and 57 ? 7 and 67 ? 7 and 77 ? 
 
 7 and 87 ? 7 and 97 ? 
 
 8. How many are 8 and 8 ? 8 and 18 ? 8 and 28 ? 
 
 8 and 38 ? 8 and 48 ? 8 and 58 ? 8 and 68 ? 8 and 78 ? 
 
 8 and 88 ? 8 and 98 ? 
 
 9. How many are 9 and 9 ? 9 and 19 ? 9 and 29 ? 
 
 9 and 39 ? 9 and 49 ? 9 and 59 ? 9 and 69 ? 9 and 79 ? 
 
 9 and 89 ? 9 and 99 ? 
 
 10. How many are 10 and 11 ? 10 and 21 ? 10 and 
 
 31 ? 10 and 41 ? 10 and 51 ? 10 and 61 ? 10 and 71 ? 
 
 10 and 81 ? 10 and 91 ? 
 
 11. How many are 10 and 12 ? 10 and 22 ? 10 and 
 
 32 ? 10 and 42 ? 10 and 52 ? 10 and 62 ? 10 and 72 ? 
 10 and 82 ? 10 and 92 ? 
 
 12. How many are 10 and 4? 10 and 14? 10 and 
 24 ? 10 and 34? 10 and 44 ? 10 and 54 ? 10 and 64 ? 
 
 10 and 74 ? 10 and 84 ? 10 and 94 ? 
 
 13. How many are 11 and 3 ? 11 and 13 ? 11 and 
 
 23 ? 11 and 33 ? 11 and 43 ? 11 and 53 ? 11 and 63 ? 
 
 11 and 73 ? 11 and 83 ? 11 and 93 ? 
 
 14. How many are 11 and 4 ? 11 and 14 ? 11 and 
 
 24 ? 11 and 34 ? 11 and 44 ? 11 and 54 ? 11 and 64 ? 
 11 and 74 ? 11 and 84 ? 11 and 94 ? 
 
 15. How many are 10 and 5 ? 10 and 15 ? 10 and 
 
ADDITION. 
 
 13 
 
 35 ? 10 and 45 ? 10 and 55 ? 10 and 65 ? 10 and 75 f 
 
 10 and 85 ? 10 and 95 ? 10 and 25 ? 
 
 16. How many are 11 and 5 ? 11 and 15 ? 11 and 
 25 ? 11 and 35 ? 11 and 45 ? 11 and 55 ? 11 and 65 ? 
 
 11 and 75 ? 11 and 85 ? 11 and 95 ? 
 
 17. How many are 3 and 8 ? 3 and 18 ? 3 and 28 ? 
 
 3 and 38 ? 3 and 48 ? 3 and 58 ? 3 and 68 ? 3 and 78?; 
 3 and 88 ? 3 and 98 ? 
 
 18. How many are 8 and 4 ? 8 and 14 ? 8 and 24 ? 
 
 8 and 34 ? 8 and 44 ? 8 and 54 ? 8 and 64 ? 8 and 74 ? 
 
 8 and 84 ? 8 and 94 ? 
 
 19. How many are 7 and 5 ? 7 and 17 ? 7 and 27 ? 
 
 7 and 37 ? 7 and 47 ? 7 and 57 ? 7 and 67 ? 7 and 77 ? 
 
 7 and 87 ? 7 and 97 ? 
 
 20. How many are 8 and 6 ? 8 and 16 ? 8 and 26 ? 
 
 8 and 36 ? 8 and 46 ? 8 and 56 ? 8 and 66 ? 8 and 
 76 ? 8 and 86 ? 8 and 96 ? 
 
 LESSON IV, 
 
 1 . 
 
 8 
 
 and 
 
 9 
 
 arc 
 
 how 
 
 many? 
 
 2. 
 
 11 
 
 and 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 3. 
 
 10 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 4. 
 
 7 
 
 and 
 
 14 
 
 are 
 
 how 
 
 many ? 
 
 5. 
 
 6 
 
 and 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 6. 
 
 9 
 
 and 
 
 15 
 
 are 
 
 how 
 
 many ? 
 
 7. 
 
 11 
 
 #nd 
 
 18 
 
 are 
 
 how 
 
 many ? 
 
 8. 
 
 15 
 
 and 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 9. 
 
 14 
 
 and 
 
 13 
 
 are 
 
 how 
 
 many ? 
 
 10. 
 
 16 
 
 and 
 
 14 
 
 are 
 
 how 
 
 many ? 
 
 11. 
 
 21 
 
 and 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 12. 
 
 24 
 
 and 
 
 13 
 
 are 
 
 how 
 
 many ? 
 
 13. 
 
 25 
 
 and 
 
 15 
 
 are 
 
 how 
 
 many % 
 
 14. 
 
 27 
 
 and 
 
 13 
 
 are 
 
 how 
 
 many ? 
 
 15. 
 
 23 
 
 and 
 
 17 %re 
 
 2 
 
 how 
 
 many ? 
 
14 
 
 ADDITION. 
 
 16. 
 
 29 
 
 and 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 17. 
 
 30 
 
 and 
 
 20 
 
 are 
 
 how 
 
 many ? 
 
 18. 
 
 34 
 
 and 
 
 15 
 
 are 
 
 how 
 
 many ? 
 
 19. 
 
 32 
 
 and 
 
 18 
 
 are 
 
 how 
 
 many ? 
 
 Remark.—T he symbol = is the sign of equality , and when 
 placed between two quantities it denotes that they are equal to 
 each other. Thus 10 cents = 1 dime, is read, 10 cents equal 
 1 dime. 
 
 The symbol +, is called plus; and denotes that the quanti¬ 
 ties between which it is placed, are to be added. Thus, 4 + 2 
 = 6 , shows that 4 and 2 are to be added: and is read, four 
 plus two equals 6. 
 
 20. 33 + 44 are how many ? 
 
 21. 35 + 15 are how many ? 
 
 22. 36 + 12 are how many? 
 
 23. 40 + 36 are how many? 
 
 24. 40 + 29 are how many? 
 
 25. 44 + 20 are how many ? 
 
 26. 48 + 32 are how many? 
 
 27. 45 + 35 are how many? 
 
 28. 4 + 8 + 6 are how many? 
 
 29. 8 + 2 + 7 are how many ? 
 
 30. 10 + 7 + 3 are how many ? 
 
 31. 12 + 10 + 9 are how many ? 
 
 32. 15 +12 + 6 are how many ? 
 
 33. 18 + 4 + 10 are how many ? 
 
 34. 24 + 16 + 12 are how many? 
 
 35. 22 + 33 + 11 are how many? 
 
 36. 15 + 16 + 2 are how many? 
 
 37. 28 + 12 + 15 are how many ? 
 
 38. 46 + 24 + 19 are how many ? 
 
 39. 12 + 8 + 6 + 4 are how many ? 
 
 40. 24 + 10 + 6 + 12 are how many ? 
 
 41. 22 + 32 + 6 —10 are how many? 
 
 42. 37 + 23 + 15 are how many ? 
 
 43. 64 + 26 + 12 — 8 are how many ? 
 
ADDITION. 
 
 15 
 
 LESSON V. 
 
 1. Three hoys, James, Joseph, and Jacob gave some 
 money to a beggar; James gave him 6, Joseph 8, and 
 Jacob 10 cents ; how many cents did they give him ? 
 
 2. Gave 8 cents to John, 4 cents to Morgan, and 2 
 cents to Samuel; how many cents did all receive ? 
 
 3. Henry has 3 marbles, Harvey has 10, and Harry 
 has 7; how many marbles have all ? 
 
 4. Gave 7 nuts to one boy, 6 to another, and 7 to 
 another; how many nuts did the three boys receive ? 
 
 5. Bought a basket of strawberries for 7 cents, a 
 basket of cherries for 4 cents, and a basket of plums 
 for 8 cents; how many cents did all cost ? 
 
 6. Lydia has 9 pinks, Mary 10, and Ann 7 ; how 
 many pinks have they all ? 
 
 7. Bought a knife for 14 cents, and a ball for 12 
 cents; how much did both cost ? 
 
 8. Gave 18 cents for an arithmetic, 2 for a pencil, 
 and 10 for a slate; how much did all cost? 
 
 9. James had 12 cents, and his mother gave him 
 13 more ; how many had he then ? 
 
 10. Robert shot 9 birds, Richard shot 11, and James 
 shot 12 ; how many did they shoot ? 
 
 11. A boy bought a pound of butter for 14 ceftts, a 
 pound of meat for 8 cents, and a bunch of lettuce for 
 7 cents; how many cents did these articles cost ? 
 
 12. Bought a pound of raisins for 10 cents, a pound 
 of candies for 12 cents, and a pound of cinnamon for 
 15 cents; how much was the whole cost? 
 
 13. John had 20 marbles, Matthew 9, and Morgan 
 12 ; how many had they in all ? 
 
 14. James bought a pigeon for 9 cents, a robin for 
 10 cents, and a squirrel for 12 cents; how much did 
 all cost him ? 
 
 15. A lady bought some pins for 15 cents, some 
 
16 
 
 ADDITION, 
 
 thread for 10 cents, and some lace for 18 cents; how 
 many cents did all these articles cost her ? 
 
 16. A gentleman bought a hat for 6 dollars, a vest 
 for 5 dollars, and a coat for 20 dollars; how many 
 dollars did he pay for them all ? 
 
 17. A man bought a watch for 40 dollars, a gold 
 chain for 15 dollars, and a gold pen for 5 dollars; 
 how much did he pay for these three articles? 
 
 18. Jackson gave 25 cents to his sister, and 23 to 
 his mother ; how many cents did he give away ? 
 
 19. Bought a barrel of flour for 7 dollars, a barrel 
 of pork for 12 dollars, and a barrel of fish for 11 dol¬ 
 lars ; how much was the whole cost ? 
 
 20. Bought a horse for 60 dollars, a cow for 20 
 dollars, and a colt for 25 dollars ; how much did all cost ? 
 
 21. If your father should give you 12 cents, your 
 mother 14 cents, and your sister 4 cents; how many 
 cents would you then have ? 
 
 22. A boy spent 11 cents for confectionery, 9 cents 
 for a ball, and 5 cents for a top ; how many cents did 
 he spend for all ? 
 
 23. A man bought some butter for 57 dollars, and 
 some molasses for 23 dollars ; how many dollars did 
 both cost ? 
 
 24. A boy traveled 17 miles one day, and 23 the 
 next y how far did he travel in the two days ? 
 
 25. A lady bought a hat for 7 dollars, a dress for 
 9 dollars, and a gold watch for 60 dollars; how many 
 dollars did all cost? 
 
 26. A mechanic sold a wagon for 57 dollars, and a 
 sleigh for 43 dollars ; how much did he receive for 
 both ? 
 
 27. A boy saw 24 pigeons on one tree, and 36 on 
 another; how many did he see in all? 
 
 28. In a certain recitation 21 questions were an¬ 
 swered correctly, and 9 incorrectly ; how many ques¬ 
 tions were asked during the recitation ? 
 
ADDITION. 
 
 17 
 
 29. Gave 87 dollars for a cliaise, 2 dollars for a whip, 
 and 11 dollars for a buffalo robe ; how much was given 
 for all ? 
 
 30. If a horse is worth 60 dollars, and a sleigh 75 
 dollars, what is the value of both ? 
 
 31. Matthew is 15 years old, Morgan is 7, and 
 Martin is 10 ; what is the sum of their ages ? 
 
 32. A man bought a load of hay for 7 dollars, a 
 load of rye for 36 dollars, and a load of wheat for 57 
 dollars ; how much was the whole cost ? 
 
 33. A man is 48 years old, and his wife is 32 years 
 old; what is the sum of their ages? 
 
 34. A farmer bought a horse for 60 dollars, and a 
 yoke of oxen for 75 dollars; how much did the horse 
 and oxen together cost him ? 
 
 35. John gave 11 candies to his brother, 9 to his 
 sister, and kept 12 himself; how many candies had he 
 at first ? 
 
 36. Simeon hoed 12 rows of corn, Simon 15, James 
 13, and John 11 ; how many rows did they together 
 hoe? 
 
 37. A merchant sold 30 barrels of flour one week, 
 37 the next week, and 33 the following week ; how 
 many barrels did he sell during the three weeks ? 
 
 38. A merchant sold a barrel of sugar for 5 dollars, 
 a barrel of rum for 15 dollars, and a hogshead of mo¬ 
 lasses for 23 dollars; how much did he receive for all 
 these articles ? 
 
 39. A man bought a firkin of butter for 9 dollars, 
 a keg of molasses for 7 dollars, a box of cheese for 4 
 dollars, and a box of raisins for 5 dollars ; how much 
 was the entire cost ? 
 
 40. A lady bought a silk dress for 18 dollars, a muff 
 for 12 dollars, a shawl for 17 dollars, and a pair of 
 gloves for 1 dollar; the entire cost is required. 
 
 2 * 
 
18 
 
 SUBTRACTION. 
 
 CHAPTER II. 
 
 LESSON I. 
 
 1. If I have 3 apples, and give 1 of them to Rich¬ 
 ard, how many shall I have left ? 
 
 Solution. —If I have 3 apples and give 1 to Richard, I will 
 have remaining the difference between 3 and 1 which is 2 apples. 
 
 2. William had 4 chestnuts, and gave 1 to his broth¬ 
 er ; how many had he left ? 
 
 3. Martha had 5 books, and on her way to school, 
 lost one of them ; how many had she left ? 
 
 4. Cornelia had 6 apples and gave 1 to her brother ; 
 how many had she left ? 
 
 5. Rachel had 10 pins and lost 1 of them; how 
 many had she left ? 
 
 6. Martha had 12 pears and give 2 to Elizabeth ; 
 how many had she left ? 
 
 7. If you had 5 candies and should give 2 of them 
 away, how many would you have left ? 
 
 8. James had 6 apples and gave 2 away ; how many 
 had he remaining? 
 
 9. Cornelia says she learned 12 letters yesterday 
 and has forgotten 3 of them; how many does she re¬ 
 member ? 
 
 10. James had 10 marbles and lost 3; how many 
 had he left ? 
 
 11. Mary found 9 roses on her bush, and picked off 
 4 of them ; how many remained on the bush ? 
 
 12 . 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 4 
 
 5 
 7 
 9 
 9 
 
 less 
 
 less 
 
 less 
 
 less 
 
 less 
 
 2 ? 
 
 3? 
 
 3? 
 
 4? 
 
 3? 
 
 : 
 
SUBTRACTION. 
 
 19 
 
 / 
 
 17. How many 
 
 18. How many 
 
 19. How many 
 
 20. How many 
 
 21. How many 
 
 22. How many 
 
 23. How many 
 
 24. How many 
 
 25. How many 
 
 26. How many 
 
 27- How many 
 
 28. How many 
 
 29. How many 
 
 30. How many 
 
 are 
 
 9 
 
 less 
 
 7? 
 
 are 
 
 9 
 
 less 
 
 5? 
 
 are 
 
 11 
 
 less 
 
 4? 
 
 are 
 
 10 
 
 less 
 
 4? 
 
 are 
 
 11 
 
 less 
 
 5? 
 
 are 
 
 14 
 
 less 
 
 4? 
 
 are 
 
 8 
 
 less 
 
 5? 
 
 are 
 
 13 
 
 less 
 
 3? 
 
 are 
 
 14 
 
 less 
 
 5? 
 
 are 
 
 17 
 
 less 
 
 7? 
 
 are 
 
 15 
 
 less 
 
 5? 
 
 are 
 
 13 
 
 less 
 
 10 ? 
 
 are 
 
 23 
 
 less 
 
 3? 
 
 are 
 
 27 
 
 less 
 
 7? 
 
 Remark. —The symbol —, is called minus ; and denotes that 
 the quantity on the right of it is to be taken from the quantity 
 on the left. Thus, 6 — 4 — 2 shows that 4 is to be subtracted 
 from 6 ;—and is read, 6 minus 4 equal 2. 
 
 31. 
 
 8 — 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 32. 
 
 9 — 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 33. 
 
 lO- 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 34. 
 
 ll— 
 
 8 
 
 are 
 
 1)0 w 
 
 many ? 
 
 35. 
 
 12- 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 36. 
 
 13 — 
 
 •8 
 
 are 
 
 how 
 
 many ? 
 
 37. 
 
 14 — 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 38. 
 
 18 — 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 39. 
 
 22 — 
 
 12 
 
 arc 
 
 how 
 
 many ? 
 
 40. 
 
 24- 
 
 14 
 
 are 
 
 how 
 
 many? 
 
 41. 
 
 12 — 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 42. 
 
 28- 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 43. 
 
 20 — 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 44. 
 
 20- 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 45. 
 
 20 — 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 46. 
 
 20- 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 47. 
 
 20 — 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 48. 
 
 20 — 
 
 15 
 
 are 
 
 how 
 
 many ? 
 
 49, 
 
 24- 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
20 
 
 SUBTE 
 
 ACT 
 
 ION. 
 
 50, 
 
 25 — 10 + 5 
 
 are 
 
 how 
 
 51. 
 
 26 — 10 + 4 
 
 are 
 
 how 
 
 52. 
 
 28-10 + 2 
 
 are 
 
 how 
 
 53. 
 
 27-10 + 5 
 
 are 
 
 how 
 
 54. 
 
 29 — 10 + 6 
 
 are 
 
 how 
 
 55. 
 
 32-10 + 8 
 
 are 
 
 how 
 
 56. 
 
 34-10 + 7 
 
 are 
 
 how 
 
 57. 
 
 36 — 10 + 8 
 
 are 
 
 how 
 
 58. 
 
 35 — 10 + 4 
 
 are 
 
 how 
 
 59. 
 
 37 — 10 + 7 
 
 are 
 
 how 
 
 60. 
 
 38 — 10 + 8 
 
 are 
 
 how 
 
 61. 
 
 39 — 10 + 9 
 
 are 
 
 how 
 
 62. 
 
 47 — 10 + 6 
 
 are 
 
 how 
 
 63. 
 
 40 — 12 + 9 
 
 are 
 
 how 
 
 64. 
 
 42 — 20 + 7 
 
 are 
 
 how 
 
 65. 
 
 45 — 20 + 5 
 
 are 
 
 how 
 
 66. 
 
 46 — 20 + 6 
 
 are 
 
 how 
 
 67. 
 
 47 — 20 + 8 
 
 are 
 
 how 
 
 68. 
 
 47-37 + 4 
 
 are 
 
 how 
 
 69. 
 
 49 — 19 + 9 
 
 are 
 
 how 
 
 70. 
 
 71. 
 
 52 — 22 + 10 
 
 lire 
 
 how 
 
 54-34 + 11 
 
 are 
 
 how 
 
 72. 
 
 56 — 46 + 12 
 
 are 
 
 how 
 
 73. 
 
 57-27 + 14 
 
 are 
 
 how 
 
 74. 
 
 58 — 48 + 9 
 
 are 
 
 how 
 
 75. 
 
 62 — 30 + 10 
 
 are 
 
 how 
 
 76. 
 
 65 — 40 + 15 
 
 are 
 
 how 
 
 77. 
 
 68 — 48 + 16 
 
 are 
 
 how 
 
 78. 
 
 74 — 34 + 15 
 
 are 
 
 how 
 
 79. Gave 
 
 7 cents for a s 
 
 .pool of thr< 
 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many tJ 
 many ? 
 many ? 
 many ? 
 many ? 
 many? 
 many ? 
 
 the lemon ? 
 
 80. Paid 18 cents for a pound of butter, and 8 cents 
 for a pound of meat; how much more was paid for the 
 butter than for the meat ? 
 
 81. James bought 18 candies, and gave John 7 of 
 them ; how many had he left ? 
 
SUBTRACTION. 
 
 21 
 
 82. Sold a quantity of wool for 27 dollars, and re¬ 
 ceived in payment a barrel of flour worth 5 dollars; 
 how many dollars remain due? 
 
 83. James has 27 marbles, and John has 17 ; how 
 many more has James than John? 
 
 84. Harry is 15 years old, and Ilenry is 9 years 
 old; how many years older is Harry than Henry ? 
 
 85. A teacher being ashed how many pupils he had, 
 answered that he usually had 37 but at present he had 
 only 27 ; how many were absent? 
 
 86. A man purchased a watch for 37 dollars, but 
 found he had only 24 dollars with him; how much 
 must he borrow to pay the balance ? 
 
 87. Mr. A has 94 sheep, and B has 44 ; how many 
 more sheep has A than B ? 
 
 88. Morgan gave 23 cents for some cake, and 14 
 cents for some cinnamon; how much more did the 
 cake cost than the cinnamon ? 
 
 89. Michael had 29 cents and lost 14 ; how many 
 had he left ? 
 
 90. In a certain recitation 47 questions were asked, 
 and 9 of them were answered incorrectly ; how many 
 were correctly answered ? 
 
 91. A man sold 23 sheep from a flock consisting of 
 93 ; how many sheep remained? 
 
 92. Mr. B bought a horse for 35 dollars, and sold it 
 for 46 dollars ; how much did he gain ? 
 
 93. A cow was bought for 25 dollars and sold for 
 19 dollars; how much was the loss? 
 
 94. A merchant bought a quantity of goods for 95 
 dollars, but being damaged was obliged to sell them 
 for 80 dollars ; how much did he lose? / • ** 
 
 95. From a vessel containing 57 gallons, 27 gallons 
 leaked out; how much remained in it ? 
 
 96. A merchant bought a quantity of silk for 47 
 dollars, and sold it for 67 dollars; how much did he 
 gain by the bargain. 
 
 ■V (r 
 
22 ADDITION AND SUBTRACTION. 
 
 97. A butcher has 57 sheep, and 44 lambs; how 
 many more sheep has he than lambs? 
 
 98. Paid 97 dollars for a quantity of sugar, and 43 
 
 dollars for some molasses; how much more did the 
 sugar cost than the molasses ? * . 
 
 - 4 ♦♦»- 
 
 LESSON II. 
 
 CHAPTER FIRST COMBINED WITH THE PRECEDING LESSON. 
 
 1. A boy has 7 chestnuts in one hand, and 4 in the 
 other; how many more has he in one hand than in 
 the other; and how many in both ? 
 
 2. Bought a barrel of fish for 8 dollars, and some 
 quinces for 3 dollars; how much more did the fish 
 cost than the quinces ? What was the cost of both ? 
 
 3. Gave 15 dollars for a cow and 6 dollars for a 
 sheep; how much more was given for the cow than 
 for the sheep ? How much was given for both ? 
 
 4. Phineas gave 50 cents for a grammar, and 25 
 cents for an arithmetic ; how much was the cost of 
 both ? How much did one cost more than the other ? 
 
 5. Paid 15 dollars for a barrel of rum, and 6 dollars 
 for a barrel of flour ; how much was the cost of both ; 
 and how much more did the rum cost than the flour ? 
 
 6. Sold a firkin of butter for 10 dollars, a keg of 
 cheese for 5 dollars, and received in payment a barrel 
 of flour worth 6 dollars ; how much remains due ? 
 
 7. James gave 12 cents for oranges, 15 cents for 
 
 cake, and had 13 cents remaining; how much had he 
 at first ? ' / 
 
 8. Mary bought a comb for 10 cents, a spool of 
 thread for 12 cents, and a paper of needles for 8 cents ; 
 —she handed the clerk 37 cents; how much change 
 ought she to receive ? 
 
ADDITION AND SUBTRACTION. 23 
 
 9. A'man sold a cow for 20 dollars, a calf for 4 
 dollars, and a sheep for 3 dollars ; and in payment re¬ 
 ceived a wasron worth 17 dollars ;—how much remains 
 due? 
 
 10. A lady bought a ribbon for 24 cents, some tape 
 for 8 cents, and some thread for 12 cents,—she had only 
 60 cents ; how much remained after she paid for these 
 articles? /* 
 
 11. Stephen, at a game of marbles, won 4 and lost 
 6, and then had only 8 remaining; how many had he 
 at first ? 
 
 12. Sampson having 9 apples, gave 4 to his mother, 
 and 3 to his sister ;—for his generosity his father gave 
 him 13 more; how many had he then? * 
 
 13. A man bought some cloth for 12 dollars, and 
 sold it for 18 dollars ; how much was his gain ? 
 
 14. A farmer bought a horse for 63 dollars, and 
 exchanged it for a yoke of oxen,—these lie sold for 87 
 dollars ; how much did he gain by the operation ? 
 
 15. A man bought a yoke of oxen for 97 dollars, 
 their services amounted to 40 dollars, and their keep¬ 
 ing to 13 dollars,—he then sold them for 80 dollars ; 
 did he gain or lose, and how much ? 
 
 16. A box of raisins was bought for 3 dollars, a 
 firkin of butter for 15 dollars, and were both sold for 
 20 dollars ; how much was gained ? 
 
 17. A farmer sold a cow for 29 dollars, which was 
 5 dollars more than she cost; how much did she cost ? 
 
 18. A drover bought some sheep for 40 dollars, some 
 cattle for 130 dollars, and sold them all for 200 dol¬ 
 lars ; how much was his gain ? 
 
 19. A jeweler bought a watch for 20 dollars, a 
 chain for 10 dollars, a key for 2 dollars, and sold them 
 all for 42 dollars; how much did he gain by the bar¬ 
 gain ? 
 
 20. 24 + 12 + 9 are how many ? 
 
 21. 10 + 30 + 15 are how many ? 
 
24 ADDITION AND SUBTEACTION. 
 
 22. 14 +16 +11 are how many ? 
 
 23. 36 + 9 —12 are how many ? 
 
 24. 38 + 22 —15 are how many ? 
 
 25. 43 + 37 — 20 are how many? 
 
 26. 13 + 26 — 25 are how many ? 
 
 27. 44 — 22 + 10 —12 are how many? 
 
 28. 27 + 23 — 20 + 2 are how many? 
 
 29. 15 + 25 — 30 + 15 are how many? ) 
 
 30. 20 + 40 — 30 + 10 are how many? 
 
 31. A boy bought a ball for 6 cents; for how much 
 must he sell it to gain 4 cents ? 
 
 32. A merchant bought a hogshead of molasses for 
 47 dollars, and paid 3 dollars for cartage ; for how 
 much must he sell it to gain 12 dollars ? 
 
 33. A grocer bought a hogshead of sugar for 
 30 dollars; for what must he sell it to gain 18 dol¬ 
 lars ? 
 
 34. A drover bought sheep as follows: of one man 
 he bought 24, of another 8, and of another 22 : he 
 then sold 20 of them ; how many remained unsold ? 
 
 35. A watch cost 40 dollars ; how must it be sold 
 to gain 13 dollars ? 
 
 36. Four boys bought a mellon ; one gave 3 cents, 
 another 4, another 8, and the other 6; how much did 
 they pay for the melon? 
 
 37. Mary bought 16 candies at one shop, and 13 at 
 another,—on her way home she ate 11 of them; how 
 many had she left ? 
 
 38. Matthew had 9 nuts, Mary gave him 10 more, 
 and John gave him enough to make his number 39 ; 
 how many did John give him ? 
 
 39. A farmer had 25 sheep in one field and 15 in 
 another,—he then bought enough more to make his 
 number 56 ; how many did he buy ? 
 
 40. John has 34 marbles, and Albert 25 ; how many 
 have they both ; and how many more has John than 
 Albert ? 
 
MULTIPLICATION. 
 
 25 
 
 CHAPTER III. 
 
 
 
 
 LESSON I. 
 
 
 1. 
 
 Two 
 
 times 
 
 1 
 
 are 
 
 how 
 
 many ? 
 
 2. 
 
 Two 
 
 times 
 
 2 
 
 are 
 
 how 
 
 many ? 
 
 3. 
 
 Two 
 
 times 
 
 3 
 
 are 
 
 how 
 
 many ? 
 
 4. 
 
 Two 
 
 times 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 5. 
 
 Two 
 
 times 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 6. 
 
 Two 
 
 times 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 7. 
 
 Two 
 
 times 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 8. 
 
 Two 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 9. 
 
 Two 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 10. 
 
 Two 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 11. 
 
 Two 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 12. 
 
 Two 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 13. What will 2 oranges cost, at 3 cents a piece? 
 
 Solution.—I f 1 orange cost 3 cents, 2 oranges will cost two 
 times 3 cents; which are 6 cents. 
 
 14. What will 2 peaches cost, at 2 cents a piece ? 
 
 15. What will 2 apples cost, at 3 cents a piece? 
 
 16. What will 2 pine-apples cost, at 8 cents a piece ? 
 
 17. What will 2 pounds of meat cost, at 5 cents a 
 pound ? 
 
 18. What will 2 pounds of cinnamon cost, at 11 cents 
 a pound? 
 
 19. What will 2 pounds of raisins cost, at 12 cents 
 a pound ? 
 
 20. What will 2 citrons cost, at 10 cents a piece? 
 
 21. What will 2 quarts of cherries cost, at 9 cents 
 a quart ? 
 
 22. What will 2 lemons cost, at 4 cents a piece? 
 
 23. Three times 2 are how many ? 
 
 24. Three times 3 are how many? 
 
 25. Three times 4 are how many ? 
 
 3 
 
26 
 
 MULTIPLICATION. 
 
 26. Three 
 
 times 
 
 5 
 
 are 
 
 how 
 
 many? 
 
 27. Three 
 
 times 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 28. Three 
 
 times 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 29. Three 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 30. Three 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 31. Three 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 32. Three 
 
 times 
 
 11 
 
 are 
 
 how 
 
 masy ? 
 
 33. Three 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 J 
 
 34. Four 
 
 times 
 
 3 
 
 are 
 
 how 
 
 many? 
 
 35. Four 
 
 times 
 
 4 
 
 are 
 
 how 
 
 many ? 
 
 36. Four 
 
 times 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 37. Four 
 
 times 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 38. Four 
 
 times 
 
 7 
 
 arc 
 
 how 
 
 many ? 
 
 39. Four 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 40. Four 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 41. Four 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 42. Four 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 43. Four 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 44. What will 3 quarts of cherries cost, at 6 cents a 
 quart ? 
 
 45. What will 3 lead pencils cost, at 5 cents a piece ? 
 
 46. What will 3 quarts of milk cost, at 4 cents a 
 quart ? 
 
 47. What will 3 yards of ribbon cost, at 7 cents a yd.? 
 
 48. What will 4 quarts of chestnuts cost, at 6 cents 
 a quart ? 
 
 49. What will 4 yards of edging cost, at 5 cents a 
 yard ? 
 
 50. What will 3 ounces of snuff cost, at 8 cents an 
 ounce ? 
 
 51. What will 4 ounces of cinnamon cost, at 7 cents 
 an ounce? 
 
 52. What will 3 pounds of cheese cost, at 10 cents 
 a pound ? 
 
 53. What will 4 sheets of wadding cost, at 8 cents 
 a sheet? 
 
 54. What will 3 yards of calico cost, at 11 cents a 
 yard ? 
 
MULTIPLICATION. 
 
 27 
 
 55. What will 4 skeins of silk cost, at 9 cts. a skein? 
 
 56. What will 3 yards of ribbon cost, at 12 cents a 
 yard ? 
 
 57. What will 4 pounds of starch cost, at 12 cents 
 a pound ? 
 
 58. What will 4 candlesticks cost, at 1 lets, a piece ? 
 
 59. What will 4 tops cost, at 10 cents a piece ? 
 
 60. What will 5 apples cost, at 4 cents a piece ? 
 
 61. 
 
 Five 
 
 times 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 62. 
 
 Five 
 
 times 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 63. 
 
 Five 
 
 times 
 
 9 
 
 are- 
 
 how 
 
 many ? 
 
 64. 
 
 Five 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 65. 
 
 Five 
 
 times 
 
 5 
 
 are 
 
 how 
 
 many ? 
 
 66. 
 
 Five 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 67. 
 
 Five 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 68. 
 
 Five 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many? 
 
 69. 
 
 Six 
 
 times 
 
 6 
 
 are 
 
 how 
 
 many ? 
 
 70. 
 
 Six 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 71. 
 
 Six 
 
 times 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 72. 
 
 Six 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 73. 
 
 Six 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 74. 
 
 Six 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 75. 
 
 Six 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 76. Seven times 6 are how many ? 
 
 77. Seven times 8 are how many? 
 
 78. Seven times 7 are how many? 
 
 79. Seven times 10 are how many? 
 
 80. Seven * times 9 are how many? 
 
 81. Seven times 12 are how many? 
 
 82. Seven times 11 are how many? 
 
 83. What will 5 barrels of flour cost, at 6 dollars a 
 barrel ? 
 
 84. What will 5 bushels of potatoes cost, at 5 dimes 
 a bushel ? 
 
 85. What will 6 primers cost, at 6 cents a piece? 
 
 86. What will 5 barrels of fish cost, at 7 dollars a 
 barrel ? 
 
28 
 
 MULTIPLICATION. 
 
 
 
 
 87. What will 6 pounds of mutton cost, at 7 cents 
 a pound ? 
 
 88. What will 5 barrels of sugar cost, at 12 dollars 
 a barrel ? 
 
 89. What will 6 pounds of sturgeon cost, at 10 cents 
 a pound ? 
 
 90. What will 6 pounds of almonds cost, at 12 cents 
 a pound ? 
 
 91. What will 5 barrels of pork cost, at $10 a bbl. ? 
 
 92. What will 6 pounds of candles cost, at 9c. a lb. ? 
 
 93. What will 5 coats cost, at 9 dollars a piece ? 
 
 94. What will 6 handkerchiefs cost, at 11 cents a 
 piece ? 
 
 95. What will 6 inkstands cost, at 8 cents a piece? 
 
 96. What will 7 lamps cost, at 9 dimes a piece ? 
 
 97. What will 7 plows cost, at 8 dollars a piece ? 
 
 98. What will 7 boxes of caps cost, at 10c. a box? 
 
 99.. What will 7 quires of paper cost, at 12 cents a 
 
 quire ? 
 
 100. What will 7 letter-folders cost, at 11 cents a 
 piece ? 
 
 101. Eight 
 
 102. Eight 
 
 103. Nine 
 
 104. Eight 
 
 105. Nine 
 
 106. Eight 
 
 107. Nine 
 
 108. Eight 
 
 109. Nine 
 
 110. Eight 
 
 111. Nine 
 
 112. What will 9 bunches of roses cost, at 9 cents a 
 bunch ? 
 
 113. What will 8 pen-knives cost, at 12 cts. a piece? 
 
 114. What will 9 bunches of grapes cost, at 12 cents 
 a bunch ? 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 8 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 7 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 9 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 10 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 11 
 
 are 
 
 how 
 
 many ? 
 
 times 
 
 12 
 
 are 
 
 how 
 
 many ? 
 
 
 - 
 
 mu 
 
 
 
 HUH 
 
 
 
 jj,« f : .S y .' 
 
 •: J a ij. 
 
 " A ) t ;■ l * » V * J t " ■ t 
 
 . . 
 
 < \ ’ ■ * 
 
 ' i * >»• 
 
 \ i V * *• 
 
 Mo. 
 
 HU;,' 
 
 ' \ ‘ * ' • *; » 1 A V * • <’ ■ l . k > •• 
 
 V ,\M '• - : 
 
 ■ 1 V I, 1 '*' : • >■ 
 
 VvS.iK' 
 
 
 ' . V' ’ \ ' . 
 
 ■ M 
 
 ■ • 'v::l 
 
MULTIPLICATION. 29 
 
 115. What will 11 yards of calico cost, at 11 cents 
 a yard ? 
 
 116. What will 10 halls of cotton cost, at 12 cents 
 a ball ? 
 
 117. What will 11 pounds of ginger cost, at 12 cents 
 a pound ? 
 
 118. What will 10 blocks of tape cost, at 8 cents a 
 block ? 
 
 119. What will 12 yards of cloth cost, at 12 dimes 
 a yard ? 
 
 120. What will 13 pair of boots cost, at $4 a pair? 
 
 
 LESSON II. 
 
 CHAPTERS FIRST AND SECOND COMBINED WITH THE PRECEDING LESSON. 
 
 1. At 7 cents a piece, what will 9 pine-apples cost? 
 
 2. If the postage on 1 letter is 3 cents, what will be 
 the postage on 8 letters ? 
 
 3. If it require 8 yards of calico to make 1 dress, 
 how many yards will it require to make 7 dresses ? 
 
 4. If John obtain 2 credit-marks in 1 day, how many 
 will he have in 15 days ? 
 
 5. A man hired a horse to ride 12 miles, at the rate 
 of 5 cents a mile; how much must he pay ? 
 
 6. Margaret’s cloak contains 7 yards of merino, 
 worth 9 dimes a yard ; what is the value of her cloak ? 
 
 7. If a stage-coach go 9 miles in an hour, how far 
 will it go in 7 hours ? 
 
 8. At 2 dollars a week, how much will 20 weeks’ 
 board amount to ? 
 
 9. The fare by railroad from Albany to Boston is 
 5 dollars for 1 person ; how much will it be for a 
 family of 9 persons ? 
 
 3 * 
 
30 
 
 MULTIPLICATION. 
 
 10. Helen liad 8 rose bushes, and there were 7 roses 
 on each ; how many roses had she in all ? 
 
 11. At 3 dimes a gallon, what will 15 gallons of 
 molasses cost? 
 
 12. There are 10 rows of trees in an orchard, and 
 12 trees in each row; how many trees are there in the 
 orchard ? 
 
 13. A traveler meeting 13 beggars, gave to each of 
 them 3 dimes; how many dimes did he give to all of 
 them ? 
 
 14. A woman bought 11 yards of cloth and paid for 
 it with butter,—giving 9 pounds, for a yard ; how many 
 pounds of butter did it take' to pay for the cloth ? How 
 much did the cloth cost provided the butter was-worth 
 10 cents a pound ? 
 
 15. In a certain corn field there are 24 rows, and 
 30 hills in each row ; how many hills in the field ? 
 
 16. What will 40 steel pens cost, at 2 cents a 
 piece ? 
 
 17. What will 8 pair of snuffers cost, at 3 dimes a 
 pair ? 
 
 18. When 2 dimes are paid for 1 duck, what will be 
 the cost of 8 ducks ? of 10 ducks ? of 12 ducks ? 
 
 19. When hay is worth 8 dollars a ton, what is the 
 value of 2 tons ? of 4 tons ? of 3 tons ? of 7 tons ? of 
 5 tons ? of 10 tons ? of 12 tons ? of 14 tons? 
 
 20. At 2 dimes a piece, how many cents will 4 books 
 cost? 6 books? 10 books? 12 books? 11 books? 7 
 books? 16 books? 13 books? 14 books? 
 
 21. If 5 cents will buy 1 primer, what will be the 
 cost of 4 primers ? of 6 ? of 9 ? of 8 ? of 10 ? 
 
 22. 6 plates, at 5 dimes a piece, will cost how 
 much ? 
 
 23. At 5 dimes a piece, how much will 4 handker¬ 
 chiefs cost ? 6? 8? 10? 12? 14? 11? 16? 
 
 24. At 6 dimes a piece, how many cents will 2 geese 
 cost? 4? 5? 8? 10? 12? 9? 7? 
 
MULTIPLICATION. 
 
 31 
 
 25. At 12 cents a piece, how much will 3 candle¬ 
 sticks cost ? How much will 6? 5 ? 8? 9? 10? 7? 
 
 26. If I pay 5 cents for riding 1 mile, how much 
 must I pay for riding 7 miles? 8 miles? 9? 6 ? 10 ? 12 ? 
 
 27 . At 7 cents a yard, how much will 5 yards of 
 ribbon cost ? 6 yards ? 8 yards? 9 yards? 10 yards? 
 12 yards ? 
 
 28. If a tooth-brush cost 18 cents, how much will 4 
 cost ? 
 
 29. 9 turkeys will cost how much, at 8 dimes a piece ? 
 
 30. At 14 cents a quire, how much will 2 quires of 
 paper cost ? 3 quires ? 4 quires ? 5 quires ? 
 
 31. How much will 7 pictures cost, at 5 cents a 
 piece? at 6 cents a piece? at 8 cents a piece? at 10 
 cents a piece ? 
 
 32. How much will 8 knives cost at 6 dimes a piece ? 
 at 10 dimes a piece? 
 
 33. At 10 dimes a piece,how much will 4 caps cost* 
 5? 6? 8? 9? 12? 14? 17? 19? 21? 25? 
 
 34. At 40 cents a day, how much will 2 day’s work 
 amount to ? 5 days work ? 
 
 35. If one paper of candies cost 6 cents, how much 
 will 3 papers cost? 5 papers? 8 papers? 12 papers? 
 
 36. At 7 dollars a hundred, how much will 4 hun¬ 
 dred feet of cedar boards cost? 9 hundred feet? 10 
 hundred feet ? 
 
 37. If 1 bushel of wheat cost 60 cents, how much 
 will 6 bushels cost? 4 bushels? 5 bushels? 
 
 38. How much will 8 muffs cost at 5 dollars each? 
 
 39. How much will 19 lead pencils cost, at 5 cents 
 each ? 
 
 40. How much will 11 boxes of cheese cost, at 4 
 dollars a box ? at 5 dollars a box ? at 8 dollars a box ? 
 
 41. How much will 12 barrels of pork cost at 5 dol¬ 
 lars a barrel ? at 8 dollars ? at 9 dollars ? at 10 dollars ? 
 
 42. How much will 9 tons of hay cost, at 13 dol¬ 
 lars a ton ? 
 
32 
 
 ADDITION, SUBTRACTION, 
 
 43. James is 9 years old, and liis father is 4 times 
 as old as he; how old is his father ? 
 
 44. Jane’s frock contains 7 yards of silk, worth 8 
 dimes a yard ; what was the value of the silk ? Pro¬ 
 vided the making cost 2 dollars ; how much was the 
 
 • cost of her dress ? 
 
 45. If a barrel of flour will serve 12 men 8 days, 
 how long will it serve 1 man ? 
 
 46. If I earn 12 dollars in a month and spend 8, 
 how much shall I have at the end of 12 months ? 
 
 47. If I earn 12 dollars a month, and pay 25 cents 
 a week for washing, and 2 dollars a week for board, 
 how much will I have at the end of 40 weeks (10 
 months) ? 
 
 48. If I buy 9 tons of hay, at 12 dollars a ton, and 
 and sell 6 tons, at 15 dollars a ton, and the 3 remain¬ 
 ing tons, at 10 dollars a ton ; how much shall I gain 
 by the operation ? 
 
 49. Bought 11 yards of broadcloth, at 4 dollars 
 a yard, but, being damaged, I was obliged to lose 
 18 dollars by the sale of it; how much did I receive 
 for it ? 
 
 50. If I buy 12 barrels of pork, at 8 dollars a bar¬ 
 rel, and sell it all for 108 dollars, how much shall I 
 gain by so doing? J'2 
 
 51. A man bought a horse for 80 dollars, paid 2 
 dollars a week for his keeping, and received 4 dollars 
 a week for his work ;—at the expiration of 10 weeks 
 he sold him for 70 dollars; how much did he gain by 
 the operation ? 
 
 52. For how much must I sell 4 barrels of wheat 
 which cost me 8 dollars a barrel, to gain 8 dollars? 
 
 53. What is the cost of 9 cows, at 25 dollars 
 each ? 
 
 54. Provided a hunter should kill 5 pigeons and 
 wound 4 at every shot; how many would he kill and 
 wound respectively, by shooting 8 times? / 
 
AND MULTIPLICATION. 
 
 33 
 
 55. If a man travel 29 miles in a day, how many 
 miles will he travel in 6 clays ? 
 
 56. How much will 8 months’ wages amount to, at 
 18 dollars a month ? 
 
 57. If 10 men eat 18 pounds of butter in 1 week, 
 how long would it last 1 man ? 
 
 58. If 80 dollars will pay for 4 dinners for 20 men, 
 how many dinners would it buy for 1 man ? 
 
 59. Bought 3 yards of cloth for a coat, at 7 dollars 
 a yard, the buttons and cord cost 2 dollars, buckram 
 and wadding 1 dollar,—paid for making it 6 dollars; 
 for how much must I sell it to gain 5 dollars ? 
 
 60. If 17 men can do a piece of work in 9 days, 
 how many days would it take 1 man to perform the 
 same work ? 
 
 61. Two men start from the same place, and travel 
 in opposite directions;—one at the rate of 7 miles an 
 hour, the other, 9 miles an hour; how far apart will 
 they be in 2 hours ? 
 
 62. Two men start from the same place, and travel 
 the same way ;—one at the rate of 3 miles an hour, the 
 other, 8 miles an hour; how far apart will they be at 
 the end of 8 hours ? 
 
 63. Two men are 50 miles apart, and approach each 
 other 4 ;—one at the rate of 2 miles an hour, the other, 
 3 miles an hour ; how far apart will they be at the end 
 of 5 hours ? 
 
 64. If 1 orange is worth 4 apples, how many apples 
 must be given for 13 oranges ? 
 
 65. A man earned 80 cents a day, and paid 50 cents 
 a day for his board and washing; how much had he 
 left at the expiration of 6 days ? 
 
 66. Jane bought 4 yards of silk, at 2 dollars a yard, 
 
 3 shawls, at 10 dollars each, and some delaine for 10 
 dollars; she paid 5 ten-dollar bills ; how much ought 
 she to receive back ? 
 
 67. Mary bought 5 yards of silk, at 8 dimes a yard, 
 
34 ADDITION — MULTIPLICATION. 
 
 and 8 yards of linen, at 9 dimes a yard ; how many 
 yards did she buy, and how much did all cost? 
 
 68. In a certain school there are 12 girls, and 3 
 times as many boys, less 8; how many boys in the 
 school, and how many boys and girls together? 
 
 69. John has 7 books, and Mary has 4 times as 
 many, less 18 ; how many has Mary, and how many 
 have both ? 
 
 70. Albert has 9 marbles, Aaron 3 times as many, 
 less 7, and Amos has twice as many as both, less 
 8; how many has each, and how many have they 
 together ? 
 
 71. Perry worked for Elisha 4 days, at 6 dimes a 
 day ;—Elisha gave him 7 bushels of corn, at 3 dimes a 
 bushel; how much was then due Perry ? 
 
 72. A merchant bought 25 pounds of sugar for 125 
 cents, and sold 15 pounds of it, at 6 cents a pound, and 
 the remaining 10 pounds, at 4 cents a pound; how 
 much did he gain by so doing ? 
 
 73. If the interest on 1 dollar for a year is 6 cents, 
 how much is the interest on 13 dollars for the same 
 time ? 
 
 74. What will 27 pounds of beef cost, at 4 cents a 
 pound ? 
 
 75. When beef is 5 cents a pound, and pork 9 
 cents; how much more will 9 pounds of pork cost than 
 9 pounds of beef? 
 
 76. Mary bought 35 quarts of milk, and on her way 
 home she spilled 4 times 2 quarts, less 3 quarts ; how 
 many quarts had she remaining ? 
 
 77. Henry is 4 feet in height and John is 5 ; and 5 
 times the sum of their heights, considered as a num¬ 
 ber, is equal to their father’s age + 15 years. Re¬ 
 quired, the father’s age. 
 
 78. If an orange cost 2 cents, a lemon twice as 
 much, and a melon 4 times as much as the orange and 
 
DIVISION. 
 
 35 
 
 lemon together, less 14 cents, how much more will 3 
 melons cost than 3 oranges and 3 lemons ? 
 
 79. James has 9 walnuts, John twice as many 
 
 less 8, and Joseph twice as many as James and 
 John + 7 ; how many has each, and how many have 
 all ? 0 , 
 
 80. If an apple cost 2 cents, an orange three times 
 as much less 4 cents, and a # pine-apple three times as 
 much as the apple and orange + 5 cents, what will be 
 the cost of all three ? 
 
 -■»♦♦ ♦ «*»-- 
 
 / 
 
 1 . 
 
 Solution. 
 
 2 . 
 
 3. 
 
 4. 
 
 5. 
 
 6 . 
 
 7. 
 
 8 . 
 9. 
 
 10 . 
 
 11 . 
 
 12 . 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20 . 
 
 CHAPTER IY. 
 
 LESSON I. 
 
 8 are how many times 2 ? 
 
 8 are 4 times 2, [because 4 times 2 are 8.] 
 
 6 ■ 
 
 are 
 
 how 
 
 4 
 
 are 
 
 how 
 
 10 
 
 are 
 
 how 
 
 12 
 
 are 
 
 how 
 
 14 
 
 are 
 
 how 
 
 6 
 
 are 
 
 how 
 
 9 
 
 are 
 
 how 
 
 12 
 
 are 
 
 how 
 
 15 
 
 are 
 
 how 
 
 18 
 
 are 
 
 how 
 
 21 
 
 are 
 
 how 
 
 24 
 
 are 
 
 how 
 
 16 
 
 are 
 
 how 
 
 18 
 
 are 
 
 how 
 
 20 
 
 are 
 
 how 
 
 22 
 
 are 
 
 how 
 
 24 
 
 are 
 
 how 
 
 26 
 
 are 
 
 how 
 
 28 
 
 are 
 
 how 
 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 3 ? 
 many times 3 ? 
 many times 3 ? 
 many times 3 ? 
 many times 3 ? 
 many times 3 ? 
 many times 3 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 2 ? 
 many times 4 ? 
 
I' 
 
 36 DIVISION. 
 
 21. At 2 cents a piece, how many apples can you 
 buy for 4 cents ? 
 
 Solution. —If for 2 cents I can buy 1 apple, for 4 cents I can 
 buy as many apples as 2 is contained times in 4, which are 2. 
 
 Remark. —The following solution is preferred to the above, if 
 the pupils are acquainted with Fractions. 
 
 Solution. —If for 2 cents I can buy 1 apple for 1 cent I can 
 buy i of an apple; and for 4 cents, 4 times which are |, or 2 
 apples. 
 
 22. At 2 cents a piece, how many oranges can I buy 
 for 6 cents? 
 
 23. At 2 cents a piece, how many peaches can be 
 bought for 8-cents? 
 
 24. At 3 dimes a yard, how many yards of calico 
 can be bought for 12 dimes? 
 
 25. At 3 cents a piece, how many lemons can be 
 bought for 9 cents ? 
 
 26. At 2 cents a yard, how many yards of tape can 
 
 be bought for 10 cents? % 
 
 27. At 2 dimes a bushel, how many bushels of 
 apples may be had for 12 dimes? 
 
 28. How many pounds of ginger, at 2 dimes a 
 pound may be had for 14 dimes? 
 
 29. How many baskets of strawberries, at 3 cents 
 a basket can be had for 15 cents ? 
 
 30. For 16 dollars ; how many yards of cloth can 
 be had, at 2 dollars a yard ? 
 
 31. For 18 apples; how many oranges can be bought 
 at the rate of 2 apples for 1 orange ? 
 
 32. How many primers, at 2 cents a piece, can be 
 bought for 24 cents ? 
 
 33. How many barrels of flour, at 2 dollars a bar¬ 
 rel, can be bought for 20 dollars ? 
 
 34. For 22 dollars ; how many sheep may be bought, 
 at 2 dollars a piece? 
 
 35. How many melons may be had for 18 dimes, at 
 3 dimes a piece ? 
 
 
T3 
 
 DIVISION. 37 
 
 36. At 3 cents a piece, how many tops may be had 
 for 6 cents ? 
 
 37. If 1 peck of beans cost 3 dimes, how many 
 pecks can be bought for 21 dimes ? 
 
 38. At 3 cents a mile, how many miles can I ride 
 for 24 cents ? 
 
 39. How many bushels of rye, at 4 dimes a bushel, 
 may be bought for 12 dimes? 
 
 40. How many books, at 4 dimes each, can be 
 bought for 20 dimes ? 
 
 41. 8 are how many times 4 ? 
 
 42. 12 are how many times 4 ? 
 
 43. 16 are how many times 4 ? 
 
 44. 10 are how many times 5 ? 
 
 45. 15 are how many times 5 ? 
 
 46. 20 are how many times 5 ? 
 
 47. 28 are how many times 7 ? 
 
 48. 32 are how many times 4 ? 
 
 49. 30 are how many times 5 ? 
 
 50. 35 are how many times 5 ? 
 
 51. 36 are how many times 4 ? 
 
 52. 40 are how many times 5 ? 
 
 53. 44 are how many times 4 ? 
 
 54. 30 are how many times '6 ? 
 
 55. 48 contains 8 how many times ? 
 
 Solution. — 48 contains 8, 6 times [because 6 times 8 are 48.] 
 
 56. 24 contains 8 how many times? 4 ? 12 ? 3?, 
 
 57. 36 contains 9 how many times? 6? 3? 2? 
 
 58. 54 contains 2 how many times ? 3 ? 9 ? 
 
 59. 75 contains 3 how many times? 5 ? 15? | 
 
 60. 68 contains 2 how many times? 4? 1 
 
 61. At 5 dimes each, how many turkeys can be had 
 for 25 dimes ? 
 
 62. If the wages of 1 day is 4 dimes, what will be 
 the wages for 9 days ? 
 
 63. How many days will a man be required to work 
 for 12 dimes, if he receive 4- dimes a day ? 
 
 
38 
 
 DIVISION. 
 
 64. If a boy spends 5 cents a day, bow many days 
 will it take him to spend 15 cents ? 
 
 65. A boy bad 20 marbles, and divided them 
 equally among his 5 brothers; bow many did each 
 receive ? 
 
 66. A boy divided 28 cents equally among 4 poor 
 women ; bow many cents did each receive ? 
 
 67. A farmer gave 4 of bis laborers 32 bushels of 
 corn; bow many bushels did each receive? 
 
 68. If 5 quarts of molasses cost 30 cents, wliat will 
 1 quart cost ? 
 
 69. At 5 cents a yard, bow many yards of ribbon 
 may be bad for 35 cents ? bow many for 50 cents ? 
 
 70. IIow many pine-apples, at 8 cents each, can be 
 obtained for 40 cents ? for 56 cents ? 
 
 71. If a man travel 45 miles in 9 hours, bow many 
 miles does be travel in 1 hour ? 
 
 72. If a man travel 5 miles in an hour, bow many 
 hours will it take him to travel 40 miles ? 
 
 73. How many yards of cloth, at 4 dollars a yard, 
 can you buy for 32 dollars ? 
 
 74. In a certain orchard there are 48 trees standing 
 in. rows, and 6 trees in each row ; bow many rows are 
 there in the orchard ? 
 
 75. For 56 dollars, bow many barrels of pork can 
 be bought, at 8 dollars a barrel ? 
 
 76. If a man can travel 6 miles in an hour, bow 
 long will it take him to travel 42 miles ? 
 
 77. How many yards of cloth, at 4 dollars a yard, 
 can you buy for 36 dollars ? 
 
 78. A butcher gave 39 dollars for sheep, at the rate 
 of 3 dollars a head ; how many sheep did he buy ? 
 
 79. 45 dollars were given for 9 barrels of flour; 
 how much was it a barrel ? 
 
 80. How long would it take to travel 72 miles, at 
 the rate of 3 miles an hour ? 
 
 
DIVISION. 
 
 39 
 
 LESSON II. 
 
 1. 20 are how many times 2 ? 4 ? 10 ? 
 
 2. 22 are how many times 11 ? 
 
 3. 24 are how many times 3 ? 4 ? 2 ? 
 
 4. 25 are how many times 5 ? 
 
 5. 28 are how many times 2 ? 7 ? 
 
 6. 30 are how many times 2 ? 3 ? 5 ?' 
 
 7. 32 are how many times 2? 4? 16? 8? 
 
 8. 34 are how many times 17 ? 
 
 9. 40 are how many times 2? 4 ? 5 ? 8 ? 
 
 10. 44 are how many times 2 ? 11 ? 
 
 11. 46 are how many times 23 ? 
 
 12. 48 are how many times 2? 3? 4? 6? 
 
 13. 50 are how many times 2 ? 10 ? 
 
 14. 56 are how many times 2? 7 ? 
 
 15. 57 are how many times 3 ? 
 
 16. 60 are how many times.2 ? 3? 4? 5? 6? 
 
 17. 64 are how many-times 2? 4 ? 8? 
 
 18. 66 are how many times 2 ? 3 ? 6 ? 
 
 19. 68 are how many times 2 ? 4 ? 
 
 20. 70 are how many times 10? 2? 
 
 21. 72 are how many times 2 ? 4? 6 ? 8 ? 
 
 22. 5 are* how many times 2, and how many je^ 
 maining ? 
 
 Remark.—'W henever there is a 
 tioned simply as a remainder. 
 
 23. 7 are how many times 
 
 24. 17 are how many times 
 
 25. 18 arc how many times 
 
 26. 34 are how many times 
 
 27. 25 are how many times 
 
 28. 16 are how many times 
 
 29. 32 are how many times 
 
 30. 63 are how many times 
 
 31. 74 are how many times 
 
 remainder, it may be men- 
 
 2? 
 
 
 
 
 4? 
 
 2? 
 
 5? 
 
 
 6? 
 
 4 ? 
 
 2? 
 
 
 4? 
 
 6? 
 
 5? 
 
 2? 
 
 5? 
 
 4? 
 
 2? 
 
 3? 
 
 9? 
 
 4? 
 
 8? 
 
 7? 
 
 7? 
 
 5? 
 
 6? 
 
 
 9? 
 
 4? 
 
 5? 
 
 6? 
 
 2? 
 
 4? 
 
 6? 
 
 7? 
 
40 
 
 DIVISION. 
 
 32. 
 
 33. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 80 are how many times 2 ? 3 ? 4 ? 
 
 84 are how many times 2 ? 3 ? 4 ? 
 
 15 are how many times 4 ? 6 ? 7 ? 
 
 29 are how many times 2 ? 3 ? 4 ? 
 
 90 are how many times 2 ? 4 ? 6 ? 
 
 144 are how many times 2 ? 4 2 6 
 
 5? 6? 7? 8? 
 5? 6? 7 ? 8? 
 8 ? 
 
 5 ? 6? 7? 
 
 8? 9* 11 ? 
 
 ? 8 ? 12 ? 
 
 —_—» ♦• »•- - - 
 
 / 
 
 LESSON III. 
 
 1. At 2 cents each, how many lemons can you buy 
 for 14 cents? 
 
 Solution. —If 1 lemon cost 2 cents, for 14 cents I can buy 
 as many lemons as 2 is contained times in 14, which are 7. 
 
 Another Solution.—I f for 2 cents I can buy 1 lemon, for 1 
 cent I can buy 1 half of a lemon, and for 14 cents, 14 times 1 
 half, which are 14 halves, or 7 lemons. 
 
 2. How many boxes of cheese, at 4 dollars a box, 
 
 may be had for 12 dollars? 
 
 3. If one hundred pounds of hay cost 3 dollars, how 
 many hundred may be had for 15 dollars ? 
 
 4. If one barrel of flour support 20 persons one 
 week, how many persons will it support 4 weeks ? 
 
 5. If 1 man can ride 1 mile for 4 cents, how far 
 
 can 2 men ride for 80 cents ? 
 
 6. If 10 men accomplish a certain piece of work in 
 2 days, how long will it take 1 man to do the same ? 
 
 7. If 3 yards of cloth make one coat, how manj 
 
 coats will 18 yards make? 
 
 8. If I receive 12 dollars interest in one year, in 
 how many years will I receive 144 dollars interest ? 
 
 9. A man traveled 7 miles in 1 hour, at the same 
 rate, how long would it take him to travel 63 miles ? 
 
 10. If 1 cow cost 13 dollars, how many cows may 
 be had for 65 dollars ? 
 
 11. How many pens can you buy for 27 cents, if 1 
 pen cost 3 cents ? 
 
 
MULTIPLICATION AND DIVISION. 41 
 
 12. If 8 apples are worth 40 chestnuts, how many 
 chestnuts is 1 apple worth ? 
 
 13. How many cents is 1 lemon worth, if 12 lemons 
 are worth 48 cents ? 
 
 14. How much will 1 cord of wood cost, if 20 cords 
 cost 40 dollars ? 
 
 15. If 1 pound of beef cost 7 cents, how much will 
 19 pounds cost ? 
 
 16. For 147 cents, how many pounds of sugar can 
 be bought, at 7 cents a pound ? 
 
 17. If 9 yards of cloth cost 53 dollars, for how 
 much must it be sold a yard to gain 10 dollars ? 
 
 18. If 7 barrels of flour cost 38 dollars, and were 
 sold, at 7 dollars a barrel, what was the gain ? 
 
 19. How many peaches, at 4 cents each, may be 
 bought for 96 cents ? 
 
 20. How many yards of cloth, at 4 dollars a yard, 
 can be bought for 116 dollars? 
 
 21. How many oranges, at 3 cents each, must be 
 given for 18 lemons worth 4 cents each ? 
 
 22. If 15 sheep cost 75 dollars, what will 1 sheep 
 cost ? 
 
 23. Which will cost the most, 4 barrels of wheat 
 flour, at 9 dollars a barrel, or 12 barrels of corn, at 4 
 dollars a barrel, and how much ? 
 
 24. How many barrels of beef, at 3 dollars a barrel, 
 can be bought for 54 dollars ? 
 
 25. How many pounds of fish, at 5 cents a pound, 
 may be had for 95 cents ? 
 
 26. At 7 cents a pound, how many pounds of lead 
 may be had for 84 cents ? 
 
 27. How long will it require to travel 105 miles, at 
 the rate of 5 miles an hour ? 
 
 28. A person divided 72 peaches equally among 6 
 boys; how many did each receive ? 
 
 29. 148 marbles were divided equally among some 
 
42 MULTIPLICATION AND DIVISION. 
 
 boys ; bow many boys were there, provided each boy 
 received 2 marbles? 
 
 30. How many pounds of butter, at 14 cents a 
 pound, can be bought for 28 apples, at 3 cents each ? 
 
 31. At 7 cents a bottle, how many bottles of ink can 
 you buy for 14 sheets of paper, at 2 cents a sheet ? 
 
 32. In how many days can 1 man do as much as 7 
 men in 8 days ? 
 
 33. In how many days can 2 men do as much work 
 as 6 men in 3 days ? 
 
 34. In how many days can 4 men earn as much as 
 8 men in 6 days ? 
 
 35. In how many days can 15 men earn as much 
 as 3 men in 25 days? 
 
 36. In how many months will 6 horses eat as much 
 as 18 horses in 5 months? 
 
 37. How many men can in 7 days earn as much as 
 
 28 men in 4 days ? ! 
 
 38. In 10 days 6 men will earn as much as how 
 many men in 5 days ? 
 
 39. How many yards of cloth, at 4 dollars a yard, 
 may be had for 4 sets of chairs, at 12 dollars a set ? 
 
 40. A farmer gave 13 barrels of flour, worth 4 dol¬ 
 lars a barrel, for 26 yards of cloth \ how much was 
 the cloth a yard ? 
 
 --- 
 
 LESSON IV. 
 
 CHAPTERS FIRST, SECOND, THIRD, AND FOURTH COMBINED. 
 
 1. 4 times 6 are how many times 2 ? 
 
 Solution.— 4 times 6 are 24. 24 are 12 times 2. Therefore, 
 
 4 times 6 are 12 times 2. 
 
 2. 4 times 9 are how many times 3 ? 
 
 3. 4 times 8 are how many times 2 ? 
 
\ 
 
 FUNDAMENTAL RULES. 43 
 
 4. 4 times 10 are how many times 5 ? 
 
 5. 4 times 12 are how many times 6 ? 
 
 6. 4 times 14 are how many times 7 ? 
 
 7. 5 times 9 are how many times 15 ? 
 
 8. 5 times 8 are how many times 4 ? 
 
 9. 5 times 12 are how many times 15 ? 6? 
 
 10. 6 times 7 are how many times 2 ? 
 
 11. 6 times 8 are how many times 12 ? 3? 
 
 12. 4 times 6 are how many times 8? 
 
 13. 7 times 15 are how many times 5 ? 
 
 14. 12 times 7 are how many times 21 ? 
 
 15. 8 times 7 are how many times 4? 
 
 16. How many times 12 are 9 times 4 ? 
 
 17. How many times 20 are 5 times 4? 
 
 18. How many times 9 are 3 times 21, +9 ? 
 
 19. How many times 5 are 7 times 15, +10 — 5 ? 
 
 20. How many times 9 are 3 times 36, — 2 + 11 ? 
 
 21. How many times 12 are 9 times 4, +24 — 12? 
 
 22. How many times 21 are 9 times 14, +42 ? 
 
 23. How many times 7 are 3 times 14, +21 —14? 
 
 24. How many times 5 are 8 times 10, +5 —15 ? 
 
 25. How many times 5 arc 10 times 6, +15 + 5? 
 
 26. How many times 5 are 6 times 15, +10 + 15 ? 
 
 27. 10 times 4, + 2 are how many times 7 ? 2 ? 
 
 28. 8 times 9,-2 are how many times 5 ? 
 
 29. 12 times 8,-8 are how many times 2 ? 
 
 30. 26 times 11, — 6 are how many times 28 ? 
 
 31. 7 times 8, + 4 are how many times 12 ? 
 
 32. 6 times 7, + 4 are how many times 2 ? 
 
 33. 5 times 8, + 8 are how many times 6 ? 
 
 34. 4 times 9, — 4 are how many times 8 ? 
 
 35. 9 times 5, — 3 are how many times 7 ? 
 
 36. 7 times 12, — 14 + 5 are how many times 5? 
 
 37. 4 times 15, + 7 — 3 are how many times 8 ? 
 
 38. 6 times 7, + 14 — 2 are how many times 9 ? 
 
 39. 11 times 13, + 11 — 14 are how many times 7 ? 
 
 40. 11 times 15, — 10 + 15 are how many times 17 ? 
 
44 
 
 SIMPLE PROPORTION. 
 
 LESSON V. 
 
 PRACTICAL QUESTIONS COMBINING CHAPTERS THIRD AND FOURTH. 
 
 1. If 2 apples cost 4 cents, how much will 3 apples 
 o cost ? 
 
 Solution.— If 2 apples cost 4 cents, 1 apple will cost 1 half of 
 4 cents, which is 2 cents. If 1 apple costs 2 cents, 3 apples will 
 cost 3 times 2 cents, which are 6 cents. 
 
 2. If 2 pears cost 16c., how much will 5 pears cost ? 
 
 3. If 4 quinces cost 12 cents, how much will 3 
 quinces cost ? 
 
 4. If 6 oranges cost 18 cents, how much will 9 
 oranges cost ? 
 
 5. If 7 peaches cost 21 cents, how much will 9 
 peaches cost ? 
 
 6. If 4 lemons cost 24 cents, how much will 7 
 lemons cost ? 
 
 7 . If 3 yards of tape cost 18 cents, how much will 
 
 6 yards cost? 
 
 8. If 7 hair-brushes cos"| 28 dimes, how many cents 
 will 6 hair-brushes cost? 
 
 9. If 9 yards of muslin cost 108 cents, how much 
 will 7 yards cost ? 
 
 10. If 11 books cost 44 dimes, how many cents will 
 
 7 books cost? 
 
 11. If 12 ink-stands cost 96 cents, what will 2 cost ? 
 
 12. If 10 lead-pencils cost 30 cents, how much will 
 be the cost of 7 ? of 9 ? of 2 ? of 15 ? of 12 ? 
 
 13. How much will 13 yards of silk cost, if 5 yards 
 cost 45 dimes ? 
 
 14. If a man travel 15 miles in 3 hours, how far, at 
 this rate, can he travel in 9 hours ? 5 hours ? 7 hours ? 
 
 15. If the cartage of a load of plaster 20 miles cost 
 4 dollars, how far could it be carried for 12 dollars ? 
 
 16. How many pair of pantaloons can be cut out of 
 21 yards of cloth, if 3 pair can be cut out of 9 yards 
 of the same kind of cloth ? 
 
SIMPLE PROPORTION. 
 
 45 
 
 17. How mueli will 30 pounds of sugar cost, if 6 
 pounds cost 42 cents ? 
 
 18. How much will 18 pounds of veal cost, if 6 
 pounds cost 42 cents? 
 
 19. How much will 75 pounds of pork cost, if 9 
 pounds cost 75 cents? 
 
 20. How much will 20 weeks’ board amount to, if 7 
 weeks’ board cost 14 dollars? 
 
 21. How much will be the wages for 1 year, if 4 
 months’ wages amount to 48 dollars ? 
 
 22. How much will be the cost of 25 bushels of 
 apples, if 13 bushels cost 260 cents? 
 
 23. How much will 14 pounds of cheese cost, if 6 
 pounds cost 54 cents? 
 
 • 24. If 7 quarts of milk cost 35 cents, how much 
 
 will 36 quarts cost? / 
 
 25. If 4 men can do a certain piece of work in 12 
 days, in how many days will 3 men do the same 
 work ? 
 
 26. I gave 72 dollars for a quantity of cotton, and 
 * sold it for 12 yards of cloth; how much did the cloth 
 
 cost me a yard ? 
 
 27. Gave 15 pounds of sugar for 5 pounds of but¬ 
 ter ; how much did the butter cost a pound, provided 
 
 8 pounds of sugar were worth 56 cents? . 
 
 28. If 4 chestnuts are worth 8 walnuts, how many 
 walnuts are 27 chestnuts worth? 
 
 29. If 7 yards of broadcloth are worth 35 dollars, 
 how many boxes of butter, at 3 dollars a box, would 
 
 9 yards of this cloth buy ? 
 
 30. A man bought 4 barrels of flour for 20 dollars, 
 and gave 3 of them for cider, at 3 dollars a barrel; 
 how many barrels of cider did he get ? 
 
 31. A man bought 14 barrels of cider for 56 dol¬ 
 lars, and gave 5 barrels of it for cloth, at 2 dollars a 
 yard; how many yards did he receive ? 
 
 32. A merchant having 15 yards of cloth worth 75 
 
46 
 
 SIMPLE PROPORTION. 
 
 dollars, gave 10 of them for pork, worth 10 dollars a 
 barrel; how many barrels did he receive ? 
 
 33. When 9 bushels of rye were worth 45 dimes, 
 12 bushels were given for 15 yards of cloth; how 
 much did the cloth cost a yard ? 
 
 34. If 35 yards of cloth cost 140 dollars, how much 
 will 95 yards of the same cloth cost ? 
 
 35. Two boys are 32 rods apart,*and both running 
 in the same direction, the hindermost boy gains on the 
 other 4 rods each minute; in how many minutes will 
 he overtake him? 
 
 36. How many boxes will be required to contain 
 56 bushels, provided each box contains 8 bushels? 
 
 37. How many barrels of onions, at 3 dollars a bar¬ 
 rel, must be given for 21 boxes of raisins, at 2 dollars 
 a box ? 
 
 38. A farmer bought 9 yards of cloth, at 4 dollars 
 
 a yard, and paid for it with cider, at 3 dollars a barrel; 
 how many barrels did it take ? ' 
 
 ^ 39. How long would it take a man to lay up 24 
 dollars, if he save 2 dollars a week ? 
 
 40. A farmer hired a laborer and agreed to give 
 him 6 dollars for every 3 days’ work; how much did 
 he receive a week, allowing 6 working days in a 
 week? how much a month, allowing 4 weeks to the 
 month ? 
 
 41. If 4 oranges are worth 12 cents, how many 
 
 oranges must be given for 6 pine-apples, worth 12 
 cents each ? . 
 
 42. How many yards of cloth, at 2 dollars a yard, 
 can be bought for 4 reams of paper, at 5 dollars a 
 ream ? 
 
 43. 6 men bought a horse for 80 dollars, and paid 
 2 dollars a week for keeping him ;—at the end of 10 
 weeks they sold him for 82 dollars; how much did 
 each man lose ? 
 
 44. If 2 apples are worth 1 orange, and 2 oranges 
 
TABLES AND REDUCTION. 
 
 47 
 
 are worth 1 lemon ; how many lemons can he bought 
 for 48 apples ? 
 
 45. If 5 oranges are worth 1 pine-apple, and 2 pine¬ 
 apples are worth 1 melon ; how many oranges may be 
 bought for 4 melons ? 
 
 46. A fox is 80 rods before a hound, and the hound 
 gains 5 rods on the fox every 10 minutes ; in how 
 many minutes will the fox be caught ? 
 
 47. If 7 men can do a certain job of work in 12 
 days, in how many days could 21 men do the same 
 work? - 
 
 48. In how many days can 9 men do as much work 
 as 7 men can in 18 days? 
 
 49.. How many men in 10 days can perform the 
 same amount of work, that 8 men can in 5 days? 
 
 50. Bought 5 firkins of butter for 35 dollars ; for 
 what must I sell it to gain 10 dollars ? what is the gain 
 on each firkin ? 
 
 -»- 
 
 CHAPTER Y. 
 
 LESSON I. 
 
 Table op United States Currency. 
 
 10 Mills (m.) make 1 Cent, marked c. 
 
 10 Cents “ 1 Dime, “ d. 
 
 10 Dimes “ 1 Dollar, u $. 
 
 10 Dollars “ 1 Eagle, « E. 
 
 1. How many mills in 4 cents ? 
 
 Solution. —In 1 cent there are 10 mills, and in 4 cents there 
 are 4 times 10 mills, or 40 mills. 
 
 2. How many mills in 3 cents? In 5 cents? In 8 
 cents ? 
 
 3. How many cents in 2 dimes ? In 4 dimes ? In 
 5 dimes? In 6 dimes? In 9 dimes? In 10 dimes? 
 
48 
 
 TABLES AND REDUCTION. 
 
 4. How many dimes in $1 ? In $2 ? In $3 ? In 
 
 $4 ? In $5 ? In $6 ? 
 
 5. How many dimes in 1 eagle and $4? In 2 eagles 
 and $8 ? 
 
 6. How many cents in $1 ? In $2 ? In $3? In 
 $4 ? In $5 ? In $8 ? 
 
 7. How many dollars in 80 dimes ? 
 
 Solution.—T here are 10 dimes in $1, therefore, 1 tenth of 
 the number of dimes equals the number of dollars. 1 tenth of 
 80 is 8. Therefore, in 80 dimes there are $8. 
 
 8. How many dimes in 60 cents? In 70 cents? 
 In 90 cents ? 
 
 9. How many dollars in 200 cents? In 500 cents ? 
 In 800 cents? In 360 cents? In 705 cents? 
 
 10. If 3 yards of muslin cost 6 dimes, how many • 
 yards can be bought for 1 dollar ? 
 
 11. How many pounds of pepper can you buy for 
 1 eagle, if 12 pounds cost 6 dimes? T 
 
 12. How many pounds of candies can you buy for 
 14 eagles, if 10 pounds cost 140 cents ? [ g >-■ 
 
 LESSON II. 
 
 Table op English Money. 
 
 4 Farthings (far.) make 1 Penny, marked d. 
 
 12 Pence “ 1 Shilling, “ s. 
 
 20 Shillings “ 1 Pound “ £. 
 
 A Sovereign ( sov .) is equal in value to 1£. 
 
 1. How many shillings in 4£ 15 shillings? 
 
 Solution. —There are 20 shillings in 1£, therefore, 20 times 
 the number of pounds equal the number of shillings. 20 times 
 4 are 80 shillings +15, are 95 shillings. 
 
 2. How many pence in 1 shilling? In 4 shillings? 
 In 3 shillings? In 7 shillings? In 9 shillings? 
 
 3. How many shillings in l£ ? In 2£? In 3£ ? 
 In 6£ ? 
 
TABLES AND REDUCTION. 
 
 49 
 
 4. How many pence in 2£ 10 shillings 5 pence? 
 
 5. How many pounds in 60 shillings ? In 80s. ? 
 In 120s. ? 
 
 6. How many pounds in 480 pence ? In 7200?. ? 
 
 7. At 4 shillings a bushel, how many pounds will 
 40 bushels of potatoes cost ? 
 
 8. At 10 pence a piece, how many pounds will 48 
 pine-apples cost ? 
 
 9. At 5 shillings a yard, how many yards of cloth 
 can be bought for 2£ 15 shillings ? 
 
 
 v\ 
 
 oJ 
 
 
 LESSON III. 
 
 Table of Troy Weight. 
 
 24 Grains ( gr .) 
 
 20 Pennyweights 
 12 Ounces 
 
 make 1 Pennyweight, marked pwt. 
 “ 1 Ounce, “ oz. 
 
 “ 1 Pound, “ lb. 
 
 1. How many pennyweights in 240 grains? 
 
 2. How many pennyweights in 4 ounces ? In 5 
 ounces ? In 6 ounces ? 
 
 3. How many ounces in 1 pound ? In 3 pounds ? 
 In 5 pounds ? In 8 pounds ? 
 
 4. In 24 ounces how many pounds ? In 48 ounces ? 
 In 36 ounces ? In 60 ounces ? In 84 ounces ? 
 
 5. How many ounces in 20 pennyweights ? In 40 ? 
 In 60 ? In 70 ? 
 
 6. If 7 grains of gold cost 168 dimps, how much 
 will 10 pennyweights cost? 
 
 7. What will 1 pennyweight of gold cost, if 2 
 grains cost 18 dimes? //(j 
 
 8. How many pennyweights in 4 ounces and 6 
 pennyweights ? 
 
 9. How many pounds in 480 pennyweights ? 
 
 10. How many grains in 2 oz., 2 pwt., and 2 gr. 
 
 5 
 
50 
 
 TABLES AND DEDUCTION. 
 
 LESSON IV. 
 
 Table of Avoirdupois Weight. 
 
 16 Drams, (dr.) make 1 Ounce, marked oz. 
 
 16 Ounces “ 1 Pound, “ lb. 
 
 25 Pounds “ 1 Quarter, “ qr. 
 
 4 Quarters, or 100 lbs. “ 1 Hundred-weight, “ cwt. 
 
 20 Hundred-weight, “ 1 Ton, “ 71 
 
 1. How many drams in 2 oz. ? In 4 oz. ? In 10 oz. ? 
 
 2. How many ounces in 2 lbs. ? In 4 lbs. ? In 8 lbs. ? 
 
 3. How many quarters in 100 pounds? in 400 
 pounds? in 600 pounds? in 1200 pounds? 
 
 4. How many pounds in 3 qrs. ? In 2 qrs. ? In 7 qrs, ? 
 
 5. How many quarters in 2 hundred-weight ? " 
 
 6. In 8 quarters how many hundred-weight? 
 
 7. If 30 lbs. of hay cost 6 dimes, what will 3 quar¬ 
 ters cost ? will 1 cwt. ? will 2 cwt. and 1 qr. ? . 
 
 8. What will 2 tons of iron cost, if 1 lb. cost 1 
 dime ? 
 
 9. What will 40 tons of hay cost, at 2 dimes a qr. ? - - 
 
 10. What will 2 cwt. of sugar cost, at a dime a 
 
 pound ? at 5 cents a pound ? g ' 
 
 ‘ 
 
 -— o - - 
 
 LESSON V. 
 
 Table of Long Measure. 
 
 12 Inches (in.) make 1 
 
 3 Peet “ 1 
 
 51 Yards, or 16| feet “ 1 
 
 40 Rods “ 1 
 
 8 Furlongs, or320 rods, “ 1 
 
 3 Miles “ 1 
 
 69j Miles “ 1 
 
 360 Degrees “ 1 
 
 1. How many inches ii 
 In 5 ft. ? In 10 ft. ? 
 
 Foot, 
 
 marked ft. 
 
 Yard, 
 
 il 
 
 yd. 
 
 Rod, 
 
 «( 
 
 rd. 
 
 Furlong, 
 
 ii 
 
 fur. 
 
 Mile 
 
 it 
 
 mi. 
 
 League, 
 
 n 
 
 lea. 
 
 Degree, “ 
 
 Circle of the earth. 
 
 deg. or °. 
 
 1 ft.? 
 
 In 2 ft. ? 
 
 In 4 ft. ? 
 
TABLES AND REDUCTION. 
 
 51 
 
 2. How many feet in 2 yds. ? In 6 yds. ? In 5 yds.? 
 In 12 yds. ? 
 
 3. How many yards in 2 rods ? In 4 rds. ? In 8 
 rds.? In 10 rds? 
 
 4. How many furlongs in 4 miles ? In 6 mi. ? In 
 9 mi. ? 
 
 5. How many inches 4 yds. 2 ft. 10 in. ? 
 
 6. In 216 inches, how many yards? In 288 in. ? 
 
 7. How many rods in 1 mile ? 
 
 8. How many miles in 1760 yards ? ' 
 
 9. How many feet in 2 rods, 3 yds., 2 ft., 11 in. ? 
 
 10. How many feet in 1 mile ? 
 
 -« »>«».. >-■ 
 
 no / 
 
 LESSON VI. 
 
 Table of Cloth Measube. 
 
 24 Inches 
 
 make 
 
 i 
 
 Nail, 
 
 Quarter of a yard, 
 
 marked 
 
 na. 
 
 4 
 
 Nails 
 
 a 
 
 i 
 
 U 
 
 qr . 
 
 4 
 
 Quarters 
 
 u 
 
 i 
 
 Yard, 
 
 u 
 
 yd. 
 
 3 
 
 Quarters 
 
 u 
 
 i 
 
 Ell Flemish, 
 
 u 
 
 E. FI. 
 
 5 
 
 Quarters 
 
 u 
 
 i 
 
 Ell English, 
 
 u 
 
 E. E._ 
 
 6 
 
 Quarters 
 
 u 
 
 i 
 
 Ell French, 
 
 u 
 
 E. Fr. 
 
 1. In 4 yds. 3 qrs., how many quarters ? 
 
 2. In 7 yds. 2 qrs., how many Ells French ? 
 
 3. In 3 yds. 3 qrs., how many Ells Flemish ? 
 
 4. In 8 Ells English, how many yards ? 
 
 5. In 7 Ells Flemish, how many yards and quarters ? 
 
 6. In 3 Ells French, how many yards and quarters ? 
 
 7. In 4 Ells Fr., and 8 Ells FI., how many yards ? 
 
 8. In 1 qr., how many inches? 
 
 9. What will 6 E. E. of cloth cost, if 6 nails cost 
 48 cents ? 
 
 10. What will 3 E. E, + 2 E. Fr. of cloth cost, if 
 3 nails cost 12 cents ? 
 
 TIMERS t«0F 
 
 tumois ubrmn 
 
52 
 
 TABLES AND KEDUOTION. 
 
 LESSON VII. 
 
 Table of Land oil Square Measure. 
 
 144 Square inches, (sq. in.) 
 9 Square feet 
 30^ Square yards 
 40 Square rods 
 4 Roods 
 640 Acres 
 
 make 
 
 1 Square foot, 
 
 1 Square yard, 
 
 sq.ft. 
 
 U 
 
 sq. yd. 
 
 U 
 
 1 Square rod, or 
 
 pole, P. 
 
 u 
 
 1 Rood, 
 
 B. 
 
 u 
 
 1 Acre, 
 
 A. 
 
 u 
 
 1 Square mile, 
 
 sq. m. 
 
 1. How many square feet in 4 sq. yds. ? In 8 
 sq. yds. ? 
 
 2. How many poles in 4 roods ? In 0 roods ? 
 
 3. How many acres in 40 roods? In 160 roods? 
 
 4. How many square yards in 81 sq. ft.? In 108 
 sq. ft. ? 
 
 5o How many square } r ards in 1 rood 10 rods ? 
 
 »♦ » 
 
 LESSON VIII. 
 
 Table of Cubic Measure. 
 
 1128 Cubic inches (cu. in.) 
 27 Cubic feet 
 24| Cubic feet 
 16 Cubic feet 
 8 Cord feet, or ) 
 
 128 Cubic feet J 
 
 make 1 Cubic foot, cu. ft. 
 
 11 1 Cubic yard, cu. yd. 
 
 “ 1 Perch of stone, pch. 
 
 “ 1 Cord foot, c. ft. 
 
 “ 1 Cord of wood, 0. 
 
 1. How many cubic feet in 4 cubic yards? 
 
 2. How many cubic feet in 4 perch of stone ? 
 
 3. How many cords in 96 cord feet? In 72 c. ft.? 
 
 4. How many cords in 128 cu. ft.? In 384 cubic 
 feet? 
 
 5. How many cord feet in 4 cords ? In 6 cords? 
 In 9 cords? 
 
TABLES AND REDUCTION. 
 
 53 
 
 4 
 
 Gills (gi.) 
 
 LESSON IX. 
 
 Table oi* Wine Measure. 
 
 make 1 Pint, 
 
 marked pt. 
 
 2 
 
 Pints 
 
 a 
 
 1 Quart, 
 
 a 
 
 qt. 
 
 4 
 
 Quarts 
 
 a 
 
 1 Gallon, 
 
 a 
 
 gal. 
 
 42 
 
 Gallons 
 
 a 
 
 1 Tierce, 
 
 a 
 
 tier. 
 
 314 Gallons 
 
 a 
 
 1 Barrel, 
 
 a 
 
 bar. 
 
 2 
 
 Bar. or 63 Gallons “ 
 
 1 Hogshead, 
 
 a 
 
 hhd. 
 
 2 
 
 Hogsheads 
 
 a 
 
 1', u 
 
 1 Pipe, 
 
 a 
 
 pi. 
 
 2 
 
 Pipes 
 
 1 ! Tun, 
 
 a 
 
 tun. 
 
 1. How many gills in 3 pints ? In 4 pints? 
 
 2. In 3 qts., hqw many gills ? 
 
 3. In 12 gallons, how many pints? 
 
 4. What will 5 gal. of rum cost, if 4 gi. cost 5 cents? 
 
 5. How many pints in 2 pipes? 
 
 6. A merchant bought a hogshead of molasses for 
 20 dollars, and sold it, at the rate of 15 cents for 3 
 pints ; how much did he gain by the bargain ? 
 
 7. How much will a gallon of wine cost, if 7 gills 
 cost 21 cents ? 
 
 8. In 1 tierce, how many pints ? 
 
 9. In 4 quarts and 2 pints, how many gills ? 
 
 10. In 1 tun, how many gills ? 
 
 11. In 1 barrel, how many pints? 
 
 - <! »♦ '«< » 
 
 LESSON X. 
 
 Table of Dey Measure. 
 
 2 Pints make 1 Quart, marked qt. 
 
 8 Quarts “ 1 Peck, “ pk. 
 
 4 Pecks “ 1 Bushel, “ bu. 
 
 1. In 1 peck how many pints ? 
 
 2. 2 pecks will fill how many pint measures ? 
 
 3. In 3 pecks and 3 quarts how many pints ? 
 
54 
 
 TABLES AND REDUCTION. 
 
 4. In 1 bushel and 3 pecks, how many quarts ? 
 
 5. In 1 bushel, how many quarts ? how many 
 pints ? 
 
 6. If 8 pints of nuts cost 24 cents, what will 3 pecks 
 cost at the same rate? */ ■ 
 
 7. A market woman bought 4 quarts of strawber¬ 
 ries for 29 cents, and sold them, at 5 cents a pint; how 
 much did she gain ? 
 
 8. A person sold 2 bushels and 1 peck of currants, 
 
 at 2 cents a pint, and in payment received 1 bushel of 
 gooseberries, at 4 cents a pint; how much remains 
 due ? - - :l 
 
 9. What will 5 quarts of wheat cost, if 1 bushel 
 cost 128 cents? 
 
 10. A farmer sold 1 bu., 3 pk. and 1 pt. of clover- 
 seed, at 640 cents a bushel, and in payment received 
 1 bu., 2 pk. and 3 quarts of grass-seed, at 320 cents a 
 bushel; how much remains due ? 
 
 •————^-- 
 
 LESSON XI. 
 
 Table of Time. 
 
 60 
 
 Seconds (sec.) 
 
 make 
 
 1 Minute, marked 
 
 on. 
 
 60 
 
 Minutes 
 
 U 
 
 1 Hour, 
 
 66 
 
 hr. 
 
 24 
 
 Hours 
 
 u 
 
 1 Day 
 
 66 
 
 d. 
 
 1 
 
 Days 
 
 u 
 
 1 Week, 
 
 u 
 
 w. 
 
 4 
 
 Weeks 
 
 u 
 
 1 Month, 
 
 66 
 
 mo. 
 
 12 
 
 Calendar months 
 
 u 
 
 1 Year, 
 
 u 
 
 yr. 
 
 52 
 
 Weeks 
 
 u 
 
 1 Year, 
 
 1 Common Year, 
 
 u 
 
 yr. 
 
 365 
 
 Days 
 
 u 
 
 u 
 
 yr. 
 
 366 
 
 Days 
 
 16 
 
 1 Leap Year, 
 
 u 
 
 yr. 
 
 100 
 
 Years 
 
 u 
 
 1 Century, 
 
 16 
 
 G. 
 
 The following table exhibits the divisions of the year, 
 the names of the months, and the number of days in 
 each:— 
 
TABLES AND 
 
 EEDUCTION. 
 
 55 
 
 IJ 
 
 > 1st month, January, 
 
 has 
 
 31 days. 
 
 £ < 
 
 | 2d 
 
 u 
 
 February, 
 
 tt 
 
 28, 
 
 in leap year 29, 
 
 i 
 
 ; 3d 
 
 u 
 
 March, 
 
 April, 
 
 it 
 
 31 days. 
 
 ■g \ 
 
 4th 
 
 a 
 
 it 
 
 30 
 
 U 
 
 Ph i 
 
 1 
 
 [ 5th 
 
 u 
 
 May, 
 
 tt 
 
 31 
 
 tt 
 
 <D \ 
 
 [ 6th 
 
 u 
 
 June, 
 
 July, 
 
 It 
 
 30 
 
 tt 
 
 !< 
 
 7 th 
 
 u 
 
 it 
 
 31 
 
 it 
 
 i l 
 
 Ul 
 
 [ 8th 
 
 ti 
 
 August, 
 
 it 
 
 31 
 
 it 
 
 i < 
 
 [ 9 th 
 
 tt 
 
 September, 
 
 tt 
 
 30 
 
 it 
 
 11 
 
 10 th 
 
 u 
 
 October, 
 
 a 
 
 31 
 
 u 
 
 < ’ 
 
 [ 11th 
 
 u 
 
 November, 
 
 a 
 
 30 
 
 tt 
 
 U i 
 1 
 
 [ 12th 
 
 it 
 
 December, 
 
 tt 
 
 31 
 
 a 
 
 S3 
 
 £ 
 
 The following lines will help to remember the num¬ 
 ber of days in each month : 
 
 “Thirty days hath September, 
 
 April, June, and November; 
 
 February twenty-eight, alone, 
 
 All the rest have thirty-one, 
 
 Except in Leap Year; then is the time 
 When February has twenty-nine.” 
 
 |W° In our calculations on interest we shall reckon 30 days to 
 the month , and 12 months to the year , although not strictly accu¬ 
 rate. 
 
 % 
 
 1. In 2 hours how many seconds? 
 
 2. In 2 weeks and 5 days, how many days ? 
 
 3. In 48 hours, how many days ? 
 
 4. 7200 seconds, how many hours? 
 
 5. How many hours in a week ? 
 
 6. In 1 day, 12 hours and 10 minutes; how many 
 
 minutes ? > 
 
 7. How many hours in a month ? 
 
 8. If a boy can do a piece of work in 40 minutes, 
 how many hours would it take him to perform 12 
 times as much work ? c t' . 
 
56 
 
 FRACTIONS. 
 
 9. If I can do a piece of work in 10 minutes, how 
 many hours would it take to perform a piece of work 
 12 times as large ? 
 
 10. How many days in 3 weeks and 5 days? 
 
 LESSON XII. 
 
 Miscellaneous Table. 
 
 12 Units 
 
 make 1 Dozen. 
 
 12 Dozen 
 
 U 
 
 1 Gross. 
 
 12 Gross 
 
 U 
 
 1 Great Gross. 
 
 20 Units 
 
 u 
 
 1 Score. 
 
 24 Sheets of Paper 
 
 u 
 
 1 Quire. 
 
 20 Quires 
 
 a 
 
 1 Ream. 
 
 56 Pounds 
 
 u 
 
 1 Bushel of Corn. 
 
 60 Pounds 
 
 u 
 
 1 Bushel of Wheat. 
 
 196 Pounds 
 
 u 
 
 1 Barrel of Flour. 
 
 
 
 ( 1 Barrel of Beef, 
 
 200 Pounds 
 
 u 
 
 ( Pork, or Fish. 
 
 1. What will 2 reams 
 
 of 
 
 paper cost, at 15 ce 
 
 quire 
 
 2. How many sheets of paper in 1 ream ? 
 
 3. How many years in “ 3 score years and 10” ? 
 
 4. How many units in a gross ? 
 
 5. How many units in 6 dozen dozen ? 
 
 6. How many units in a half of a dozen dozen ? 
 
 ■il M 
 
 CHAPTER YI. 
 
 LESSON I. 
 
 1. John has 6 nuts, and Joel 1 half as many; how 
 many has he ? 
 
 Solution. —If John has 6 nuts, and Joel 1 half as many, Joel 
 must have 1 half of 6, or 3 nuts. 
 
 •I'L'-'til • • \ . 
 
 • , • . •• • ■ ■ 
 
 ' . .. 
 
FRACTIONS. 
 
 57 
 
 2. Mary had 4 dresses, and Rachel 1 half as many ; 
 how many had she ? 
 
 3. Jacob is 8 years old, and John is 1 half as old ; 
 how old is John ? 
 
 4. Moses having 2 marbles, gave 1 half of them to 
 his brother ; how many had he left? 
 
 5. If you divide 6 apples equally between 2 boys, 
 what part of them will each have ? 
 
 6. What is 1 half of 6 ? 
 
 7. How many halves in 1 ? 
 
 8. If an orange cost 8 cents, and a peach 1 half as 
 much, what is the cOst of the peach ? 
 
 9. James had 12 cakes, and John 1 half as many ; 
 how many had John? 
 
 10. If 3 apples cost 6 cents, what part of 6 cents 
 will 1 apple cost? 
 
 11; What is 1 third of 6 ? 
 
 12. What is 1 half of 8 ? 10? 12? 14? 16? 18? 
 20 ? 
 
 13. If 3 quarts of strawberries cost 18 cents, what 
 part of 18 cents will 1 quart cost? What part of 18 
 cents will 2 quarts cost ? 
 
 14. What is 1 third of 18 ? 1 half of 18 ? 
 
 15. If 4 pounds of raisins cost 8 dimes, what part 
 of 8 dimes will 1 pound cost ? 2 pounds ? 3 pounds ? 
 4 pounds? 5 pounds? 6 pounds? 
 
 16. What is 1 fourth of 8 ? of 12 ? of 16 ? of 20 ? 
 
 17. What is 1 fifth of 15? of 10? of 20? of 30? 
 
 18. If 1 fifth of 15 is 3, what is 2 fifths of 15? 3 
 fifths? 4 fifths? 6 fifths? 8 fifths? 
 
 19. What is 1 sixth of 12? 
 
 20. If 1 sixth of 12 is 2, what is 2 sixths of 12? 3 
 sixths? 4 sixths? 5 sixths? 7 sixths? 8 sixths? 
 
 21. What is 1 seventh of 21 ? 
 
 22. If 1 seventh of 21 is 3, what is 2 sevenths of 21 ? 
 3 sevenths ? 4 sevenths ? 5 sevenths ? 6 sevenths ? 
 
 23. If 1 pound of candies cost 12 cents, what part 
 
58 
 
 FRACTIONS. 
 
 of a pound can you buy for 1 cent ? for 2 cents ? for 3 
 cents ? for 5 cents ? for 8 cents ? 
 
 24. If a coat cost $20, and a pair of pantaloons 1 
 fourth as much, how much will the pantaloons cost ? 
 
 25. If 7 barrels of cider cost $28, what part of $28 
 will 1 barrel cost ? 4 barrels ? 7 barrels ? 5 barrels ? 
 
 26. What is 1 seventh of $28? 2 sevenths of $28? 
 4 sevenths ? 5 sevenths ? 7 sevenths ? 6 sevenths ? 
 
 27. If 1 pound of cheese cost 6 cents, how much 
 will 1 third of a pound cost ? 2 thirds ? 
 
 28. If 12 lemons cost 36 cents, what part of 36 
 cents will 1 lemon cost? 2 lemons? 4 lemons? 5 
 lemons? 8 lemons? 10 lemons? 9 lemons? 7 lemons? 
 
 29. What is 1 twelfth of 36 ? 2 twelfths of 36 ? 4 
 twelfths? 5 twelfths? 6 twelfths? 9 twelfths? 10 
 twelfths? 14 twelfths? 
 
 30. What do you understand by 1 third? 2 thirds? 
 
 Answer.— When a thing has been divided into three equal 
 parts, 1 of these parts is called 1 third, and 2 of these parts are 
 called 2 thirds. 
 
 31. What do you understand by 1 half? 
 
 32. What do you understand by 1 fourth ? 2 fourths ? 
 3 fourths ? 
 
 33. What do you understand by 1 fifth? 2 fifths? 
 3 fifths ? 4 fifths ? 
 
 34. How many thirds make a whole one ? 
 
 35. How many fourths in 1 ? 
 
 36. What do you understand by 2 sixths ? 4 sixths ? 
 
 37. What do you understand by 3 sevenths? 2 
 sevenths? 4 sevenths? 5 sevenths? 
 
 38. How many sixths in 1 ? 
 
 39. How many ninths in 1 ? 
 
 40. How many eighths in 1 ? 
 
 41. How many sevenths in 1 ? 
 
 42. How many tenths in 1 ? 
 
 43. How many twentieths in 1 ? 
 
FRACTIONS. 
 
 59 
 
 44. What do you understand by 7 twelfths? 6 
 twelfths? 9 twelfths? 8 twelfths? 
 
 45. James had 9 marbles, and Jacob had 2 thirds 
 as many ? how many had he ? 
 
 Solution.—I f James has 9 marbles, and Jacob, 2 thirds as 
 many, he must have 2 thirds of 9 marbles. 1 third of 9 is 3, and 
 2 thirds are 2 times 3, which are 6 marbles, Jacob’s number. 
 
 46. Mary bought 12 candies, and Sarah bought 2 
 thirds as many ; how many did Sarah buy ? 
 
 47. Rachel has 12 primers, Mary 3 fourths as many, 
 and Anthony 2 thirds as many as Mary ; how many 
 have Mary and Anthony respectively ? 
 
 48. Albert is 15 years old, and Ebenezer is 4 fifths 
 as old; how old is he ? 
 
 49. Augustus has 40 cents, and Augusta has 5 
 eighths as many ; how many has she ? 
 
 50„ Morgan had 36 marbles, and gave 4 sixths of 
 them to Martin ; how many did he give to Martin, and 
 how many had he left ? 
 
 51. Moses had 24 fire-crackers, and Nathan has 7 
 sixths as many ; how many has he? 
 
 52. Mifflin had 45 cents, and Matthew had 5 ninths 
 as many; how many had he ? 
 
 53. Dubois is 20 years old, and his father is 9 fifths 
 as old ; what is his father’s age ? 
 
 54. A farmer had 84 sheep, and a wolf killed 1 
 third of them; how many had he remaining? 
 
 / 55. In a certain school there are 12 girls, and 7 
 fourths as many boys ;—required the number of boys, 
 and the number of boys and girls together. 
 
 56. In a certain recitation 36 questions were asked, 
 and 1 ninth of them answered wrong; how many 
 were correctly answered ? 
 
 57. 4 fifths of all the words given out in a spelling 
 lesson were spelled correctly, and 8 were misspelled; 
 of how many words did the lesson consist ? 
 
60 
 
 FRACTIONS. 
 
 58. Montgomery bought 9 filberts for 1 cent; what 
 part of a cent did 1 cost ? 2 ? 3? 6? 7 ? 9? 
 
 59. A horse was bought for $60, and sold for 7 fifths 
 of what it cost; how much was the gain? 2_ 
 
 60. A received $140 for 14 weeks’ labor, and paid 
 
 1 fifth of it for board; how much did he save each 
 week? o , 
 
 61. How many are 4 fifths of 75? % 
 
 62. How many are 7 eighths of 24 ? / 
 
 63. Mr. A’s wife is 40 years old, and 9 eighths of her 
 age equals his ; what is his age ? 
 
 64. What is 2 ninths of 36 ? 4 ninths? 3 fourths? 
 4 sixths ? 5 sixths ? 4 twelfths ? 9 twelfths ? 
 
 65. How many are 3 fourths of 48 ? 4 sixths ? 5 
 eighths? 7 eighths? 6 eighths? 5 sixths? 2 thirds? 
 
 66. 3 ninths of 27 are how many? 4 ninths? 7 
 ninths ? 8 ninths ? 2 thirds ? 
 
 67. 3 fourths of 24 are how many times 3 ? 
 
 Solution.— 1 fourth of 24 is 6, and 3 fourths are 3 times 6, 
 or 18. 18 are 6 times 3. 
 
 68. 5 sevenths of 63 are how many times 3 ? 
 
 69. 3 eighths of 64 are how many times 6 ? 
 
 70.9 thirds of 18 are how many times 3 ? 
 
 71. 4 fifths of 25 are how many times 2 ? 
 
 72. 6 ninths of 18 are how manv times 6 ? 
 
 73. 7 ninths of 90 are how many times 2 ? 
 
 74. 4 thirds of 39 are how many times 2 ? 
 
 75. 15 seventeenths of 34 are how many times 6 ? 
 
 76. How many times 17 are 17 eighteenths of 36 ? 
 
 77. How many times 8 are 12 thirteenths of 26 ? 
 
 78. How many times 5 are 10 thirds of 36 ? 
 
 79. How many times 4 are 2 thirds of 27, — 2 ? 
 
 80. How many times 6 are 3 halves of 48, 4* 12 ? 
 
 81. Stephen having 40 apples, gave 3 fifths of them 
 to one companion, and 3 eighths of them to another; 
 how many had he remaining ? 
 
 82. A had $120 ; 1 third of it he spent for a watc'h, 
 
FRACTIONS. 
 
 61 
 
 1 fourth of it for a suit of clothes, and 3 tenths of it 
 for a sleigh; how much had he remaining? 
 
 83. Mr. B, being asked the cost of his hat, replied, 
 
 2 thirds of 30 dollars is 4 times its cost; required 
 the cost of the hat ? 
 
 84. 14 ninths of $27 is equal to 7 times the cost of 
 a pair of boots; required the cost of the boots. 
 
 85. An individual, having $90 on interest, received 
 2 forty-fifths of the principal for the interest; how 
 much interest did he receive? 
 
 86 . The interest received on $360, was 1 eighteenth 
 of the principal; how much was the interest ? 
 
 87. B is worth $ 2000 , and 3 fourths of his fortune 
 is 3 times A’s ; required A’s fortune. 
 
 88 . 3 eighths of the number of hours in a day, is 3 
 times the number of hours I work; how many hours 
 do I work ? 
 
 89. A pole, whose length is 16 feet, is in the air 
 and water; and 3 fourths of the whole length,—4 feet, 
 equals the length in the air; required the length in 
 the water. 
 
 — 90. 3 fifths of $ 2000 , + $ 120 , equals B’s fortune; 
 how much is B worth ? 
 
 91. The building of a certain house cost $560, and 
 4 sevenths of this, + $80, is 1 tenth of the cost of the 
 farm on which it stands. Required the cost of the 
 farm ? 
 
 92. 5 eighths of 72, +■ 13, are how many times 2 ? 
 
 93. The interest on $960 for 5 years, was equal to 
 1 third of the principal; how much was the yearly 
 interest ? 
 
 •? 94. What will 2 thirds of 12 pounds of coffee cost, 
 at 13 cents a pound ? / ’ 7 
 
 95. What will 3 fourths of a gallon of alcohol cost, 
 
 at 9 cents a pint ? > • 
 
 96. AVhat will 1 sixteenth of a bushel of flax-seed 
 cost, at 5 cents a pint ? ^ 
 
 6 
 
62 
 
 FEACTI ONS. 
 
 97. IIow much will 7 fifteenths of 30 pine-apples 
 cost, at 2 dimes each ? 
 
 98. How much will 7 ninths of a hogshead of mo¬ 
 lasses cost, at 4 dimes a gallon ? 
 
 99. How many cents will 3 fifths of 100 oranges 
 cost, at 1 half dime each ? 
 
 100. If 1 pennyweight of gold cost $2, how much 
 will 2 fifths of an ounce cost ? 
 
 101. What will he the cost of 2 thirds of 36 pounds 
 of butter, at 2 dimes a pound ? 
 
 102. 2 thirds of 24, + 3 fourths of 16, are how 
 many times 7 ? 
 
 103. 2 thirds of 30, -f 3 fifths of 40, are how many 
 times 8 ? 
 
 104. 3 sevenths of 21, + 3 eighths of 40, are how 
 many times 6 ? 
 
 105. How far can I walk in 3 eighths of a day, at 
 the rate of 3 miles an hour ? 
 
 106. If Marcus earn 1 dime in an hour, how many 
 cents can he earn in 3 eighths of a day ? 
 
 107. If a horse travel 10 miles in an hour, how 
 many times 10 miles can he travel in 5 twelfths of a 
 day ? 
 
 108. How many cents will 1 quart of gin cost, if 1 
 gill cost 15 mills ? 
 
 109. IIow many dollars will 4 sixths of a pound of 
 gold cost, if 1 pennyweight cost 12 dimes ? / 
 
 110. How many eagles will 25 fourths of a gallon 
 of brandy cost, at 1 half dime a gill ? / 
 
 -«-<>--•—*>-- 
 
 LESSON II. 
 
 1. If 1 third of an orange cost 2 cents, what will 1 
 orange cost ? 
 
 Solution.—T f 1 third of an orange cost 2 cents ; 3 thirds, or 
 1 orange, will cost 3 times 2 cents, which are 6 cents. 
 
FRACTIONS. 
 
 63 
 
 2. If 1 half of a pound of raisins cost 8 cents, what 
 will 1 pound cost ? 
 
 3. Bought 1 third of a barrel of sugar for $3 ; how 
 much will 2 thirds of a barrel cost, at the same rate ? 
 
 4. If 1 third of a pound of pork cost 5 cents, how 
 much will 2 pounds cost? 
 
 5. 2 is 1 third of what number ? 
 
 Solution.—T f 1 third of some number is 2, 3 thirds, which is 
 that number, are 3 times 2, or G. 
 
 6. 5 is 1 half of what number ? 
 
 7. It 1 fourth ot a lemon cost 2 cents, what will 1 
 cost ? 
 
 b. It 1 fourth of a melon cost 5 cents, what will 1 
 cost ? 
 
 9. 3 is 1 fourth of what number? 
 
 10. 7 is 1 third of what number? 
 
 11. 12 is 1 fifth of what number? 
 
 12. 7 is a fourth of what number? 
 
 What will 4 filths of a pound of cinnamon cost, 
 if 1 fifth of a pound cost 5 cents ? 
 
 14. If 1 fifth of a yard of cloth cost $2, what will 
 a yard cost ? 
 
 15. It 1 sixth of a gallon of vinegar cost 2 cents, 
 what will 1 gallon cost ? 
 
 16. A man, being asked the value of his horse, said, 
 that 1 eighth of its value is $12; what is the value 
 of the horse ? 
 
 17. A man gave 15 cents for his lodging, which 
 was 1 seventh as much as his breakfast cost him ; how 
 much did he give for his breakfast ? 
 
 18. Bought 1 eighth ot a yard of cloth for 4 dimes; 
 what will a yard cost at that rate ? 
 
 19. If 1 tenth of a yard of cloth cost 47 cents, how 
 much is that a yard? 
 
 20. What will 1 yard of cloth cost, if 1 ninth of a 
 yard cost 5 cents ? 
 
64 
 
 FRACTIONS. 
 
 21. What will 1 bushel of corn cost, if 1 seventh of 
 a bushel cost 5 cents ? 
 
 22. What will a hogshead of molasses cost, if 1 
 eighth of a hogshead cost $3. 
 
 23. What will be the cost of 2 cords of wood, if 1 
 eleventh of a cord cost 30 cents? 
 
 24. If 1 twelfth of the distance from Albany to 
 Wilbraham is 9 miles, what is the entire distance ? 
 
 25. 9 is 1 tenth of what number? 
 
 26. 15 is 1 seventh of what number? 
 
 27. 16 is 1 fifth of what number?' 
 
 28. 12 is 1 fifth of 6 times what number ? 
 
 29. 15 is 1 sixth of 5 times what number? 
 
 30. 18 is 1 fourth of 6 times what number? 
 
 31. 10 is 1 eighth of 20 times what number? 
 
 32. 15 is 1 seventh of 5 times what number? 
 
 33. 20 is 1 eighth of 16 times what number? 
 
 34. 30 is 1 third of C times what number? 
 
 35. A boy’s hat cost $3, which was 1 fifth of the 
 cost of his coat. The cost of the coat is required. 
 
 36. Mr. B’s saddle cost $9, which was 1 fortieth of 
 6 times the cost of his horse. The cost of the horse 
 is required. 
 
 37. Henry gave five cents for a piece of pie, which 
 was 1 twentieth of 4 times as much as liis breakfast 
 cost him ; what was the cost of his breakfast ? 
 
 38. A man, being asked his age, answered, that 
 his youngest son’s age, which was 12 years, was just 
 1 twelfth of 3 times his age. Required the father s 
 age. 
 
 "39. Mrs. B’s shawl cost $9, which was 1 tenth of 
 3 times the cost of her dress; what was the cost of 
 her dress ? 
 
 40. John said to James, who is now 10 years old, 
 your age is 1 eighth of 4 times my age. How old is 
 John ? 
 
fractions. 
 
 65 
 
 LESSON III. 
 
 1. If 2 thirds of a melon cost 4 cents, what will 1 
 melon cost ? 
 
 Solution. —If 2 thirds of a melon cost 4 cents, 1 third will 
 cost 1 half of 4 cents, which is 2 cents, and 3 thirds, which is 1 
 melon, will cost 3 times 2 cents, which are 6 cents. 
 
 2. If 2 thirds of an orange cost 5 cents, what will 1 
 orange cost ? 
 
 O 
 
 3. If 3 fourths of a pound of candies cost 9 cents, 
 what will 1 pound cost ? 
 
 4. If 4 thirds of a pound of spice cost 16 cents, 
 what will 1 pound cost ? 
 
 5. If 3 fourths of a pound of cinnamon cost 12 
 cents, what will 1 pound cost ? 
 
 6. If $4 will buy 2 fifths of a barrel of fish, what 
 will 1 fifth of a barrel cost ? 
 
 7. What will 1 yard of cloth cost, if 4 sixths of a 
 yard cost 120 cents? 
 
 8. What will 1 hogshead of molasses cost, if 5 
 sevenths of a hogshead cost $15. 
 
 9. 8 is 2 thirds of what number ? 
 
 Solution. —If 2 thirds of some number is 8, 1 third of that 
 number is 1 half of 8, which is 4; and, 3 thirds, which is that 
 number, are 3 times 4, which are 12. Therefore, 8 is 2 thirds 
 
 of 12. 
 
 Remark. —Representing the conditions and solution of ques¬ 
 tions by symbols will aid young pupils in comprehending the 
 more difficult parts of arithmetical analysis. The condition and 
 analysis of the preceding question may be represented, thus; 
 
 If 
 
 = | of some number =8, 
 
 = 4 of that number =4, 
 
 ■ =| } which is that number, =12. 
 
66 
 
 FRACTIONS. 
 
 15. 12 is 2 thirds of what number? 
 
 16. 4 is 2 thirds of what number? 
 
 17. 10 is 2 sevenths of what number? 
 
 18. 9 is 3 fourths of what number? 
 
 19. 12 is 3 fourths of what number? 
 
 20. 12 is 6 elevenths of what number ? 
 
 21. 14 is 7 eighths of what number? 
 
 22. 14 is 2 sevenths of what number? 
 
 23. 6 is 3 tenths of what number? 
 
 24. 9 is 3 sevenths of what number? 
 
 25. 15 is 5 sixths of what number? 
 
 26. 15 is 3 halves of what number? 
 
 27. 18 is 9 eighths of what number? 
 
 28. 20 is 5 thirteenths of what number? 
 
 29. 24 is 8 'fifths of what number ? 
 
 30. 26 is 13 ninths of what number ? 
 
 31. 2 thirds of 12 is 2 fifths of what number? 
 
 32. 3 fourths of 12 is 3 eighths of what number? 
 
 33. 3 fourths of 8 is 2 seventh^ of what number ? 
 
 34. 3 fifths of 25 is 5 fourths of what number ? 
 
 35. 2 sevenths ot 14 is 4 ninths of what number? 
 
 36. 4 sevenths of 21 is 3 tenths of what number? 
 
 37. 2 thirds of 15 is 5 fourths of what number? 
 
 38. 7 eighths ot 48 is 3 halves of what number? 
 
 39. 8 ninths of 36 is 4 fifths of what number? 
 
 40. 7 thirds of 18 is 3 fifths of what number? 
 
 41. A watch cost $16, and 3 halves of the cost of 
 the watch is 8 thirds of the cost of the chain. What 
 was the cost of the chain ? 
 
 42. A horse was sold for $96, which was 8 sevenths 
 of what it cost; what was the cost of the horse ? 
 
 43. In a certain school there are 36 ladies, and 5 
 fourths ot the number of ladies equals 3 fifths of the 
 number of gentlemen. How many gentlemen were 
 there in the school ? 
 
 44. Mary is 14 years old, and 4 sevenths of her 
 age is 2 thirds of Ilezekiah’s age ; what is his age ? 
 
 i 
 
fractions. 
 
 67 
 
 45 . A piece of clotli containing 12 yards was sold 
 for $60, which was 5 fourths ot what it cost; how 
 much did it cost, and what was the gain on each yard '. 
 
 46. A has 48 geese, and 3 fourths ot his number is 
 equal to 9 sevenths of B’s number; how many geese 
 
 llcLS B * 
 
 47. The head of a fish is 12 inches long, and 3 
 fourths of the length of the head is 3 fifteenths of the 
 length of the body. Required the length ot the fish. 
 
 48 A farm was sold for $1200, which was only 6 
 sevenths of what it was worth. How much was lost 
 
 by the bargain ? . , ,, 
 
 49 . $48 is*3 fifths of the cost of 12 yards of cloth ; 
 
 for what must it be sold a yard to gain $16 on the 
 
 whole? „ 
 
 50. A man gave 60 dollars for a suit of clothes, 
 
 which was 1 fifth of his yearly income ; 1 sixth of the 
 remainder he spent for a watch, and what then le- 
 mained was 4 fifths of his brother’s yearly income. 
 What was the yearly income of each ? 
 
 - -0 --- 
 
 LESSON IV. 
 
 2 thirds 
 
 is 
 
 written thus 
 
 2 
 
 n • 
 
 O 
 
 1 half 
 
 tt 
 
 it 
 
 n 
 
 1 
 
 2* 
 
 1 third 
 
 tt 
 
 it 
 
 u 
 
 1 
 
 3 * 
 
 1 fourth 
 
 tt 
 
 it 
 
 u 
 
 I 
 
 4 * 
 
 1 sixth 
 
 it 
 
 u 
 
 u 
 
 1 
 
 6 * 
 
 1 seventh 
 
 it 
 
 n 
 
 u 
 
 1 
 
 7* 
 
 3 fourths 
 
 tt 
 
 u 
 
 it 
 
 3 
 
 4 * 
 
 7 eighths 
 
 tt 
 
 tt 
 
 it 
 
 7 
 
 8 * 
 
 9 tenths 
 
 tt 
 
 tt 
 
 u 
 
 9 
 
 1 0* 
 
 5 sevenths 
 
 it 
 
 u 
 
 u 
 
 5 
 
 7* 
 
 2 fifths 
 
 it 
 
 tt 
 
 it 
 
 2 
 
 5 * 
 
 5 thirds 
 
 it 
 
 u 
 
 it 
 
 5 
 
 3* 
 
 &c. 
 
 tt 
 
 tt 
 
 tt 
 
 &c. 
 
08 
 
 REDUCTION OF FRACTIONS. 
 
 I 
 
 Remark.—T he above expressions are called fractions. The 
 figure above the short horizontal line is called the numerator, and 
 the figure belo w the line is called the denominator. For example 
 
 m the fiaction £, the 3 is the numerator, and the 4 is the denom- 
 inator. 
 
 The denominator of a fraction shows into how many equal 
 parts the thing is divided ; and the numerator shows how many 
 ^ of these parts are taken. y 
 
 1. If you cut an orange into 3 equal parts, what is 
 1 ot these parts called ? 
 
 i 3 l01 - n ° a ! )0 cut 3nto 4 G€ l lml pieces, what will 
 1 ot thnse pieces be called ? 2 ? 3 ? 42 
 
 3 If a bushel of apples be divide^ into 6 equal 
 parts, what will 1 of these parts be called ? 3 ? 4 2 0 2 
 
 4. If a basket of peaches be divided in 8 equal 
 parts, what will 3 ot these parts be called ? 5 ? 6 ? 7 ? 
 
 5. How can you find 2 thirds of an apple ? 
 
 6. How can you find 3 fourths of an orange & 
 
 7. In | how many times 1 ? 
 
 Solution.—I n 1 there are 2 halves, therefore I half the num¬ 
 ber of halves equals the number of ones. 1 half of 4 is 2 • 
 therefore, f equals 2. 1 4 13 z > 
 
 In f how many times 1 ? 
 
 In f how many times 1 ? 
 
 In - 1 /- how many times 1 ? 
 
 In R 2 how many times 1 2 
 
 In V how many times 1 ? 
 
 In f how many times 1 ? 
 
 In J 3 2 how many times 1? 
 
 In f how many times 1 ? 
 
 In - 1 /- h°w many times 1 ? 
 
 In - 1 / how many times 1 ? 
 
 In - 1 / how many times 1 ? 
 
 In Y how many times 1 ? 
 
 In | how many times 1 ? 
 
 In - 1 / how many times 1 ? 
 
 In - 1 / how many times 1 ? 
 
 In y°- how many times 1 ? 
 
 8 . 
 
 9 . 
 
 
REDUCTION OF FRACTIONS. 69 
 
 24. 
 
 In 
 
 2 4 
 
 4 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 25. 
 
 In 
 
 3 6 
 
 4 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 26. 
 
 In 
 
 5 
 
 5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 27. 
 
 In 
 
 m 
 
 5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 28. 
 
 In 
 
 2 5 
 
 5 ~ 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 29. 
 
 In 
 
 1 5 
 
 5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 30. 
 
 In 
 
 5 5 
 .5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 31. 
 
 In 
 
 6 0 
 
 5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 32. 
 
 In 
 
 1 8 
 
 6 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 33. 
 
 In 
 
 3 6 
 
 9 
 
 how 
 
 many 
 
 times 
 
 1 ? 
 
 34. 
 
 In 
 
 4 8 
 
 8 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 35. 
 
 In 
 
 5 0 
 
 1 0 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 36. 
 
 In 
 
 4 5 
 ] 5 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 37. 
 
 In 
 
 7 2 
 
 1 8 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 38. 
 
 In 
 
 1 0 0 
 
 2 — 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 39. 
 
 In 
 
 5 6 
 
 7' 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 40. 
 
 In 
 
 C 3 
 
 9 
 
 how 
 
 many 
 
 times 
 
 1? 
 
 41. What kind of a fraction is it called, when the 
 numerator is less than the denominator ? 
 
 42. What kind of a fraction is it called, when the 
 denominator is greater than the numerator ? 
 
 43. When is the value of a fraction greater than a 
 unit ? 
 
 44. When the denominator is less than the numera¬ 
 tor, what kind of a fraction is it called ? 
 
 45. What kind of a fraction is it called, when the 
 numerator is larger than the denominator ? 
 
 Remark. —This is called reducing fractions to whole or mixed 
 numbers. A mixed number is a whole number with a fraction 
 added to it. Thus 3J is a mixed number. 
 
 Whenever the numerator is less than the denominator, the value 
 is less than a unit, and the expression is called a proper fraction ; 
 ■—but when the numerator is equal to or greater than the denom¬ 
 inator the value is equal to or greater than a unit, and the ex¬ 
 pression is called an improper fraction. 
 
 46. Reduce | to a mixed number. 
 
 47. Reduce f to a mixed number. 
 
70 
 
 
 ADDITI 
 
 ON 
 
 0 F 
 
 FEACTI 
 
 ONS . 
 
 48. 
 
 Reduce 
 
 1 5 
 
 ~4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 49. 
 
 Reduce 
 
 1 9 
 
 3 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 50. 
 
 Reduce 
 
 2 JI 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 51. 
 
 Reduce 
 
 2_1 
 
 5 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 52. 
 
 Reduce 
 
 5 Z 
 
 _ 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 53. 
 
 Reduce 
 
 8 9 
 
 1 2 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 54. 
 
 Reduce 
 
 9 JL 
 
 8 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 55. 
 
 Reduce 
 
 2 5 
 
 3 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 56. 
 
 Reduce 
 
 3 7 
 g 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 57. 
 
 Reduce 
 
 4'7 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 58. 
 
 Reduce 
 
 7 8 
 
 7 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 59. 
 
 Reduce 
 
 3 7 
 
 6 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 60. 
 
 Reduce 
 
 _3_4 
 
 8 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 --- 
 
 LESSON V. 
 
 1. James had £ of an apple, and John gave him £ 
 more ; how many had he then ? 
 
 2. Mary had -f of an orange, and her father gave 
 her £ of an orange more ; how many had she then ? 
 
 3. Robert had f of a melon, and bought f of an¬ 
 other ; how many had he then ? 
 
 4. Susan had £ of a pint of walnuts, and gave £ of 
 a pint to her sister; how much had she left? 
 
 5. James bought - 1 / of a pound of candies, and on 
 his way home ate £ of a pound; how much had he 
 left ? 
 
 6. John gave \ of a pound of raisins to James, f of 
 a pound tollary, and kept f of a pound himself; how 
 many had he at first ? 
 
 7. Mortimer gave f of a dollar for a hat, $lf for a 
 vest, and had $3| remaining; how much had he at 
 first? 
 
 8. Jane had 5 pounds of cinnamon, and Harriet had 
 2£ pounds ; how many more had Jane than Harriet? 
 
ADDITION, &C., OF FRACTIONS. 7l 
 
 9. Henry gave § of a dollar for his breakfast, f of a 
 dollar for his dinner, and | of a dollar for his supper; 
 how much did his day’s board cost him ? 
 
 10. -9- -f- f are how many ? 
 
 11* I + f are how many ? 
 
 12. f + f are how many? 
 
 13. t 9 o+t 8 o are how many? 
 
 14. f + f- are how many ? 
 
 15. */+ | are how many? 
 
 16. + f are how many? 
 
 17. + -+ are how many ? 
 
 18. f + V 1 are.how many? 
 
 19. 1 + f + f are how many? 
 
 20. £ + f + £ are how many ? 
 
 21. r 7 o + tV + r 9 o arc h°w many ? 
 
 22. f + £ + j are how many ? 
 
 23. -f- less £ are how many ninths? 
 
 24. y 7 - less y 7 - are how many ? 
 
 25. +-— | are how many ? 
 
 26. y 3 -— f are how many? 
 
 27. - 3 y — | are how many ? 
 
 28. y — | are how many ? 
 
 29. - 3 g 7 -— £ are how many? 
 
 30. + 9 -— | are how many ? 
 
 31. -y.— j_p. are how many? 
 
 32. -y- — A are how many? 
 
 33. ||— |Jare how many? 
 
 34. f + 1 — £ are l 10 \v many ? 
 
 35. £ + | — f are how many ? 
 
 36. £ +-Li— | are how many? 
 
 37. |£—-f || are how many? 
 
 38. | of 60—| of 24 are how many? 
 
 39. 1 of 40 — | of 10 are how many ? 
 
 40. | of 15+| of 9—| of 12 are how many? 
 
72 MULTIPLICATION OF FRACTIONS. 
 
 LESSON VI. 
 
 1 . At | of a cent a piece, what will 2 apples cost? 
 
 Solution.— If 1 apple cost f of a cent, 2 apples will cost 
 twice | of a cent, which are f or 1| cents. 
 
 2 . At | of a cent a piece, what will 5 apples cost? 
 
 3 . At | of a dime a pound, what will 10 pounds of 
 candies cost? 
 
 4 . At If dimes a pound, how many cents will 8 
 pounds of starch cost? 
 
 5 . At | of a cent a piece, what will 25 filberts cost? 
 
 6 . At | of a dime a piece, how many cents will 8 
 chickens cost ? 
 
 7. At | of a dollar a yard, what will 15 yards of 
 linen cost? 
 
 8 . If a man spend f of a dollar a day, how much, 
 at this rate, will he spend in 23 days? 
 
 9 . If a man receive f of an eagle in a week, how 
 many dollars will he receive in 52 weeks ? 
 
 10 . If 1 pound of sugar cost If dimes, what will 12 
 pounds cost? 
 
 11 . At 5 1 cents a pound, what will 6 lbs. of beef 
 cost ? 
 
 12 . At 9 f cents a pound, what will 8 lbs. of pork 
 cost ? 
 
 13. At 6 f cents each, what will 12 lemons cost? 
 
 14. At 7f cents each, what will 20 rabbits cost? 
 
 15. At 12 ^ cents a dozen, what will 4 doz. eggs 
 cost ? 
 
 16. At Ilf cents a pound, what will 6 pounds of 
 honey cost? 
 
 17. At $74 a bal. what will 10 bals. of tobacco cost ? 
 
 18. At $ 9 f a barrel, what will 10 bals. of pork cost? 
 
 19. What will 6 boxes of raisins cost, at $3f a 
 box? 
 
MULTIPLICATION OP FRACTIONS. 73 
 
 20. What will 14 bushels of wheat cost, at $1§ a 
 bushel ? 
 
 21. What will 7 barrels of cider cost, at f>3£ a 
 barrel ? 
 
 22. If a barrel of flour cost $4, what will 5 4 barrels 
 cost ? 
 
 23. 5 times 4 and f of 4 are how many ? 
 
 24. 7 times 6 and f of G are how many ? 
 
 25. 9 times 7 and f of 7 are how many ? 
 
 26. 12 times 9 and f of 9 are how many ? 
 
 27. 5 times 10 and f of 10 are how many? 
 
 28. 13 times 4 and f of 4 are how many ? 
 
 29. 8 times 7 and 4 of 7 are how many? 
 
 30. 10 times 13 and |4 of 13 are how many? 
 
 31.7 times 20 and f of 20 are how many ? 
 
 32. How many are 4 times f ? 
 
 33. How many are 4 times 2| ? 
 
 34. How many are 3 times 4f ? 
 
 35. How many are 5 times 3f, +4 • 
 
 36. How many are 7 times 9|, +|? 
 
 37. How many are 8 times 124, —4 ? 
 
 38. How many are 9 times lOf, —f ? 
 
 39. How many are 6 times 12|, +24 ? 
 
 40. How many are 12 times 9|, ; ? 
 
 --- 
 
 LESSON VII. 
 
 1. If you give to 6 persons, each | of a dollar, how 
 
 many dollars will it take ? i 
 
 2. What will be the cost of 4 yards of cloth, at j 
 
 of a dollar a yard? 
 
 3. If 1 yard of cloth cost $1§, what will 10 yards 
 cost? 
 
 4. How many oranges will it require to give to each 
 of 9 boys 14 oranges? 
 
 7 
 
74 MULTIPLICATION OF FRACTIONS. 
 
 5. How many barrels of flour does that man give 
 away, who gives to each of 12 beggars § of a barrel. 
 
 6. Anthony gave to each of his 7 companions § of 
 a pound of candies, and had ^ of a pound left; how 
 many pounds had he at first ? 
 
 7. Thornton gave to each of 9 beggars f of a dollar, 
 and had $7 remaining ; how much had he at first? 
 
 8. James gave y 1 ^ of an orange to Jackson, t 5 j to 
 Joseph, and ^ to John ; what part of an orange had 
 he remaining: ? 
 
 9. Harmon meeting 3 poor women and 5 poor men, 
 gave to each woman f of a dollar, and to each man J- 
 of a dollar, and then had only $4 remaining; how 
 much had he at first ? 
 
 10. How many quarts of chestnuts must that boy 
 have, who gives to each of 20 persons % of a quart, 
 and has 7 quarts remaining? 
 
 11. Mary, after giving to each of her 12 companions 
 as many pinks as she had roses, which were 2, had no 
 flowers remaining but her roses. How many flowers 
 had she at first ? 
 
 12. What will 1 quart of vinegar cost, if 1 pint 
 cost | of a cent? 
 
 13. If 1 gill of molasses cost | of a cent, what will 
 2 quarts cost ? 
 
 14. If 2 pints of beans cost 4 cents, what will 1 
 peck cost? 
 
 15. If 3 pecks of buckwheat cost 96 cents, what 
 will 1 pint cost ? 
 
 16. What will 10 yards of silesia cost, if 1 yard 
 cost 18|- cents? 
 
 17. How many cents will 4f yards of silk cost, if 1 
 yard cost 6 dimes ? 
 
 18. What will f of a yard of muslin cost, if 1 yard 
 cost 10 cents? 
 
 19. What will 7 spools of thread cost, if 1 spool cost 
 7f cents? 
 
MULTIPLICATION OF FRACTIONS. 75 
 
 20. What will 8f yards of silk cord cost, at 6 cents 
 a yard ? 
 
 21. If 1 yard of wadding cost 5 cents, what will 
 9 j yards cost ? 
 
 22. What will 6f yards of muslin cost, if 1 yard 
 cost 8 cents ? 
 
 23. What will 8| pounds of veal cost, at 5 cents a 
 pound ? 
 
 24. IIow much will 9£ barrels of cider cost, at $4 a 
 barrel ? 
 
 25. What will 12 hats cost, at $3£ each ? 
 
 26. AVhat will 5£ yards of gingham cost, at 4 dimes 
 a yard ? 
 
 27. What will be the cost of 13 yards of bishop 
 lawn, at $1 T 4 3 a yard ? 
 
 28. AYhat will be the cost of 8 looking glasses, at 
 $15| a piece ? 
 
 29. What amount of money will be required to 
 purchase 30 pounds of rice, at 6§ cents a pound ? 
 
 30. AYhat will be the cost of 23 pounds of crackers, 
 at 8|- cents a pound ? 
 
 31. AYhat will 9 barrels of fish cost, at $12f a barrel ? 
 
 32. If 1 grain of gold cost 9L dimes, what will 1 
 pennyweight cost? 
 
 33. If 1 gold pen cost $2f how much will 0 cost? 
 
 34. IIow many pounds of meat, at 5 cents a pound, 
 can you buy for $3f ? 
 
 35. AYhat will be the cost of 3 quarts of nuts, at 64 
 cents a peck? 
 
 36. If a coachman charge 5^- cents a mile, how 
 much must that man pay who rides 12 miles? 
 
 37. How many dollars, dimes, and cents will 12 
 yards ot cloth cost, at 62 cents a yard? 
 
 38. How many dollars and cents will 4 pecks of 
 grass seed cost, if 1 pint cost 5 cents ? 
 
 39. How much will 13 yards of shalloon cost, atl3f 
 cents a yard? 
 
76 MULTIPLICATION OF FRACTIONS. 
 
 40. How many cents will 16 bushels of potatoes 
 cost, at 2f dimes a bushel ? 
 
 r 
 
 -- 
 
 r 
 
 c 
 
 1 LESSON VIII. 
 
 ‘ IfyW" Remark;. —A fraction may be multiplied, by multiplying 
 
 the numerator (as you have already observed), or by dividing 
 * the denominator. 
 
 ‘ 1. How many are 5 times ^ ? 
 
 Solution. —5 times t 7 q are -f-%, or 3f. 
 
 : Remark. —In accordance with the above remark we have 
 
 Solution. —5 times T \ are f, or 3 A 
 
 2. How many are 3 times ? 
 
 3. How many are 9 times o 6 j ? 
 
 4. How many are 5 times f f ? 
 
 5. How many are 6 times f f ? 
 
 6. How many are 9 times T 4 ¥ ? 
 
 7. How many are 9 times if ? 
 
 8. How many are 7 times f f ? 
 
 9. 8 times if are how many ? 
 
 10. 11 times if are how many? 
 
 11. 13 times if are how many? 
 
 12. 2 times f- are how many ? 
 
 13. 5 times if are how many? 
 
 14. 6 times if are how many? 
 
 15. 7 times f £ are how many ? 
 
 16. 12 times if are how many? 
 
 17. How many times 5 are 8 times if ? 
 
 18. How many times 12 are 9 times if ? 
 
 19. How many times 8 are 11 times f f ? 
 
 20. How many times 100 are 25 times -\ 0 /? 
 
 21. How many times 20 are 35 times -W 1 ? 
 
 22. 5 times is 4 times Mary’s age; what is her 
 
 age 
 
MULTIPLICATION &C., OF FRACTIONS. 77 
 
 23. 13 times J 3 6 g 0 - equals £ of the number of dollars 
 a certain wagon cost. Required the cost of the 
 wagon. 
 
 24. 25 times equals °f the number of men 
 Gen. Santa Anna had at the battle of Buena Vista. 
 How many men had he ? 
 
 25. 6 times 2 T \°- is of the number of men he had 
 wounded. How many men were wounded ? 
 
 26. 7 times 5 T \ 9 is £ of the number of men he had 
 killed. How many were killed ? 
 
 27. 4 times A |-®- is of the number of men Gen. 
 Taylor had. How many had he ? 
 
 28. 9 times A 1 is y of the number of men he had 
 killed. How* many were killed ? 
 
 29. 8 times i s r. 0 f j low ma ny times 3 ? 
 
 30. 4 times f a is i of how many times 5 ? 
 
 31. A laborer worked 12 months, at the rate of $10f 
 a month; how much did his year’s wages amount to ? 
 
 32. It 2 quarts of wine cost 48 cents, what will 1 
 gill cost? 
 
 33. How much ought I to pay for 3 oranges, at # of 
 a cent a piece ? 
 
 34. If a certain piece of work can be performed in 
 96 hours, how many days will be required to perform 
 it by working 6 hours a day ? 
 
 35. It 1 man can dig a ditch in 15 days, how long 
 will it take 5 men to dig it ? 
 
 36.. It a certain quantity of provision serve a family 
 of 4 persons 16 days, how long would it last a family 
 of 8 persons ? 
 
 37. If 8 men can perform a certain piece of work 
 in 56 days, in how many days can 112 men do the 
 same ? 
 
 38. If 3 men can plow 18 acres in 6 days, in how 
 many days could 9 men do the same? 
 
 39. 4 men can mow a certain field in 6^- days, in 
 how many days can 5 men perform the same work ? 
 
 7* 
 
78 MULTIPLICATION &C., OF FRACTIONS. 
 
 40. A man bought 6 barrels of cider, at $3§ a 
 barrel; how many boxes of butter, at $4 a box, will it 
 take to pay for it ? 
 
 41. A merchant bought 6 yards of cloth and sold 
 it for $20 which was J g°- of what it cost; what did it 
 cost a yard ? 
 
 42. Bought 36 yards of cloth, and sold f of it for 
 $25, which was f- of what it cost; how much would 
 I have gained by selling the whole at the same rate ? 
 
 43. 7 men in -f of a day can earn $10, how long 
 would it take 1 man to earn the same ? 
 
 44. James is 3| years of age, which is i of the age 
 of Henry; and Henry is 9 times as old as George. 
 What is the age of Henry, and of George respectively? 
 
 45. i of 36 is 3 times i of what number ? 
 
 46. £ of 32 is | of three times what number l 
 
 47. §- of 60 is § of twice what number? 
 
 48. | of 40 is -f of as many dollars as Mr. B’s horse 
 
 cost; what was the cost of his horse ? 
 
 49. A person, being asked his age, said, that £ of 80 
 was | of ten times his age. What was his age ? 
 
 50. Morgan is 20 years old, and f of his age is 
 of the age of his brother. What was his brother’s 
 age ? 
 
 -♦ ♦ ♦•»«.»- 
 
 LESSON IX. 
 
 1. How many thirds are there in 3 ? 
 
 Solution. —In 1 there are 3 thirds, and in 3 there are 3 times 
 3 thirds, which are f. 
 
 The following solution is preferred to the above. 
 
 Solution. —In 1 there are 3 thirds, therefore, 3 times the 
 number of whole ones, equal the number of thirds. 3 times 3 
 are 9. Therefore, in 3 there are f. 
 
 2. How many fourths are there in 3 ? 
 
 3. How many halves are there in 6 ? 
 
DIVISION OF F Ii A C T I O N S . 
 
 *79 
 
 4. How many fifths are there in 4 ? in 5 ? 
 
 5. IIow many fifths are there in 7 ? in 8 ? 
 
 6. How many sixths are there in 4 ? in 3 ? in 5 ? 
 
 7. How many sevenths are there in 2 ? in 4 ? in 6 ? 
 
 8. How many eighths are there in 7 ? in 4? in 5 ? 
 
 9. How many fifteenths are there in 2? in 3 ? in 6 ? 
 
 10. Ilcrw many tenths are there in 4 ? in 6? in 7 
 
 11. How many fourths are there in 3 and f- ? 
 
 12. How many thirds are there in 4 and ± ? 
 
 13. How many thirds are there in 3 and f ? 
 
 14. How many halves arc there in 8 and -i ? 
 
 15. Reduce 6f to an improper fraction. 
 
 16. Reduce 9f to an improper fraction. 
 
 17. Reduce 7f to an improper fraction. 
 
 18. Reduce 5f to an improper fraction. 
 
 19. Reduce 4f to an improper fraction. 
 
 20. Among how many men, can 5f bushels of 
 wheat be distributed, provided each receives f of a 
 bushel ? 
 
 21. Among how many boys, can 7f oranges be 
 divided, provided each receives f of an orange? 
 
 22. 8 and f- are how many times f ? 
 
 Solution.— 8 and § equal 7 ¥ 4 . £ is contained in 74 31 times. 
 
 23. 9f are how many times f ? 
 
 24. 9f are how many times £ ? 
 
 25. 7f are how many times £? 
 
 26. 12f are how many times f ? 
 
 27. 74 are how many times f ? 
 
 28. 7f are how many times f ? 
 
 29. 4£ are how many times f ? 
 
 30. 10J- are how many times f ? 
 
 31. 8£ are how many times £ ? 
 
 32. 12f are how many times f ? 
 
 33. 4 times 3£ are how many times f ? 
 
 34. 9 times If are how many times £ ? 
 
 35. 5 times 6f are how many times f ? 
 
80 
 
 DIVISION OF FK ACTIONS. 
 
 36. 8 times 8| are how many times f ? 
 
 37. 6 times 2| are liow many times -2 ? 
 
 38. A boy distributed apples equally among his 
 companions, giving to each 4 of an apple; how many 
 companions had he ? 
 
 39. Homer distributed $12f equally among some 
 poor women, giving to each ; how many women 
 were there ? 
 
 40. Mary gave f of a pie to each of her 9 visitors; 
 how many pies did it take ? 
 
 41. Bought 8 yards of cloth, at $5§ a yard; how 
 many yards of silk, worth $1} a yard will it take to 
 pay for it ? 
 
 42. Bought 9 yards of cloth, worth a yard, and 
 paid for it with raisins, at a box ; how many boxes 
 did it take ? 
 
 43. How many bushels of turnips, at $f a bushel, 
 can be bought for 8 bushels of apples, at $2 a bushel ? 
 
 44. How many apples, at £ of a cent each, can be 
 bought for 6 oranges, at 2£ cents a piece ? 
 
 45. How many yards of cloth, at $4 a yard, can be 
 bought for 10 boxes of butter, at $5-2 a box ? 
 
 46. How many geese, at each, can be bought 
 for 14 ducks, at a piece? 
 
 47. How many boxes of cheese, worth $2£ a box, 
 may be had for 17 boxes of butter, at $1-2 a box? 
 
 48. How many barrels of flour, worth $5| a barrel, 
 may be had for 17 bunches of cotton, at $14. a bunch ? 
 
 49. How many sheep, at $12- a head, may be had 
 for 8 calves, at $3| each ? 
 
 50. How many quarts of alcohol, at § of a cent a 
 pint, may be had for 12 quarts of molasses, at 42 cents 
 a quart? 
 
 51. Mary and Jane together picked 5 times 
 quarts of strawberries and shared them equally with 
 their companions; how many companions had each, 
 provided each received 12 quarts? 
 
DIVISION OF FRACTIONS. 
 
 81 
 
 lesson X. 
 
 -LEHSONS NINTH AND TENTH COMBINED. 
 
 , h faction may be divided, by multiplying 
 
 the denominator , or by dividing the numerator. 
 
 1. If 2 yards of cloth cost $f, what will 1 yard 
 cost ? J 
 
 , SOI'OTION.—If 2 yards cosi 4 of a dollar, 1 yard will cost i c 
 s of a dollar, which is f of a dollar. 2 
 
 2. If 3 apples cost -f of a cent, what will 1 ar>pl< 
 
 cost ? 1 r 
 
 3. It 2 oranges cost -f of a cent, what will 1 oranm 
 
 cost ? & 
 
 4 If 3 yards of cord cost -j-f of a cent, what will ] 
 yard cost ? 
 
 5 If 2 pounds of sugar cost 8§, (or y cents,) whal 
 
 will 1 pound cost ? J 
 
 6 If 2 pine-apples cost 14| cents, what will 1 pine¬ 
 apple cost ? r 
 
 1. If f of a melon is worth 2 oranges, how much is 
 1 orange worth ? 
 
 8. If 3 apples are worth 2f quinces, what is 1 apple 
 worth ? 11 
 
 9. How many times 7 are \\ 2 
 
 10. How many times 13 are 7| ? 
 
 11. How many times 7 are 9^-? 
 
 12. How many times 21 are 16^ 2 
 
 13. How many times 8 are 33| ? 
 
 14. How many times 7 are 104? 
 
 15. How many times 11 are 40^ ? 
 
 16. How many times 18 are 14f ? 
 
 17. How many times 3 are 4j ? 
 
 18. How many times 0 are 7f ? 
 
 19. How many times 6 are 6f ? 
 
 20. How many times 15 are 33^ ? 
 
82 
 
 DIVISION OF FRACTIONS. 
 
 21. If 9 oranges are worth 8^, liow many cents is 
 1 orange worth ? 
 
 22. If 4 boxes of figs cost | of an eagle, how many 
 dollars will 1 box cost ? 
 
 23. If 7 pounds of cheese cost $ T \, how many cents 
 will 1 pound cost ? 
 
 24. If 3 cates cost t 9 <j of a dime, how many cents 
 will 1 cate cost ? 
 
 25. If 4 pounds of chocolate cost 4| dimes, how 
 many cents is that a pound ? 
 
 26. What will 1 portfolio cost, if 3 cost T 9 5 - of an 
 eagle ? 
 
 27. If 8 quarts of alcohol cost 32 dimes, how many 
 cents will 2 gills cost ? 
 
 28. What will 1 pound of sugar cost, if 4 pounds 
 .cost -1S 9 - cents ? 
 
 29. If 6 pounds of cheese cost 311 cents, what will 
 1 pound cost ? 
 
 30. If 12 eggs cost 9f cents, what will be the cost 
 of 1 egg ? 
 
 31. If 7 yards of cloth cost $241, what will 1 yard 
 cost ? 
 
 32. If 5 silk shawls cost $274, how much is that 
 apiece ? 
 
 33. If 9 pair of boots cost $32|, how much is that 
 a pair ? 
 
 34. If 9 oranges are worth 30| walnuts, how many 
 walnuts is 1 orange worth ? 
 
 35. A boy gave 8 apples for 18| marbles, how many 
 marbles did he get for 1 apple ? 
 
 36. A boy gave 7 cents for l7i crackers; liow 
 many did he get for 1 cent ? 
 
 37. Mary gave 10 pins for 23^ chestnuts ; how many 
 did she get for 1 pin ? 
 
 38. If 3 yards of broadcloth are worth 18| yards 
 of muslin, how many yards of muslin may be had for 
 1 yard of broadcloth ? 
 
DIVISION OF FRACTIONS. 
 
 83 
 
 39. If John can walk 13 miles while Josiah is walk- 
 32^ miles, how far can Josiah walk while John is 
 walking 1 mile? 
 
 40. If 2 chestnuts are worth T 2 7 of a cent, and 20 
 chestnuts are worth f of a lemon, how many cents is 
 1 lemon worth ? 
 
 41. If 2 oranges cost § of a cent, what will 1 orange 
 cost? 
 
 Solution.— If 2 oranges cost f of a cent, 1 orange will cost 
 \ of § of a cent, which is f of a cent. 
 
 42. If 3 yards of linen cost $lf, what will 1 yard 
 cost ? 
 
 43. If 7 yards of tape cost 13| cents, what will 1 
 yard cost? 
 
 44. If 2 pints of molasses cost If dimes, how many 
 cents will 1 gallon cost? 
 
 45. How many times 8 are 6f ? 
 
 46. How many times 6 are 5|? 
 
 47. How many times 4 are 4£ ? 
 
 48. How many times 2 are 13f ? 
 
 49. How many times 7 are.74? 
 
 50. How many times 8 are 9 times f-f -2 
 
 51. How many times 3 are 6 times Iff? 
 
 Solution.—I ff equals f |. 6 times are qj. 3 is con¬ 
 
 tained in - 2 5 - - 2 J1, or 3g times. 
 
 52. How many times 9 are 10 times 2 1 3 zr ? 
 
 53. How many times 7 are 5 times 3^? 
 
 54. How many times 5 are 15 times 3/^? 
 
 55. How many times 7 are 15 times If f ? 
 
 56. How many times 5 are 3 times 2| ? 
 
 57. How many times six are 4 times 5f ? 
 
 58. If If yards of cloth are worth $2f, what is 1 
 yard worth ? 
 
 59. If 6f bunches of grapes are worth 40 cents, 
 how many cents is 1 bunch worth ? 
 
 60. If 3f baskets of peaches are worth $5f, what is 
 1 basket of peaches worth ? 
 
84 
 
 FRACTIONS. 
 
 LESSON XI. 
 
 I. What is \ of 2 2 
 
 Solution.—| of 1 is $; and, if £ of 1 is £, £ of 2 is twice £, 
 which are f. Therefore £ of 2 is $- of 1. 
 
 2. What is i of 4 2 of 8 2 
 
 3. What is j- of 2 2 3 2 5 2 7 2 9 ? 
 
 4. What is i of 3? 5? 7? 9? 11? 
 
 5. What is £ of 2 2 3 ? 4 2 7 ? 8 2 
 
 6. What is J- of 2 2 3 2 5 2 7 2 9 ? 
 
 7. What is -I of 2 2 3 2 5 2 4 ? 6 ? 9 2 11 2 
 
 8. What is | of 2? 42 3? 5? 6? 7? 9? 
 
 9. What is i of 2 2 4? 7? G? 3? 122 11? 
 
 10. What is X V of 7 2 2 2 4 2 6 ? 9 2 14 2 15 2 
 
 II. If 2 apples cost 3 cents, what will 1 apple cost? 
 
 Solution. —If 2 apples cost 3 cents, 1 apple will cost ^ of 3 
 cents, which is §, or H cents. 
 
 12. If 2 apples cost 5 cents, what will 1 apple cost? 
 
 13. If 3 pens cost 8 cents, what will 1 pen cost? 
 
 14. If 3 yards of tape cost 14 cents, what will 1 
 yard cost 2 
 
 15. If 5 barrels of flour cost $21, what will 1 bar¬ 
 rel cost 2 
 
 16. If 7 pecks of dried apples cost 23 dimes, what 
 will 1 peck cost? 
 
 17. If 4 chickens cost 9 dimes, what will 1 chicken 
 cost 2 
 
 18. What will 1 pound of tamarinds cost, if 6 
 pounds cost 27 dimes 2 
 
 19. What will 1 barrel of flour cost, if 3 barrels 
 cost $25 2 
 
 20. If you divide 7 bushels of/wheat, equally, 
 among 5 persons, how much will each receive 2 
 
 21. Joshua had 13 marbles, and Lewis had \ as 
 many -f i of a marble; how many had he 2 
 
FRACTIONS. 
 
 85 
 
 22. A man divided 3 barrels of flour equally among 
 11 families ; what part of a barrel did each receive ? 
 
 23. A farmer divided 5 bushels of rye, equally, 
 among 7 of his poor neighbors; what part of a bushel 
 did he give to each ? 
 
 24. Calvin had 4 pints of nuts, and shared them, 
 equally, with 0 of his companions; how much did 
 each receive ? 
 
 25. Margaret, having 7 quarts of raspberries, shared 
 them, equally, with 8 of her playmates; what part of 
 a quart did each receive ? 
 
 26. What will 1 pound of prunes cost, if 5 pounds 
 cost 48 dimes ? 
 
 27. What will 2 boxes of figs cost, if 7 boxes cost 
 29 dimes ? 
 
 28. What will 4 quarts of strawberries cost, if 9 
 quarts cost 7 dimes ? 
 
 29. What is t of 2 ? 
 
 30. If T of 2 is f, what is § of 2 ? 
 
 31. What is f of 5 ? 
 
 Solution.—£ of 5 is and § are 2 times f, which are y°, 
 or 3 r. 
 
 32. What is £ of 3 ? of 5 ? 6 ? 7 ? 9 ? 11 ? 
 
 33. What is | of 2? of 3 ? 4 ? 9? 11 ? 13? 
 
 34. What is £ of 2 ? of 3 ? 5 ? 7 ? 9 ? 15 ? 
 
 35. What is £ of 3 ? of 5 ? 8 ? 9 ? 12 ? 20 ? 
 
 36. What is £ of 4? of 6 ? 8? 12? 11? 17? 
 
 37. What is | of 3 ? of 5 ? 6 ? 9 ? 10 ? 15 ? 
 
 38. What is T 3 T of 2 ? of 4 ? 5 ? 6 ? 10 ? 12 ? 
 
 39. What is T 5 2 of 2 ? of 4 ? 3 ? 9 ? 15 ? 21 ? 
 
 40. What is T \ of 7 ? of 8 ? 9 ? 12 ? 15 ? 25 ? 
 
 41. IIow many cents will § of a pound of candies 
 cost, if 1 pound cost 2 dimes ? 
 
 42. What will be the cost of f of a box of raisins, 
 if 1 box cost $3 ? 
 
 43. What will be the cost of f of a yard of cloth, 
 at 7 dimes a yard ? 
 
 8 
 
86 SIMPLE PROPORTION. 
 
 Pb 
 
 44. If a ton of hay cost $10, what will 2| tons 
 cost ? 
 
 45. Jeremiah is 91 years old, and f of his age equals 
 the age of his oldest son ; how old is he? 
 
 46. Bought 24 yards of cloth for $48; but, being 
 damaged 1 sold f of it, at $lf a yard, and the re¬ 
 mainder for what it cost. How much did I lose ? 
 
 47. Bought 14 yards of cloth ? and sold f of it, at 
 $2 a yard, which amounted to $2 less than the whole 
 piece cost. What did it cost a yard? 
 
 48. A horse was sold for $97, which was If times 
 as much as it cost. What did the horse cost? 
 
 49. If 9 yards of cloth cost $17, what will 3 yards 
 
 cost? - f ' 
 
 50. If 7 j T ards of cloth cost $25, what will 9 yards 
 cost ? 
 
 51. What will 2 pounds of opium cost, if 5 pounds 
 cost $42 ? 
 
 52. If 5 pounds of indigo cost $32, what will 2 
 pounds cost? 
 
 53. A wagon was sold for $90, which was f- of what 
 it cost. How much did it cost? 
 
 54. Two men started from the same place, and 
 traveled the same way ; one at the rate of 92 miles in 
 10 hours ; the other at the rate of lj 1 ^ miles in f of an 
 hour; how far apart will they be in 2 hours? 
 
 55. By a pipe 4f gallons of water run into a cistern 
 in 1 minute; how much did the vessel hold provided 
 it was filled in 9 minutes ? 
 
 56. If 7 men can perform a certain piece of work 
 in 13f days; how long would it take 4 men to do the 
 same ? 
 
 * 
 
 57. If 5 persons consume a barrel of flour in 9 
 weeks, what part of a barrel would they consume in 5 
 
 weeks ? 
 
 58. If a man earn $f in a day, and a boy $f, how 
 much will they both earn in 6 days ? 
 
87 
 
 iff $ y 
 
 it 
 
 SIMPLE PROPORTION. 
 
 59. Antliony spent 4 of all liis money, and the re^ 
 mainder he gave tor 8 yards of cloth, at $2y a }aid , 
 
 how much had lie at first ? 
 
 60. From a piece of cloth a tailor cut 5 garments, 
 each containing 3y yards; and there remained 2j 
 yards; how many yards did the piece contain ? 
 
 ^ 61. 1 What will 9 pounds of rice cost, if 7 pounds 
 
 cost 43 cents? . . . 
 
 62. An individual, after spending y-f ot all his 
 money, had only $40 remaining; how much had he 
 
 first ? 
 
 63. An old lady bought 30 eggs, at the rate of 2 
 
 for 5 cents; what did they cost? ^ 
 
 64. How much will 13 pounds of coftee cost, if 26 
 
 pounds cost $7 ? . 
 
 65. What will 7 gallons of molasses cost, it 6 pints 
 
 cost 27 cents ? 
 
 66. If 5 lamps cost $7y what will 7 lamps cost ? 
 
 67. If 5 horses can, in 4f days, consume 20 bushels 
 of oats, in how many days can 11 horses consume the 
 
 same? * - . . ,» 
 
 68. If 15 gold pens cost $20, what will 5 ot them cost i 
 
 69. If - of an acre of land be worth $14, what are 
 10 acres worth ? 
 
 70. $25 is 4 of the cost of B’s watch; what was 
 
 the cost of his watch ? • . 
 
 71. Mortimer’s hat cost $5, and f of the cost ot his 
 hat is T V of the cost of his coat; what was the cost of 
 
 his coat? - 
 
 72. If a man in T 4 y of a day walk 8 miles, how tar 
 
 can he walk in 5 days ? 
 
 73. From a piece of cloth containing 20 E. Ir., a 
 tailor cut 8 suits of clothes, each containing 2f yards; 
 how many yards remained ? 
 
 74. If a man can cut 1 cord of wood in 5 hours, 
 how many cords can he cut in 4 days, by working 12 
 hours a day ? 
 
88 
 
 W 
 
 l y . • _ t > 
 
 y \ r /c f 
 
 7* / 
 
 SIMPLE PEOPOETION, 
 
 75. A man bought 7 sheep, at the rate of 9 for 
 $5^4 what did they cost him ? 
 
 76. A boy bought 13 oranges,—giving 9 apples for 
 
 3 oranges ; how many apples did his oranges cost him ? ] 
 
 77. If 25 cents buy 7 lemons, how many cents will 
 
 9 lemons cost? .. / 
 
 78. | of 45 equals £ as many dollars as Andrew 
 has ; how many dollars has he? £ c, 
 
 79. $30-| is y of all the money A had ; how much 
 money had he ? 
 
 80. What will 3 pecks of flax-seed cost, if 3 pints 
 cost 3 dimes ? 
 
 81. What will 1 quart of clover-seed cost, if 2 pecks 
 cost $3 and 2 dimes. 
 
 82. 4i times 7 is i of what number ? 
 
 83. § of 36 is i of what number? 
 
 84. i of 36 is -f- times what number ? : * 
 
 85. | of A’s age is 3 times B’s age; and B is 9 
 years old. What is A’s age ? 
 
 86. An individual, being asked the number of hours 
 he labored each day, answered, li times the number 
 ot hours in a day is 3 times as many hours as I labor. 
 How many hours did he labor each day ? 
 
 87. | of 15 is -i of what number? 
 
 88. i of 21 is 11 times what number? 
 
 89. | of 24 is If times what number? 
 
 90. Wright is 16 years old, and 1£ times his age is 
 If times Charles’s age. How old is Charles? 
 
 »■ 
 
 LESSON XII. 
 
 LESSONS EIGHTH, NINTH, AND TENTH COMBINED. 
 
 S1W° Remark. — Pupils must exercise their own judgment in 
 employing the shortest of the methods given in lessons eighth and 
 tenth for multiplying and dividing. 
 
 1. If 3 barrels of flour cost $13£, what will 6 cost? 
 
 Solution.—$ 13£ equals If 3 barrels of flour cost $- 5 3 -, 
 
SIMPLE PROPORTION. 
 
 89 
 
 Tr 
 
 
 6 barrels, which are 2 times 3 barrels, will cost 2 times 
 which are $- 5 2 5 -, or $27|. 
 
 2. If 5 pounds of opium cost $27^, what will 20 
 
 pounds cost 2 ; 7 > - \ - */*.•:► 
 
 3. If 3 pounds of sugar cost l7f cents, wliat will 
 
 24 pounds cost ? 
 
 4. How many apples will pay for 9 oranges, if 8 
 apples are worth 12f oranges ? 
 
 Solution.—121 oranges equal - 64 - oranges. If - r /- oranges are 
 worth 8/apples £ of an orange is worth of 8 apples, which is 
 ^ or l of an apple-; and J, which is 1 orange, are worth 5 
 times g, or | of an apple, and 9 oranges are worth 9 times 
 which are - 4 8 -, or 5| applet. 
 
 Remark. —In solving questions in Proportion never seek the 
 value of a unit of the denomination like the answer. 
 
 5. How many chestnuts will pay for 9 walnuts, if 
 7 chestnuts are worth lOf walnuts? 
 
 6. If 8 barrels of flour cost $33f, what will 20 
 barrels cost ? 
 
 7. If it require 9f yards of cloth to make 3 coats, 
 how many yards will it require to make 8 coats .' „ 
 
 8. If 8 men can perform a certain piece of work in 
 9f days, how long will it take 5 men to perform the 
 
 same? # • 
 
 9. What will be the cost of 6 sheep, if 15 cost $10|? 
 
 10. If 1 person consume lOgV bushels of wheat in 
 a month, how much will 13 persons consume in the 
 
 same time ? / 3 C . 
 
 11. If 9£ cents will buy 4 peaches, what will be the 
 
 cost of 9 peaches ? J % 
 
 12. If $9 T V will pay for 5 weeks’ board, how many 
 dollars will pay for 8 weeks’ Doard ? g 
 
 13. If 6 orifices will fill a vessel in 3f hours, how 
 many of the same size will be required to fill it in y'y 
 
 of an hour ? v - i'¬ 
 ll. If 9 men can build a boat in 5| days, in how 
 many days could 6 men build it ? 
 
 8 * 
 
 v . *’c .. * j & * ~ z ''s ’ 1 y 
 
 u 
 
 
90 
 
 SIMPLE 
 
 PROPORTION., 
 
 < ■ L 
 
 15. If 2 men in 4 days can earn $ 12 , how many • 
 dollars can 7 men earn in the same time ? 
 
 16. If I pay 17§- cents for riding 4 miles, how much 
 must I pay for riding 6 miles ? j t ■ 
 
 17. What will 1 year’s board cost, at $5§ for 4 
 
 weeks? £ Y 
 
 18. If 9 barrels of fish cost $54£, what will 27 bar¬ 
 rels cost ? 7 - . v J j y ? / ! i 
 
 19. How raatiy dollars will 1 barrel of tobacco cost, 
 
 if 17 barrels cost 514 eagles? 7 
 
 20 . If 13 pounds of tea cost 10 | dimes, what will 
 5 pounds cost? 
 
 21 . If 7 1 tons of hay keep 6 horses through the I 
 winter, how many tons will keep 9 horses the same 
 time ? 
 
 22 . A fox is 40 rods before a hound and runs 3 rods 
 to the hound’s 5 ; how many rods must the hound run 
 to overtake the fox ? 
 
 23. How many dollars will a man earn in 14 days, 
 if he earn $3^ in 4 days ? 
 
 24. A merchant bought 8 pieces of cloth, each 
 piece containing 5 yards for $32£; how much did it 
 cost a piece, and how much a yard ? / TZ t » 1 7 ; 
 
 25. If in a certain time 6 horses eat 14f bushels of 
 oats, how many bushels will 8 horses eat in the same 
 time ? 
 
 26. A boy sold 3 lemons, at the^rate of 6 for 8 
 cents ; how much did he receive for them ? 
 
 27. A boy gave 4^ cents for oranges, at the rate of 
 5 oranges for 7 4 cents; how many did he buy ? 
 
 28. If a piece of mahogany weighing 9 pounds, is 
 worth $ 2 f, what \s the ; value of 42 pounds, at the 
 same rate? 
 
 29. If a pole 8 feet long cast a shadow 4f feet, what 
 will be the length of the shadow of a pole which is 15 
 feet long, at the same time of day ? 
 
 30. At a certain time of day, a pole 5 feet long 
 
 / 
 
 V 
 
 ,L I 
 
4 
 
 * / 4 
 
 I 
 
 REDUCTION OF FRACTIONS. 91 
 
 f- *i 4* ~ 4 - 
 
 casts a shadow 7^ feet; what is the length of that pole 
 which at the same time, casts a shadow 4£ feet ? 
 
 31. If it require $2If worth of provision to serve 8 
 men 2 days, how many dollar’s worth will serve 5 men 
 4 days ? 
 
 32. Vvdiat is the length of a pole the shadow of 
 which is 12 feet long, at the same time, a pole 2f feet 
 in length casts a shadow 4 feet long. v 
 
 n-<,* 2% 
 
 1i ;' i l; 
 
 LESSON XIII. 
 
 Bemark.—B y inspecting Lessons 8th and 10th, we observe, 
 that, multiplying both numerator and denominator by the same 
 number, does not alter the value of the fraction. Hence, to 
 convert a fraction to an equivalent fraction having a different 
 denominator, we may multiply both numerator and denominator 
 by any number which will cause the fraction to have the re¬ 
 quired denominator. 
 
 1. James gave his sister J of an apple ; how many 
 fourths was that ? 
 
 2. ~ is how many sixths? 
 
 3. Byron gave his sister \ of an apple, and his 
 brother J of an apple ; how many fourths did he give 
 away ? 
 
 4. \ is how many sixths ? 
 
 5. is how many sixths ? 
 
 6. j and i are how many sixths ? 
 
 7. f are how many sixths? 
 
 8. | are how many twelfths ? 
 
 9. f are how many twelfths? 
 
 10. J are how many eighteenths ? 
 
 11. f are how many tenths ? 
 
 12. § are how many tenths? 
 
 13. f are how many twentieths ? 
 
 14. is how many tenths? 
 
 15. Harris gave f of an orange to his sister; how 
 many fifteenths did he give her ? 
 
92 ADDITION AND SUBTRACTION 
 
 16. How many sixteenths in f ? 
 
 17. How many sixteenths in f ? 
 
 18. How many sixteenths in £ ? 
 
 19. How many fourteenths in ? 
 
 20. How many fourteenths in 4 2 
 
 21. How many fourteenths in -f ? 
 
 22. How many ninths in | ? 
 
 23. How many twentieths in | ? 
 
 24. How many fortieths in | ? 
 
 25. How many forty-ninths in 4 ? 
 
 26. How many fifteenths in | ? 
 
 27. A man gave } of a bushel of potatoes to one 
 poor woman, and T 3 ¥ of a bushel to another; what 
 part of a bushel did he give to both ? 
 
 28. How could you divide an apple so as to give f 
 of it to 1 boy, and ~ of it to another ? 
 
 29. f + | are how many fifteenths? 
 
 Solution. —§ equals f 6 j, and § equals T 6 5 and 4° are 
 
 or HV 
 
 30. | + | are how many twelfths? 
 
 31. |- + -| are how many eighteenths? 
 
 32. !■ +1 are how many twenty-fourths ? 
 
 33. 4 arc how many times ? 
 
 34. What is the sum of f and f ? 
 
 35. What is the sum of 4 and § ? 
 
 36. What is the sum of ~ and f ? 
 
 37. What is the sum of f and f ? 
 
 38. What is the sum of 4 and f ? 
 
 39. What is the sum of 4 and §■ ? 
 
 40. What is the sum of f and f ? 
 
 41. What is the sum of i and 4 ? 
 
 42. What is the sum of 4 and \ ? 
 
 43. What is the sum of J-, 4 and § ? 
 
 44. What is the sum of f, | and f ? 
 
 45. From f subtract 4 ? 
 
 46. From f subtract §. 
 
 47. From 4 subtract |. 
 
OF FRACTIONS. 
 
 48. From 24 subtract -f. 
 
 49. From 4 subtract 
 
 50. From 3 subtract f. 
 
 51. From 9 subtract -f. 
 
 52. From 5 subtract |. 
 
 53. From 3 subtract 1^. 
 
 54. From 9 subtract 2|. 
 
 55. From 6 subtract 3f. 
 
 * 56. 14 — 3^ are bow many? 
 
 57. 7 — 2f are how many? 
 
 58. 9 — 3-| are how many? 
 
 59. 10 — 3f are how many? 
 
 60. 12 — 3|- are how many? 
 
 61. 13 — 7y* r are how many? 
 
 62. 9| — 4i are how many? 
 
 63. 7| —5| are how many ? 
 
 64. 3^—1 t are how many? 
 
 65. 4-| —1| are how many? 
 
 66. 5| —2| are how many? 
 
 —437. 9f —7f are how many ? 
 
 68. 2f + 3i — f are how many? 
 
 69. 4| + 5| — 2f are how many? 
 
 70. 3J- + 4T — f are how many ? 
 
 71. 9| + 3f —3 are how many? 
 
 72. f-ff — a are how many? 
 
 73. f +1 + 4 — 4 are how many ? 
 
 74. 2| are how many times T 2 ¥ ? 
 
 75. 3| are how many times T 4 o ? 
 
 76. , 9 3 are how many times • 
 
 77. i are how many times ? 
 
 78. -f are how many times T \ ? 
 
 79. I} are how many times y 3 g ? 
 
 80. 4 are how many times T 2 y ? 
 
 81. T 5 ^ are how many times ^ ? 
 
 82. 8| are how many times 24 ? 
 
 83. 10| are how many times T 9 y ? 
 
 84. I 24 are how many times 1| \ 
 
94 
 
 REDUCTION or fractions. 
 
 85. £ + } + £ is h° w much less than a whole one ? 
 
 86. £+f + f is how much less than a whole one? 
 
 87. A lady gave £ of all her money for a dress, and 
 j of it for a shawl; what part of her money had she 
 remaining. 
 
 88. £ of an army was killed, and £ taken prison¬ 
 ers ; what part of the army escaped ? 
 
 89. | of an army was killed, £ taken prisoners, and 
 500 escaped; how many were there in the army? 
 
 90. | of the length of a pole is in the ground, £ of 
 it in the water, and 12 feet in the air; what is the 
 length of the pole ? 
 
 - 91. A market woman sold £ of all her oranges to 
 
 one man and £ of them to another, and then had only 
 9 remaining; how many had she at first, and how 
 many did she sell to each ? J / 
 
 92. A man, after spending £ of his fortune, found 
 
 that $20 was £ of what he had remaining ; what was 
 his fortune ? . r 
 
 93. A hawk caught |_ of Euphemia’s chickens, a 
 cat killed £ of them, £ of them died, and she had 13 
 remaining; how many had she at first, and how many 
 were destroyed by the hawk and cat respectively ? 
 
 94. Said A to B if to my age you add its £ and its |, 
 the sum will be 38 ; how old was he? 
 
 95. A is 40 years old, and £ of his age is f of twice 
 as much as his wife’s age ; how old was his wife? 
 
 (/ X j ) ~ ^ 
 
 . --o--e—-- 
 
 M “ 3 \ 
 
 b a LESSON XIV. ;} 
 
 Remark. —By inspecting Lessons 8th and 10th, we observe, 
 that dividing both numerator and denominator of a fraction by 
 the same number, does not alter its value. Hence to reduce a 
 fraction to its lowest terms, we may divide both numerator and 
 denominator by any number that is contained in each of them 
 without a remainder. 
 
 1. 
 
 Reduce £ to its lowest terms, 
 
 / ' 
 
 - 1'J 
 
REDUCTION OP FRACTIONS. 
 
 9a 
 
 2. Reduce f to its lowest terms. 
 
 3. Reduce f to its lowest terms. 
 
 4. Reduce ff to its lowest terms. 
 
 5. Reduce ff to its lowest terms. 
 
 6. Reduce ff to its lowest terms. 
 
 7. Reduce ff to its lowest terms. 
 
 8. Reduce f f to its lowest terms. 
 
 9. Reduce ff to its lowest terms. 
 
 10. Reduce ff to its lowest terms. 
 
 11. Reduce f f to its lowest terms. 
 
 12. Reduce T 7 ff to its lowest terms. 
 
 13. Reduce ff to its lowest-terms. 
 
 14. Reduce ff to its lowest terms. 
 
 15. Reduce ff to its lowest terms. 
 
 16. Why does the value of the fraction remain the 
 same, when you divide both numerator and denominator 
 by the same number ? 
 
 ( 17. When you multiply both numerator and de¬ 
 nominator by the same number, why does it not 
 change the value of the fraction ? 
 
 18. Reduce 4 times ff to its lowest terms. 
 
 19. Reduce 1 times T \ to its lowest terms. 
 
 20. Reduce 8 times 2f to its lowest terms. 
 
 21. Reduce 6 times ff to its lowest terms. 
 
 22. Reduce 4 times ff to its lowest terms. 
 
 23. Reduce 12 times ff to its lowest terms. 
 
 24. Reduce 12 times to its lowest terms. 
 
 25. Reduce 8 times to its lowest terms. 
 
 26. Reduce 7 times ff to its lowest terms. 
 
 27 . Reduce 5 times ff to its lowest terms. 
 
 28. Reduce 4 times ff to its lowest terms. 
 
 29. Reduce 6 times ff to its lowest terms. 
 
 30. Reduce 9 times ff to its lowest terms. 
 
96 
 
 COMPOUND FRACTIONS. 
 
 LESSON XV. 
 
 1 . If you cut an apple into two equal pieces, wliat 
 will 1 of these pieces be called ? 
 
 2 . If you cut \ of an apple into two equal pieces, 
 what part of a whole apple will 1 of these pieces be 
 called ? 
 
 3 . If Alice has i of a lemon, and gives 4 of it to 
 Ann, what part of a lemon will Ann receive ? 
 
 Solution .—} equals f. Therefore, Ann receives | of § of a 
 lemon, which is ^ of a lemon. 
 
 4 . George, having Y °f a melon, gave | of it to 
 Marcus ; what part of a melon did Marcus receive ? 
 
 5 . Crary had 4 of a dollar, and gave half of it to 
 Joshua; what part of a dollar did Joshua receive? 
 
 6 . Robert had j of a dollar, and gave 4 of it for a 
 cake ; how many cents did the cake cost him ? 
 
 7. Margaret had | of a pound of candies, and Mary 
 had \ as much ; how much had Mary ? 
 
 8 . Jane had 4 of a pouud of sugar, and Ann 4 as 
 much; how much had Ann? 
 
 9 . A boy bought a of a quart of chestnuts, and 
 gave 4 of them to his sister; what part of a quart did 
 she receive ? 
 
 10 . A man owned | of a share in a bank, and sold 
 4 of that; what part of a share had he remaining? 
 
 11 . B owned j of a ship, and sold 4 of his share; 
 what part of a whole ship did he sell ? 
 
 12 . What is 4 0 f i‘t 
 
 Solution.— i of ^ is jR. 
 
 13. What is i of i? 
 
 14. What is 4 of 
 
 15. What is i of 
 
 16. What is 4 of 4 ? 
 
 17. What is 4 of t? 
 
 18. What is 4 of i? 
 
COMPOUND FRACTIONS. 
 
 97 
 
 19. What is i of 1? 
 
 20. What is T V of |? 
 
 21. A kite was up in the air and fell f of the way 
 to the ground, it then arose £ of its distance from the 
 ground ; what part of the whole distance was it above 
 the ground ? 
 
 22. Homer is | as old as his father, and Nelson is 
 £ as old as Homer; what part of the father’s age is 
 Nelson’s age ? 
 
 23. A man, owning | of a barrel of fish, accom¬ 
 modated his neighbor w’ith y of it; how much had he 
 remaining; ? 
 
 24. A man, having J- of an eagle, gave | of it to B, 
 and B gave T y of what he had to C ; vdiat part of an 
 eagle had each after this division, and how many cents 
 had each ? 
 
 25. Elizabeth had f of a pie, and gave ^ of it to 
 Harriet; how much did she receive ? 
 
 i 
 9 > 
 
 Solution. —of i is g; and if £ of } is j, \ of § is twice 
 which are f. Therefore Harriet had f of a pie. 
 
 Or, Solution. —^ of f is f. 
 
 26. 
 
 What 
 
 is 
 
 1 
 
 2 
 
 of 
 
 3 9 
 
 5 • 
 
 27. 
 
 What 
 
 is 
 
 1 
 
 4 
 
 of 
 
 2. 9 
 
 3 * 
 
 28. 
 
 What 
 
 is 
 
 1 
 
 5 
 
 of 
 
 2 2 
 
 3 * 
 
 29. 
 
 What 
 
 is 
 
 1 
 
 5 
 
 of 
 
 3 2 
 
 4 • 
 
 30. 
 
 What 
 
 is 
 
 1 
 
 7 
 
 of 
 
 3 2 
 
 4 * 
 
 31. 
 
 What 
 
 is 
 
 1 
 
 8 
 
 of 
 
 A 2 
 
 5 • 
 
 32. 
 
 What 
 
 is 
 
 1 
 
 9 
 
 of 
 
 2 9 
 
 3 * 
 
 33. 
 
 What 
 
 is 
 
 1 
 
 9 
 
 of 
 
 4 2 
 
 5 • 
 
 34. 
 
 What 
 
 is 
 
 1 
 
 8 
 
 of 
 
 .3 2 
 
 6 * 
 
 35. 
 
 What 
 
 is 
 
 1 
 
 5 
 
 of 
 
 3 2 
 
 5 • 
 
 36. 
 
 What 
 
 is 
 
 4 
 
 of 
 
 J5_ 2 
 
 1 3 * 
 
 37. 
 
 What 
 
 is 
 
 1 
 
 9 
 
 of 
 
 3 2 
 
 8 * 
 
 38. 
 
 What 
 
 is 
 
 1 
 
 f 
 
 of 
 
 1 2 
 
 7 * 
 
 39. 
 
 What 
 
 is 
 
 i 
 
 f 
 
 of 
 
 12 2 
 
 7 ’ 
 
 40. 
 
 What 
 
 is 
 
 2 
 
 3 
 
 of 
 
 1 2 
 
 4 * 
 
 9 
 
98 
 
 3 l 
 
 COMPOUND FRACTIONS. 
 
 41. 
 
 What 
 
 is £ 
 
 of 
 
 12 
 
 5 • 
 
 
 
 42. 
 
 What 
 
 is | 
 
 of 
 
 JL 2 
 
 7 ‘ 
 
 
 
 43. 
 
 What 
 
 is f 
 
 of 
 
 JL 2 
 
 9 * 
 
 
 
 44. 
 
 What 
 
 is £ 
 
 of 
 
 1 2 
 
 7 * 
 
 
 
 45. 
 
 What 
 
 is £ 
 
 of 
 
 1 2 
 s ’ 
 
 
 
 46. 
 
 What 
 
 is £ 
 
 of 
 
 1 2 
 
 9 * 
 
 
 
 47. 
 
 What 
 
 is ¥ 
 
 of 
 
 1 2 
 
 4 * 
 
 
 
 48. 
 
 What 
 
 is £ 
 
 of 
 
 1 2 
 
 8 * 
 
 
 
 49. 
 
 What 
 
 is 4 
 
 of 
 
 1 2 
 
 6 * 
 
 
 
 50. 
 
 What 
 
 is * 
 
 of 
 
 1 2 
 
 4 * 
 
 
 
 51. 
 
 What 
 
 is | 
 
 of 
 
 3 2 
 
 ¥ * 
 
 
 
 52. 
 
 What 
 
 is } 
 
 of 
 
 2 2 
 
 5 • 
 
 
 
 53. 
 
 What 
 
 is -1 
 
 of 
 
 2 2 
 
 7 * 
 
 
 
 54. 
 
 What 
 
 • 
 
 !S | 
 
 of 
 
 2 2 
 
 8 " 
 
 
 
 55. 
 
 What 
 
 is | 
 
 of 
 
 3 2 
 
 5 * 
 
 
 
 56. 
 
 What 
 
 is £ 
 
 of 
 
 i. 2 
 
 7 ' 
 
 
 
 57. 
 
 What 
 
 is j 
 
 of 
 
 3. 2 
 
 7 ‘ 
 
 
 
 58. 
 
 What 
 
 is £ 
 
 of 
 
 1 2 
 
 9 * 
 
 
 
 59. 
 
 What 
 
 is 4 
 
 of 
 
 J. 2 
 
 7 * 
 
 
 
 60. 
 
 What 
 
 1S Ti 
 
 of 
 
 2 2 
 
 3 * 
 
 
 
 61. 
 
 What 
 
 part 
 
 of 
 
 1 i 2 . 
 
 x x 3 
 
 of 
 
 1 2 
 
 5 * 
 
 62. 
 
 What 
 
 part 
 
 of 
 
 1 is £ 
 
 of 
 
 J. 2 
 
 6 • 
 
 63. 
 
 W T hat 
 
 part 
 
 of 
 
 2 is £ 
 
 of 
 
 12 
 
 3 * 
 
 Solution.— 4 of \ 
 
 is§. 1 
 
 is JL of 2. If 1 
 
 is £ 
 
 of 2, £ 
 
 i, or T*B 
 
 of 2, and 
 
 | are 2 times 
 
 Vgj or ^ °f 
 
 2. 
 
 
 64. 
 
 What 
 
 part 
 
 of 
 
 2 is j 
 
 of 
 
 1 £? 
 
 65. 
 
 What 
 
 part 
 
 of 
 
 2 is | 
 
 of 
 
 1 2 
 
 3 * 
 
 66 . 
 
 AVhat 
 
 part 
 
 of 
 
 3 is £ 
 
 of 
 
 1 2 
 
 2 * 
 
 67. 
 
 What 
 
 part 
 
 of 
 
 4 is £ 
 
 of 
 
 U 2 
 
 ± 5 * 
 
 68 . 
 
 What 
 
 part 
 
 of 
 
 5 is 1 
 
 of 
 
 2 2 
 
 3 * 
 
 69. 
 
 AVhat 
 
 part 
 
 of 
 
 9 is £ 
 
 of 
 
 11 2 
 
 A 3 ’ 
 
 70. 
 
 What 
 
 part 
 
 of 
 
 2 is £ 
 
 of 
 
 Ji 2 
 
 4 * 
 
 71. 
 
 AVhat 
 
 part 
 
 of 
 
 2 is £ 
 
 of 
 
 2 i ? 
 
 72. 
 
 AVhat 
 
 part 
 
 of 
 
 4 is £ 
 
 of 
 
 3_ 2 
 
 0 • 
 
 73. 
 
 AVhat 
 
 part 
 
 of 
 
 6 ’ is £ 
 
 of 
 
 1 2 
 
 6 * 
 
 74. 
 
 AVhat 
 
 part 
 
 of 
 
 3 is £ 
 
 of 
 
 42 2 
 * 5 * 
 
99 
 
 compound fractions. 
 
 t of I2ff 
 2 of 10# ? 
 
 75. What part of '4 is 
 
 76. What part of 7 is ? ux 1UA , 
 
 } 77 ' Anthon y had i of | of a pound of cinnamon: 
 what part of a pound had he ? ! 
 
 78. Albert lmd j of f of a quart of strawberries; 
 how many strawberries had he, provided 1 quart con- 
 tamed 42 strawberries ? ^ 
 
 A ^ nc ! S avc t of -f of a melon to his brother; 
 wnat part of a melon had he remaining? 
 
 80. Matilda bought # of a quart of milk for tea, 
 
 and spilled 3 of it; what part of a quart had she re- 
 maimng ? 
 
 81. Edwin picked J of a pail-full of blackberries, 
 and on bis way home spilled i of them ; what part of 
 a paii-full had he remaining ? 
 
 82. A merchant bought f of a hogshead of molasses, 
 
 and j of it leaked out; what part of a hogshead had 
 ne remaining? ° 
 
 t 83- Mirriam had | of a pound of candies, and gave 
 
 t of them to Augusta; what part of a pound did she 
 give Augusta? L 
 
 84. Elisha found If and gave | of it to Ephraim; 
 ^hat pait of a dollar had he remaining? 
 
 So. Andrew bought | of a pound ^of maple-sugar, 
 and gave t of it to Walter; what part of a pound did 
 
 86. Jacob, having a pine-apple, gave f of 4 of it 
 to the one that could tell how much that would be • 
 wnat part of a melon had Jacob remaining? 
 
 87. James gave f of f of a dime for a’top; how 
 much did the top cost him ? 
 
 88. Robert gave f of a dollar for a cap ; how much 
 did the cap cost him ? 
 
 89. Mary gave } of If dimes for a comb; how 
 many cents did the comb cost her? 
 
 90. Clarinda gave f of 6 dimes for a pair of gloves: 
 how many cents did the gloves cost her ? 
 
100 
 
 SIMPLE PROPORTION. 
 
 91. A man, having 4f barrels of flour, sold - of it 5 
 
 how much remained unsold ? ■■ 
 
 92. A man gave f of $31 for a silver pencil; what 
 
 was the cost ot the pencil ? . 
 
 93 Jane worked 8 f hours m a day, and Delilah 
 worked only f as many; how many hours did she 
 
 work in a day ? . 
 
 94 . B gave $32§ for a cow, which was f as much 
 
 as A gave for his; how much more did B’s cow cost 
 
 than A’s ? _ . . . ,, 
 
 95 . Darius is 18£ years old, and Daniel is f as old; 
 
 how old is he ? ... „ 
 
 96. If 1 yard of cloth cost $5f, what will f ot a 
 
 veil'd cost ? 
 
 97. If 4 yards of cloth cost $9£, what will f of a 
 
 yard cost ? 
 
 98. If 5 barrels of beef cost $18£, what will i of a 
 
 "b arre l cost ? 
 
 99. If | of an apple cost f of a cent, what will 1 
 apple cost ? 
 
 100. If d of an orange cost 14 cents, what will T e 
 of an orange cost? 
 
 101. If 4 pounds of butter cost 6J- dimes, how many 
 cents will If pounds cost? 
 
 - 
 
 LESSON XVI. 
 
 1. If 4 barrels of flour cost $14§, w T hat will f of a 
 
 cost» • 
 
 2. If 3 bushels of potatoes cost 5| dimes, what will 
 
 14 bushels cost ? 
 
 3. If 21 bushels of apples cost dimes, how many 
 
 cents will 4 of a bushel cost ? ... 
 
 4. If f of an apple cost | of a cent, w r kat will 1 
 
 apple cost ? 
 
DIVISION OP FEACTIONS. 
 
 101 
 
 5. If f of an orange cost £ of a cent, what will -3 
 
 of an orange cost ? 4 
 
 6 . If 2 £ yards of cassimere cost $ 3 £, what will 5\ 
 
 yards cost? 2 
 
 V. If 5f yards of shalloon cost $ 5 T \, what will 2 
 yards cost ? 
 
 8 . II in 3-f hours, A can do a certain piece of work, 
 how long will it take him to do a piece of work 12 . 
 times as large ? 5 
 
 9 £ of A's age is f of B’s; and £ of B’s age is f 
 oi C s age. How old are A and B respectively, pro¬ 
 vided C is 81 years old ? 
 
 10 Bought 3| boxes of goods, at $ 6 / r a box, and 
 
 paid for it with sheep, at $2 a head; how many sheep 
 did it take ? J 1 
 
 11 . How many times f is £ ? 
 
 Solution.— 1 is contained in £, f times; and, if l i s con . 
 tamed in £, f times, 1 is contained in £ 5 times £ times, whict 
 are \ 5 - times, and f is contained in it, \ of \ 5 - times, which is 
 V- times, or 1 \ times. 
 
 12 . 
 
 How 
 
 many 
 
 times 
 
 2 
 
 3 
 
 is 
 
 3 2 
 
 4 * 
 
 13. 
 
 How 
 
 many 
 
 times 
 
 2 
 
 "3 
 
 is 
 
 1 2 
 
 8 • 
 
 14. 
 
 How 
 
 many 
 
 times 
 
 3 
 
 5 
 
 is 
 
 -6 2 
 
 7 * 
 
 15. 
 
 How 
 
 many 
 
 times 
 
 3 
 
 8 
 
 is 
 
 -JL 2 
 16* 
 
 10 . 
 
 How 
 
 many 
 
 times 
 
 2 
 
 X 
 
 is 
 
 l± 2 
 
 3 * 
 
 17. 
 
 How 
 
 many 
 
 times 
 
 2 
 
 7 
 
 is 
 
 -JL 2 
 
 14* 
 
 18. 
 
 How 
 
 many 
 
 times 
 
 2 
 
 X 
 
 is 
 
 1 2 
 
 8 * 
 
 19. 
 
 How 
 
 many 
 
 times 
 
 4 
 
 5 
 
 is 
 
 93 ? 
 
 ° 7 • 
 
 20 . 
 
 How 
 
 many 
 
 times 
 
 3 
 
 4 
 
 is 
 
 2 f? 
 
 21 . 
 
 How 
 
 many 
 
 times 
 
 3 
 
 7 
 
 is 
 
 2 f? 
 
 22 . 
 
 How 
 
 many 
 
 times 
 
 5 
 
 9 
 
 is 
 
 55 2 
 
 23. 
 
 IIow 
 
 many 
 
 times 
 
 o 
 
 X 
 
 is 
 
 JL 2 
 
 10* 
 
 24. 
 
 How 
 
 many 
 
 times 
 
 4 
 
 7 
 
 is 
 
 JL2 2 
 
 1 4 • 
 
 3i? 
 
 25. 
 
 IIow 
 
 many 
 
 times 
 
 5 
 
 0 
 
 is 
 
 26. 
 
 How 
 
 many 
 
 times 
 
 7 
 
 8 
 
 is 
 
 41 2 
 
 27. 
 
 How 
 
 many 
 
 times 
 
 9* 
 
 H 
 
 is 
 
 2± 2 
 
 ^2 • 
 
102 
 
 
 DIVISION i 
 
 OF FRACTIONS. 
 
 28. 
 
 How 
 
 many 
 
 times 
 
 2 f 
 
 is 
 
 11 % 
 
 A 5 * 
 
 29. 
 
 How 
 
 many 
 
 times 
 
 H 
 
 is 
 
 51 2 
 
 °5 * 
 
 30. 
 
 How 
 
 many 
 
 times 
 
 42 
 
 3 
 
 is 
 
 53 2 
 
 31. A farmer sold a quantity of rye for $96, which 
 was only f of what it was worth ; how much did he 
 lose by the bargain ? 
 
 32. A man sold a cow for If times what she cost 
 him, and by so doing gained $6 ; how much did the 
 cow cost him ? 
 
 33. A merchant sold a quantity of goods for || of 
 what they cost, and by so doing, he lost $15 ; how 
 much did the goods cost him ? 
 
 34. A farmer, having lost 12 sheep, found, that only 
 •J of his flock remained ; how many sheep had he re¬ 
 maining ? 
 
 35. An individual being asked how many geese he 
 had, answered, that if to of his flock 24 geese were 
 added, the sum would equal If times his original 
 flock; how many geese had he ? 
 
 36. If | of a yard of cloth cost $f, what will f of a 
 yard cost ? 
 
 37. A boy, being asked his age, said, that 8f years 
 was | of twice as much as his age ; how old was 
 he? 
 
 38. If | of the candies I have cost 7f cents, what 
 will f of them cost ? 
 
 39. What will f of a barrel of flour cost, if f of a 
 barrel cost $2f ? 
 
 40. What will -f of an orange cost, if f of an orange 
 cost 2f cents ? 
 
 41. How many yards of cloth will be required to 
 make a coat, if 1| yards will make f of a coat? 
 
 42. |- of 2 are now many times f ? 
 
 43. of 8 arc how’ many times \ ? 
 
 44. | of 7 arc how many times 3 ? 
 
 45. f of 8 are how many times f ? 
 
 46. | of 12 are how many times § of 6 ? 
 
FRACTIONS. 
 
 103 
 
 47. f of 7 are how many times f of 2 ? 
 
 48 If § of 3 yards of cloth cost $1J, what will f of 
 7 yards cost ? 5 
 
 jit 9 , *£ I of ® y ards 0 of clo «i cost $2f, how much 
 Will | of 7 yards cost ? 
 
 1 nf °2 1 f °/ a b f 1TeI ° f flour cost w hat will 
 
 2 °1 f of | of a barrel cost ? 
 
 LESSON XVII. 
 
 1. 12 
 
 f of 
 
 what number ? 
 
 Solution. Iff of some number is 12, I of that number is l 
 
 0 1 ft 0r mi! atK * T whicJl is that number, are 4 times 4 which 
 
 ATfi l r Therefore 12 is £ of 16. 
 
 are 16 
 
 2 , 
 
 3, 
 
 4, 
 
 6. 
 
 '7. 
 
 8 . 
 
 9. 
 
 10 . 
 
 11 . 
 
 12 . 
 
 13. 
 
 14. 
 
 15. 
 1G. 
 
 17. 
 
 18. 
 
 19. 
 
 20 . 
 
 15 
 
 18 
 
 20 
 
 26 
 
 25 
 
 30 
 
 32' 
 
 36 
 
 36 
 
 36 
 
 24 
 
 9 
 
 12 
 
 38 
 
 16 
 
 16 
 
 16 
 
 40 
 
 40 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 3 
 5 
 2 
 T 
 
 4 
 
 5 
 2 
 3 
 J> 
 
 7 
 
 £. 
 
 8 
 8 
 9 
 6 . 
 
 7 
 
 _6 
 
 1 1 
 
 £ 
 
 2 
 
 £ 
 
 7 
 
 £ 
 
 7 
 
 A 
 
 5 
 
 £ 
 
 3 
 
 A 
 
 5 
 
 4. 
 
 7 
 2 
 5 
 
 5. 
 
 8 
 
 £ 
 
 9 
 
 of what number? 
 of what number? 
 what number? 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 Solution.— 40 is £ of 45. 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 Avhat 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 what 
 
 number? 
 number? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 
 n J^n» K ;iU W i hen P T. ls are famiUar With the analysis of these 
 solution ’ ^ termed|ate steps ma ^ be omit ‘cd, as in the above 
 
104 
 
 FRACTIONS. 
 
 21. 72 is f of what number? 
 
 22. 72 is t 9 o of what number ? 
 
 23. 12 is | of how many times 2? 
 
 24. 16 is | of how many times 3 ? 
 
 25. 18 is f of how many times 9 ? 
 
 26. 32 is 4 of how many times 4 ? 
 
 27. 46 is § of how many times 23 ? 
 
 28. 48 is | of how many times 5 ? 
 
 29. 48 is 4 of how many times<4 ? 
 
 30. 36 is 4 of how many times 2 ? 
 
 31. 30 is | of how many times 4 of 12 ? 
 
 32. 30 is 4 of how many times 4 of 10? 
 
 33. 16 is f of how many times | of 9 ? 
 
 34. 16 is T \ of how many times f of 16 ? 
 
 35. 24 is f of how many times | of 12? 
 
 36. 25 is f of how many times 4 of 9 ? 
 
 37. 35 is t 5 3 of how many times f of 9 ? 
 
 38. 40 is f of how many times f of 10 ? 
 
 39. 48 is T % of how many times | of 25? 
 
 40. 96 is | of how many times f of 16 ? 
 
 LESSON XVIII. 
 
 1. | of 6 is f of what number ? 
 
 2. a of 10 is f of what number? 
 
 3. | of 8 is f of what number ? 
 
 4. 4 of 21 is f of what number? 
 
 5. 4 of 15 is T \ of what number? 
 
 6 . y 3_ of 40 is f of what number ? 
 
 7. A of 27 is | of what number? 
 
 8. | of 27 is t 8 3 of what number? 
 
 9. | of 81 is t 9 o of what number? 
 
 10. 4 of 49 is t 6 t of what number? 
 
 11. | of 12 is 4 of how many times 2 ? 
 
 12. | of 16 is | of how many times 2 ? 
 
 13. | of 10 is 4 of how many times 4 ? 
 
fractions. 
 
 105 
 
 14. I of 16 is ^5 of liow many times 6 ? 
 
 15. jr ot 15 is f of how many times 6 ? 
 
 16. | of 20 is | of how many times 3 ? 
 
 17. £ of 12 is § of how many times 5 ? 
 
 18. | of 20 is f of how many times 3 ? 
 
 19. £ of 36 is f-i of how many times 4 ? 
 
 20. | ot 72 is | of how many times 12 ? 
 
 Solution.—| of 72 is 64. 64 is f of 96. 96 is 8 times 12. 
 
 21. f of 96 is. | of how many times 90 ? 
 
 22. f- of 117 is f of how many times 4 ? 
 
 23. £ of 56 is £ ot how many times 8 ? 
 
 24. £ of 60 is | of how many times 5 ? 
 
 25. £ ot 36 is | of how many times 12 ? 
 
 26. £ of 72 is £ of how many times 5 ? 
 
 27. f of 40 is T 5 ^ of how many times 21 ? 
 
 28. f of 32 is 4. of how many times 9 ? 
 
 29. £ of 15 is £ of how many times 2 ? 
 
 30. £ of 15 is £ of how many times 9 \ 
 
 31. f of 24 is £ of how many times 3 ? 
 
 32. £ of 45 is £ of how many times 3 ? 
 
 33. 5 of 14 is | of how many times 5 ? 
 
 34. i of 18 is f of how many times 7 ? 
 
 35. T 9 - of 40 is £ of how many times 6 ? 
 
 36. | of 45 is T 6 T of how many times 3 ? 
 
 37. £ of 35 is £ of how many times 2 ? 
 
 38. | of 81 is i of how many times 9 ? 
 
 39. | of 5 is £ of how many times 7? 
 
 40. f of 7 is f of how many times 3 ? 
 
 41. 11 s horse cost $>60, and ~ of the cost of the 
 lorsc, is y of two times the value of his wagon ; what 
 is the value of his wagon ? 
 
 • ^ coat cost $20, and £ of the cost of the coat 
 
 is f of .8 times the price of a hat; the price of the hat 
 
 is required ? 
 
 . 43 - a cow cost $30, and | of this, is f of 10 
 times the price of a sheep; what is the price of a 
 sheep ? 
 
106 
 
 FRACTIONS. 
 
 44. A’s farm is worth $1200, and § of its value, is 
 | of 10 times the value of its yearly productions; 
 what is the value of the yearly productions ? 
 
 45. The articles contained in a certain store cost 
 $500, and T 3 F of their cost is | of 3 times the amount 
 paid for the silks; how much was the cost of the 
 silks, and of the other articles respectively ? 
 
 46. A’s wedding clothes cost $180, and f- of the 
 cost of his clothes, is f of 6 times the cost of his 
 wife’s wedding dress ; how much was the cost of her 
 dress ? 
 
 47. The insurance of a ship amounted to $800, and 
 t of that is -^0 °f ^ times the value of the cargo ; 
 what is the value of the cargo ? 
 
 48. A’s house cost $1400, and f of its cost, is 3^ 
 times t of the cost of the furniture contained in it; 
 what was the cost of the furniture ? 
 
 49. Provided a house was worth $1200, and f of its 
 value was § of \ times the value of the farm on which 
 it stood ; what was the value of the farm ? 
 
 50. If a sleigh cost $100, what would be the cost of 
 a wagon, if § of the cost of the sleigh was T 2 T of twice 
 the cost of a wagon ? 
 
 51. Lambert is worth $2500, and of his fortune is 
 3T times t of Latham’s fortune ; how much is Latham 
 worth ? 
 
 Distances on the Railroad between Albany and Buffalo. 
 
 52. The distance from Albany to Schenectady, is 
 16 miles, and f of this distance, is f of t times the 
 distance from Albany to Rome ; what is the distance 
 to Rome ? 
 
 53. Fort-Plain is 56 miles from Albany, and ^ of 
 this distance is If times of the distance from Al¬ 
 bany to Rochester; what is the distance to Rochester ? 
 
 54. Waterloo is 192 miles from Albany, and f- of 
 this distance is If times the distance from Albany 
 
FRACTIONS. 
 
 107 
 
 to Utica, and 3 miles more; what is the distance to 
 Utica? 
 
 . 55 * Buffalo is 325 miles from Albany, and f of this 
 distance is 7 ~ times of the distance to Batavia, and 
 5 miles more ; what is the distance from Albany to 
 Batavia ? ' J 
 
 Distances on the Railroad between Albany and Boston. 
 
 56. Boston is 200 miles from Albany, and | of this 
 distance, is ly times 4- of the distance to West Spring- 
 field ; what is the distance to West Springfield ? 
 
 57. From Albany to the State line is 38 miles, and 
 
 1 \ times this distance, is times j of the distance to 
 Wilbraham 5 what is the distance to Wil brail am ? 
 
 58. Kinderhook is 16 miles from Albany, and £ of 
 this distance, is ~ times of the distance to Dalton 5 
 what is the distance to Dalton ? 
 
 59. Brighton is 195 miles from Albany, and | of 
 this distance is £ of 2 times the distance to Worcester 5 
 what is the distance to Worcester ? 
 
 _ 60. Grafton is 162 miles from Albany, and f of this 
 distance is — of 3 times the distance to Westfield, less 
 
 2 miles ; how far is it to Westfield ? 
 
 LESSON XIX. 
 
 1. f of 9 is |- of how many times £ of 25 ? 
 
 2 . £ of 16 is 1 of how many times ~ of 21 ? 
 
 3. I of 40 is | of how many times \ of 16 ? 
 
 4. | of 80 is | of how many times £ of 21 ? 
 
 5. | of 36 is l of how many times £ of 12 ? 
 
 6. of 45 is £ of how many times £ of 14? 
 
 7. f of 30 is | of how many times \ of 10? 
 
 8. of 48 is i of how many times £ of 7 ? 
 
 9. | of 45 is | of how many times £ of 8 ? 
 
 Solution.—| of 45 is 36. 36 is § of 162. 
 
 is 27 times 6. 
 
 £ of 8 is 6. 
 
 162 
 
108 
 
 FRACTIONS. 
 
 ylO. f of 35 is i of how many times | of 11|? 
 
 11. £ of 54 is f of how many times | of 10f ? 
 
 12. | of 25 is | of how many times f of 10 ? 
 
 13. \ of 28 is | of how many times | of 25? 
 
 14. £ of 18 is | of how many times f .of 12 ? 
 
 15. £ of 36 is £ of how many times £ of 12 ? 
 
 16. f t of 54 is I of how many times £ of 16 ? 
 
 lV. i of 32 is §- of how many times f of 9 ? 
 
 18. | of 108 is | of how many times § of § of 15 ? 
 
 19. £ of 40 is t 5 2 of how many times f of f of 20? 
 
 20. £ of 20 is | of how many times | of £ of 12 ? 
 
 LESSON XX. 
 
 1. If 1 horse eat £ of a hush el of oats in 1 day, 
 how many horses will eat a bushel in the same 
 time ? 
 
 2. If the wages of 8 weeks amount to $48, what 
 will the wages of 2£ weeks amount to ? 
 
 3. A ship’s crew of 12 men have provision for 5 
 months ; how man}?- months will it last 5 men ? 
 
 4. A man gained $14 by selling a watch for If 
 times what it cost him; how much did it cost him ? 
 
 5. There is a pole, £ of its length is under w r ater, 
 and 9 feet out; how long is the pole ? 
 
 6. A pole is standing in the water, so that 15 feet 
 is above the water, which is £ of the whole length of 
 the pole ; how long is the pole? 
 
 7. If | be 2 what will 2 be ? 
 
 8. If 8 horses can in 1 day eat 4 bushels of oats, 
 in how many days can 1 horse eat 1 bushel ? 
 
 9. If 3 horses can in 1 day eat If bushels of oats, 
 how many bushels can 1 horse eat in 4 days ? 
 
 10. If 1 horse in 2 days can eat 6 bushels of corn, 
 how many bushels will 4 horses eat in 3 days ? 
 
COMPOUND PROPORTION. 
 
 109 
 
 11. If 4 horses eat 10 bushels of grain in 2 days, 
 how many bushels will 3 horses eat in 12 days ? 
 
 12. How many tons of hay will 3 horses consume 
 in 4 days, if 4 horses in { of a day consume f of a 
 ton ? 
 
 13. How many hundred weight of hay can 3 horses 
 consume in 25 days, if 2 horses in J- of a day consume 
 4^-g- of a hundred weight ? 
 
 14. In how many days can 4 men cut 16 cords of 
 wood, if 1 man in 1 day cut | of a cord ? 
 
 15. How many men will be required to earn 20 
 dimes in 4 days, if 4 men in. 2f days earn 11 dimes ? 
 
 10. If it require 6 days for 2 men to lay 36 rods of 
 wall, how many men can in t of the time build 72 rods 
 of similar wall ? 
 
 17. It in 4 days 3 men accomplish a certain piece 
 of work, how many men will be required, to perform 
 a piece of work 4 times as large in 2 days? 
 
 18. If 4 men in 8 days perform a certain piece of 
 work, how many men will be required to accomplish 
 3 times as much work in f of a day ? 
 
 19. It 1 horse eat 1 bushel of oats in 4 days, in 
 how many days would 0 horses eat 48 bushels? 
 
 20. If f of 0 be 3, what will t of 40 be ? 
 
 21. If 3 be | of 6, what will ± of 40 be ? 
 
 22. If 2 men in } of a day earn T 5 2 of a dollar, in 
 
 how many days can 3 men earn f of a dollar ? 
 
 23. If it require of a bushel of oats to feed 4 
 horses { of a day, how many horses would it require 
 to consume 9 bushels in f of a day ? 
 
 Suggestion.- — Review unless the pupils thoroughly under¬ 
 stand the preceding Chapters. 
 
 The study of Chapter VII. may he omitted until the class 
 has learned Chapter VIII., (excepting the miscellaneous ques¬ 
 tions.) 
 
110 
 
 questions. 
 
 CHAPTER VII. 
 
 LESSON I. 
 
 1. $24 is | of twice as much as a cask of wine 
 cost; what did the wine cost ? 
 
 2. Bought 30 barrels of flour, and f of the num¬ 
 ber of barrels, equaled 4 as many dollars as they all 
 cost; what did 1 barrel cost ? 
 
 3. 35 is f of how many times § of 4 ? 
 
 4. A farmer, being asked how many sheep he had, 
 answered, that 160 was § of 10 times his number; 
 how many sheep had he ? 
 
 5. Mr. B, being asked the value of his horse, said, 
 $54 is t 6 t of 3 times its value; what is the value of 
 his horse ? 
 
 6. 72 is f of how many times f of 12 ? 
 
 7. 36 is | of how many times § of 12 ? 
 
 8. 48 is | of how many tknes \ of 18 ? 
 
 9. 56 is f of how many times % of 8 ? 
 
 10. 60 is | of how many times f- of 16 ? 
 
 11. 84 is L2- of how many- times ^ of 25 ? 
 
 12. A spent $60, which was f of 4 times as much 
 as he was worth ; how much w r as he worth? 
 
 13. B sold 9 sheep, which was T \ times ]• of his 
 whole flock; how many sheep had he remaining? 
 
 14. D, at a game of cards, lost $20, which was 4 
 
 times f of all the money he had ; how much had 
 he ? • . 
 
 15. C found $45, which ivas f of 3 times as much 
 as he already had; how much more did he find than 
 he had at first ? 
 
 16. A boy lost 9 marbles, which was | of twice as 
 many as he had at first; how many had he left ? 
 
 17. A boy gave away 8 apples, which was 4 of 
 
QUESTIO NS. 
 
 Ill 
 
 twice as many as, lie had left; how many had he at 
 first ? 
 
 18. 12 is | times of what number? 
 
 19. 36 is t 6 t times f of how many times £ of 13^ ? 
 
 20. Jeremiah is 18 years old, and his age is £ times 
 | of his father’s age ; how old is his father ? 
 
 21. Mary gave 6 cents for a comb, which was f 
 times j of all her money ; how many cents had she ? 
 
 22. Martha gave 8 cents for a pine-apple, which was 
 f times | of all her money ; how many apples could 
 she have bought with the money she had remaining, 
 at 2 cents apiece ? 
 
 23. Henry had 20 marbles, which was | of twice as 
 many as Harry had ; how many had Harry ? 
 
 24. Margaret is 16 years old, and her age is § of 3 
 times Martha’s age ; how old is Martha? 
 
 25. | is | of twice as much as what number ? 
 
 26. A man bought a horse for $60, which was £ of 
 twice as much as he sold him for; how much did he 
 gain by the bargain? 
 
 27. A horse was sold for $40, which was £ times 
 of what he was worth ; what was the value of the 
 
 horse ? 
 
 28. A man when he was married, was 20 }mars of 
 age, which was £ times £ of the age of his wife; how 
 old was she ? 
 
 29. Shepherd was worth $160, which was £ times 
 tV of his father’s fortune ; what was the father’s 
 
 1 u 7 
 
 fortune ? 
 
 30. A and B were playing cards, B lost $14 which 
 was t 7 ¥ times | as much as A then had ; and when 
 they commenced f of A’s money equaled £ of B’s. 
 IIow much had each when they began to play ? 
 
 31. A and B were playing cards, A lost $20 which 
 was T \ of the number of dollars B then had more 
 than A ; provided this sum was 1£ times as much as 
 A had at first, how much had each when they began 
 to play ? 
 
112 
 
 QUEST I O.NS. 
 
 LESSON II. 
 
 1. A boy, after spending f of all liis money, found, 
 that 16 cents was all be bad remaining; bow much 
 bad be at first? 
 
 Solution. —Let | equal the money he had at first. Then 
 after spending £ of it. he had remaining | which is f. 
 This by the condition of the question is 16 cents. If ^ of the money 
 he had at first is 16 cents, ± of it is i of 16 cents, which is 8 
 cents; and 3 , or what he had at first, are 5 times 8 , or 40 cents. 
 
 Solution 2d.—He spent § of his money; therefore, he had 
 remaining § of it, which equals 16 cents. If f of his money is 
 16 cents, he must have had 40 cents. 
 
 2. Ruth, after losing f of all lier roses, bad only 3 
 remaining ; how many had she at first ? 
 
 3. Jane gave f of all her flowers to Ann, and bad 
 4 remaining ; bow many did she give to Ann ? 
 
 4. George, after eating T 9 ¥ of all Lis oranges, bad 
 only 8 oranges remaining; bow many bad be at 
 first ? 
 
 5. A boy expended 4 of bis money for a pie, f for 
 a ball, | for a top, and bad 6 cents remaining ; bow 
 many cents bad be at first ? 
 
 G. In a certain school 4 of the scholars study gram¬ 
 mar, 4 study arithmetic, and the remainder, which is 
 10, study geography ; bow many scholars in all, and 
 bow many attending to each study ? 
 
 7. A third part of an army w r as killed, 4 part taken 
 prisoners, and 300 escaped; bow many was there in 
 the army ? 
 
 8. If from my age you subtract \ and § of my age 
 the remainder is 2 years ; bow old am I ? 
 
 9. B, being asked bow many pigeons be caught, 
 said, that if to -f of the number, 36 were added, the 
 sum would equal twice the number. How many did 
 be catch ? 
 
QUESTIONS. 
 
 113 
 
 10. If to | of the cost of B’s horse yon add $100, 
 the sura will be twice the cost of the horse ; what was 
 the cost of the horse ? 
 
 11. A gentleman, after spending -2 of his fortune and 
 i of the remainder, had $2400 remaining ; what was 
 his fortune ? 
 
 12. A gambler lost £ of all his money, and the 
 next night he won §- as much as he lost the night 
 before; he then had $90: how much had he at 
 first ? 
 
 13. John had stolen from him f of his money, and 
 the thief was not caught until he had spent j- of it; 
 the remainder, which was $40 less than John had 
 remaining, was given back; how much money had 
 John at first ? 
 
 14. A traveler had stolen from him £ of all his 
 money, and the thief was not caught until he had 
 spent | of it, the remainder ($100) was given back; 
 how much had he at first? 
 
 15. If to i of the cost of A’s watch you add 
 $10, the sum will be $21 ; what was the cost of his 
 watch ? 
 
 16. If to | of B’s age you add 15 years, the sum 
 would be 39 years ; how old is B ? 
 
 17. A drover being asked how many sheep he had, 
 said, if to i of my flock you add the number 9£, the 
 sum will be 99^; how many sheep had he? 
 
 18. ^ of the length of a pole is in the water, and 
 12 feet in the air; how long is the pole ? 
 
 19. If to \ of A’s age you add 16 years, the sum 
 will be 1-i times his age ; how old is he? 
 
 20. A man, being asked how many pigeons he 
 caught, replied, if to f of the number I caught you 
 add 20, the sum would lack 4 of being equal to li 
 times the number; how many did he catch ? 
 
 10* 
 
114 
 
 PARTNERSHIP. 
 
 LESSON III. 
 
 1. Divide tlie number 36 into two parts, wliich sliall 
 be to each other as 7 to 2. 
 
 Solution. —Since the two parts are to be to each other as 7 
 to 2, we must divide 36 into 7 + 2, which are 9 equal parts; and 
 7 of the parts will be one of the numbers, and 2 of them the 
 other, a. of 36 is 4, and 7. are 7 times 4, which are 28 (the first 
 number,) and § are 2 times 4, which are 8 (the other number.) 
 Or, in the latter part of the solution, say; ^ of 36 is 28, the 
 first number; and f of 36 is 8, the other number. 
 
 2. Two men hired a pasture for $72 ; one put in 7 
 horses, and the other 2 horses; what ought each to pay ? 
 
 3. A and B hired a pasture for $14 ; A put in 4 
 cows, and B put in 3 cows ; what ought each to pay ? 
 
 4. A and B bought a lottery ticket for $5 ; A paid 
 $3, and B paid $2. They drew a prize of $60 ; what 
 was each one’s share ? 
 
 5. Two men bought 40 mules: the first paid $5 as 
 often as the other $3. How many mules ought each 
 to receive ? 
 
 6. Mary and Elizabeth went to school 80 days, and 
 as often as Mary went 3 days, Elizabeth went 5 days; 
 how many days did each go ? 
 
 7. Reuben had 7 cents, and Blake 4 cents ; they 
 paid all their money for 22 apples ; how many ought 
 each to receive ? 
 
 8. Three men bought a lottery ticket for $12 ; the 
 first paid $2, the second $7, and the third $3. They 
 •drew a prize of $240 ; what was each man’s share ? 
 
 9. Three men hired a pasture for $24 ; the first put 
 in 2 horses, the second put in 3 horses, and the third 
 put in 4 horses ; how much ought each to pay ? 
 
 10. A man, failing in business, was able to pay only 
 | of his debts ; how much will that man receive to 
 whom lie owes $90 ? 
 
 11. A man, meeting an equal number of poor wo- 
 
PARTNERSHIP. 
 
 115 
 
 men and boys, gave to each woman 7 dimes, and to 
 each boy 2 dunes ; and to them all he gave $9 : how 
 many women and boys were there respectively ? * 
 
 , 12 * T ^'° 111 en bought a barrel of fish for $9 ; the first 
 
 paid *4, the second $5 ; what part of the barrel belongs 
 to each ? 
 
 13. A farmer gave 35 bushels of rye to two of his 
 poor neighbors; to the first he gave 1 bushel as often 
 as to the other f of a bushel: how many bushels did 
 
 14. Three men hired a pasture for $36 ; the first 
 put m 3 horses, the second 2 horses, and the third 4 
 Horses; how much ought each to pay ? 
 
 *?• T'P men . llired a Pasture for '$60 ; the first 
 put in 4 horses, for 2 weeks, and the second put in 3 
 
 i S <f ™ 4 Weeks ', • HoW much ought each to pay ? 
 
 >. three men hired a pasture for $15 ; the first 
 put m 4 sheep for 5 weeks, the second put in 8 sheep 
 foi 5 weeks, and the third put in 10 sheep for 9 weeks. 
 How much ought each to pay ? 
 
 nn D J,T,VTo entCTe n d int0 Partnership; the first 
 put in $40 .or 10 months and the second put in $80 
 
 for 5 months; they gained $95 : what was each man’s 
 snare ot the gain ? 
 
 son 8 ’ a A agr , eed t0 cut a 'field of wheat for 
 
 ' A 3e . nt 5 men , * days, and B sent 3 men for 
 10 da y s 5. how much ought each to receive? 
 
 19. Divide $56 between A and B, giving to A $1 
 as often as to B f of a dollar. 
 
 20. A and B hired a pasture for $24; A put in 4 
 sheep for 10 weeks, and B put in 2 horses for 10 
 weeks , what ought each to pay provided 2 sheep in 
 I week eat as much as a horse in the same time ? 
 
 1. bimpson, Domer, and Ever enter into a joint 
 speculation by which they clear $460. Simpson claims 
 to nave furnished £ ; Domer, §; and Eyer, \ of the 
 entire capital. IIow much according to these Calcula¬ 
 tions ought each to receive ? 
 
116 
 
 ALGEBRAIC QUESTIONS. 
 
 LESSON IV. 
 
 1. B had 4 apples more than A, and they together 
 had 14; how many had each? 
 
 Solution. —By a condition of the question B’s number is equal 
 to A’s + 4 apples; to which add A’s number, and we have 2 
 times A’s number + 4=14. Therefore, 2 times A’s number 
 equals 14 — 4, or 10; and once his number equals \ of 10 , or 
 5 apples. And B’s number is 5+4=9 apples. 
 
 2. Heman has 6 books more than Handford, and 
 both have 26 ; how many has each ? 
 
 3. Bobert has 7 marbles more than Richard, and 
 both have 35 ; how many has each ? 
 
 4. Mary has 4 roses more than Martha, and both 
 have 24 ; how many has each? 
 
 5. Alice has 7 pins more than Abner, and both have 
 29 ; how many has each ? 
 
 6. | of | is f of what number ? 
 
 7. The sum of two numbers is 36, and their differ¬ 
 ence is 16; what are the two numbers ? 
 
 8. A boy bought 4 of a melon for 8-4 cents ; how 
 
 much is that a piece ? 
 
 9. Homer and Hannah each brought an equal num¬ 
 ber of peaches ; on their way home Hannah had 4 
 more given to her, then they together had 24 ; how 
 many did each buy ? 
 
 10. Two boys had each an equal number of blocks ; 
 one lost 4 of his; and together they then had only 
 12 remaining : how many had each at first ? 
 
 11. A wagon was sold for $17§, which was § as 
 much as it cost; what did it cost ? 
 
 12. Hiram had twice as many strawberries as 
 Eugene, and both had 18 pints ; how many had-each ? 
 
 13. Ida had 6 cents more than twice as many as 
 Ira, and both had 36 ; how many had each ? 
 
 14. Susan had 4 as many cents as Sarah ; Sarah 
 
ALGEBRAIC QUESTIONS. 
 
 117 
 
 lost 10 of hers ; then together they had 50 ; how- 
 many had each at first? 
 
 15. Thomas was returning from market with twice 
 as many eggs as Timothy ; Thomas broke 4 of his 
 and Timothy 6 of his ; they then had 50 eggs remain¬ 
 ing. How many had each at first ? 
 
 16. f of a number -f 14 = 44 ; what is that 
 number ? 
 
 17. A boy being asked his age, replied, 3 times my 
 age — 7 years are 23 years. How old was he ? 
 
 18. A, being asked how much money he had, re¬ 
 plied, twice what I have + $60, is four times $400 ; 
 how much money had A ? 
 
 19. Two boys have 49 marbles, but the first has 7 
 the most; how many has each ? 
 
 20. A man bought a sheep, a cow, and a horse for 
 $70 ; the cow cost $10 more than the sheep, and the 
 horse cost $20 more than the cow. What was the 
 cost of each ? 
 
 21. A man bought a melon for 18f cents, which 
 was only | as much as his dinner cost; what was the 
 cost of his dinner ? 
 
 22. A gentleman bought a watch and chain for $80 ; 
 the chain cost i as much as the watch ; what was the 
 cost of each ? 
 
 23. A farmer bought a plow, a harness, and a 
 horse for $58 ; for the harness he gave $6 more than 
 for the plow, and for the horse $34 more than for the 
 harness. How much did he give for each ? 
 
 24. A boy bought twice as many oranges as lemons, 
 and on his way home ate 4 oranges and gave six away ; 
 and was surprised to find he had only 14 oranges re¬ 
 maining. How many of each kind did he buy ? 
 
 25. 5 times a certain number — 12 is 48 ; what is 
 that number? 
 
 26. -j of a certain number — 5 is 40; what is that 
 number ? 
 
118 ALGEBRAIC QUESTIONS. 
 
 27. A boy, being asked bis age, replied, 11 years 
 are 7 years more than § of my age ; how old was he ? 
 
 28. A boy, being asked how many sheep his father 
 had, replied, 40 are 5 less than £ of his number. How 
 many had he ? 
 
 29. A boy bought 18 lemons for f of them he 
 paid 3 cents for 2, and for the remainder he paid 3 
 cents a piece ; for what must he sell them a piece to 
 gain 10 cents on the whole? 
 
 30. James, John, and Joseph together have 96 
 peaches ; James has 2 more than John, and Joseph has 
 as many as both James and John : how many has each ? 
 
 31. Henry bought 54 oranges; for § of them he 
 paid 2 cents for 3, and for the remainder, 3 cents for 
 2; and sold i of them, at the rate of 2 cents for 3, 
 and the remainder, at 3 cents for 2. How much did 
 he gain by so doing ? 
 
 ———-—- 
 
 ■ 
 
 LESSON V. 
 
 1. If a man can do a certain piece of work in 12 
 days, what part of it can he do in 1 day ? 
 
 2. If a man can drink a barrel of beer in 20 weeks, 
 what part of it can he drink in 1 week ? 
 
 3. If it require 9 hours to empty a vessel, what part 
 of it can be emptied in 1 hour? 
 
 4. If a family consume a barrel of pork in 30 days, 
 what part of a barrel do they daily consume ? 
 
 5. If it require 19 days to perform a certain jour¬ 
 ney, what part of it can be performed in 1 day ? 
 
 6. If A can do a certain piece of work in 8 days, 
 and B could do the same in 12 days; what part of it 
 can each do in a day ? 
 
 7. If C could mow a certain field in 4 days,, and D 
 could do the same in 6 days; what part of it could 
 
119 
 
 ALGEBRAIC QUESTIONS. 
 
 each do in a day, and how much could they together 
 do * x a day ? 
 
 J. II C and D can, in 1 day, mow ^ of a field, how 
 long would it take them to mow the whole field ? 
 
 9. How many days would it take to perform a cer¬ 
 tain piece of work, if of it can be performed in 1 
 day ? 
 
 10. If George can do a certain piece of work in 3 
 days, and Granvil in 6 days; how long will it take 
 them together to do the work ? 
 
 11. If James can eat a bushel of apples in 10 days, 
 and Rud in 12 days; how long would 1 bushel last 
 both ? 
 
 12. A can cut a field of-wheat in 12 days, and B 
 can do the same in 20 days ; how long would it take 
 them to cut the field when they work together? 
 
 13. A merchant bought a hogshead of molasses for 
 $20, 10 gallons of which leaked out; how must he 
 sell the remainder a gallon to gain $6.50 ? 
 
 14. | of a barrel of flour cost $4f, what -w ill f of a 
 barrel cost ? 
 
 15. A and B can build a boat in 20 days, and with 
 the assistance of G, they can build it in 8 days. JIow 
 long would it take C to do it alone ? 
 
 16. A farmer and his son can do a piece of work in 
 6 days ; the son can do the same in 27 days. How 
 long would it take the father to do the work ? 
 
 17. Three pipes, A, B, and C can fill a cistern in 2 
 hours, A and B can fill it in 4 hours, and A and C can 
 fill it in 3 hours. How long would it take each to fill it ? 
 
 18. If a barrel of beer would last a man 35 days, 
 and, the man and his son 20 days; how long would it 
 last the son alone ? 
 
 19. A box of tea, usually, lasted a man and his 
 wife 9 months ; when the man was absent it would 
 last the wife 12 months. How long would it have 
 lasted the man alone ? 
 
120 
 
 ALGEBRAIC QUESTIONS. 
 
 20. A, B, and C can build a boat in 20 days, A r id 
 B, in 40 days, and A and C, in 30 days. How lo g 
 would it take each separately to build it ? 
 
 21. Provided A could drink a barrel of beer in 24 
 days, and B, in 36 days; bow long would it take 
 them together to drink a barrel, after f of it had 
 leaked out? 
 
 22. A market-woman bought 30 oranges, and had 
 L of them stolen; the remainder she sold at 3 cents 
 each and thereby gained | of a cent on each orange 
 bought. How much did they cost a piece ? 
 
 23. A can do a certain piece of work in 4^ days, 
 and A and B together, in 3 days. After A did ^ of 
 the work, B did the remainder ; how long did it take 
 him ? 
 
 24. If A can do a certain piece of work in f of a 
 day, how much can he do in 1 day ? 
 
 25. If a man can chop a cord of wood in | of a 
 day, how much can he chop in 1 day ? 
 
 26. Isaac can make a pair of boots in | of a day, 
 and Ira in § of a day ; how many pair can both make 
 in 1 day ? 
 
 21. Samuel can cut a cord of wood in | of a day, 
 and Theodore in § of a day ; how long would it take 
 them to cut a cord, when they worked together ? 
 
 28. If | of an apple cost -f of a cent, what will f 
 of an apple cost? 
 
 29. A can mow 1 acre of grass in f of a day, B, in 
 | of a day, and C, in j of a day. How much more 
 can A and B mow in a day than C ? 
 
 30. If a wolf can eat a sheep in | of an hour, and 
 a bear can eat it in f of an hour, how long would it 
 take them together to eat what remained of a sheep 
 after the wolf had been eating \ of an hour ? 
 
 i 
 
algebraic questions. 
 
 121 
 
 LESSON VI. 
 
 1. Lewis, meeting some beggars, gave each of them 
 2 cents, and had 12 cents remaining; if he had o-iven 
 them 4 cents each, it would have taken all the money 
 he had. How many beggars were there ? 
 
 bOLUTiON". By the last condition of the question, he gave each 
 hag-gar 2 cents more than by the first, and to them all, 12 cents 
 m°i e than by the first condition. Therefore there must have 
 
 been been as many beggars as 2 is contained times in 12, which 
 are 6 beggars. ’ 
 
 2. A boy gave to each of his playmates 3 cents, and 
 had 24. cents remaining; if he had given them each 7 
 cents, it would have taken all the money he had. 
 How many playmates had he ? 
 
 3. Mary.gave each of her playmates 5 apples; if 
 she had given them each 7 apples, it would have 
 taken 12 apples more. How many playmates had she ? 
 
 4. A certain number ot persons gave me 10 cents 
 each ; had they given me 12 cents each, it would have 
 amounted to 20 cents more. How many persons 
 were there ? 
 
 5.. | of $100 is -gf it of i times the salary of the 
 President of the United States. What is his salary ? 
 
 6. $40 is § times ¥ V of the salary of the Vice Presi¬ 
 dent of. the United States. What is his salary ? 
 
 i. Divide 35 oranges between James and Joseph, so 
 that James may have 15 more than Joseph. 
 
 8. A cask of wine was sold for $96, which was -3 of 
 twice as much as it cost; how much did it cost ? 4 
 
 9. By selling a quantity of cotton for $560, I gained 
 T or what it cost; how much did it cost ? 
 
 10. A and B are 187 miles apart, and are traveling 
 towards each other; one at the rate of 8 miles an houi^ 
 and the other, 9 miles an hour; how many hours be¬ 
 fore they will meet ? 
 
 11 
 
122 ALGEBRAIC QUESTIONS. 
 
 11. Agnes gave 2 dimes a yard for a piece of cali¬ 
 co; liad she given 3 dimes a yard, it would have cost 
 her 20 dimes more ; how many yards did the piece 
 contain ? 
 
 12. A was ordered to. buy a certain number of 
 oranges ; if he bought those, at 2 cents each, he would 
 have had no money left,—had he bought those, at 3 
 cents each, he would have wanted 10 cents more to 
 have paid for them. How many oranges was he re¬ 
 quired to buy ? 
 
 13. A lady wished to buy a certain number of yards 
 of muslin ; there were two kinds, some at 9 cents a 
 yard, and some at 12 cents a yard. Had she taken 
 that at 12 cents a yard, it would have cost 36 cents 
 more than the other kind. How many yards did she 
 wish to buy ? 
 
 14. A boy being sent to market to buy a certain 
 number of pounds of meat, found, if he bought beef, 
 at 5 cents a pound, he would have 39 cents remaining, 
 but if he bought pork, at 8 cents a pound, he would 
 have only 6 cents remaining. For how much meat 
 was he sent ? 
 
 15. If 8 times a certain number, is 36 more than 5 
 times the same number, what is that number ? 
 
 16. A boy being asked his age, said, 4 times my age 
 is 24 years more than 2 times my age ; how old was he? 
 
 17. A boy, being asked how many sheets of paper 
 he had, said, 4 times the number, is 18 less than 7 
 times the number ; how many sheets of paper had he ? 
 
 18. A person, wishing to buy some butter, found, if 
 he bought that which was 10 cents a pound, he would 
 have 20 cents remaining; but if he bought that which 
 was 12 cents a pound, he would lack 14 cents of hav¬ 
 ing money enough to pay for it. How many pounds 
 did he wish to buy ? 
 
 19. A farmer, wishing to buy a certain number of 
 sheep, found if he gave $2 a head, he would have $20 
 
ALGEBRAIC QUESTIONS. 123 
 
 remaining; but if he gave $5 a head he would lack 
 $40 of having money enough to pay for them. How 
 many sheep did he wish to buy ? 
 
 20. A, B, and C, talking of their ages ; says A to B, 
 I am 4 times as old as you; says B to C, I am | as 
 old as you, but says A to C, I am 40 years older than 
 you. Required the age of each ? 
 
 LESSON VIL 
 
 1. A laborer agreed to work 40 days upon this con¬ 
 dition ; that for every day he worked, he should 
 receive $2, and for every day he was idle he should 
 pay $1 for his board. At the expiration of the time, 
 he received $50. How many days did he work ? 
 
 Solution.—I f he had labored the whole time, he would have 
 received 40 times $2, or $80. But he received only $50: he, 
 therefore, lost by his idleness $80 — $50, or $30. For every 
 day he was idle he lost $2 (his daily wages) + $1 (the cost of 
 his board) which are $3. If in 1 day he lose $3 ; he will lose 
 $1 in 4 of a day, and $30 in 30 times 4 of a day, or 10 days. 
 Therefore, he was idle 10 days, and worked 40 — 10 days, or 
 30 days. 
 
 2. A man agreed to work 60 days on this condi¬ 
 tion ; that for every day he worked he should receive 
 $li, and for everyday he was idle, he should pay If- 
 for his board. At the expiration of the time, he re¬ 
 ceived $68. How many days did he work ? 
 
 3. A man w r as hired for 80 days, on this condition; 
 that for every day he worked, he should receive 6 
 dimes, and for every day he was idle, he should forfeit 
 4 dimes. At the expiration of the time, he received 
 $40. How many days did he work ? 
 
 4. How many times § of 12 is £ of 48 ? 
 
 5. A and B bought a quantity of flour for $50; A 
 paid $1 as often as B | of a dollar; what part of the 
 flour belongs to each % 
 
124 algebraic questions. 
 
 6. A, B, and C built a house, -which cost $500, of 
 -which B paid $100 more than A, and C paid as much 
 as A and B both ; how much did each pay ? 
 
 *7. A merchant sold a quantity of cloth for $84, and 
 thereby lost f of what it cost; what did it cost ? 
 
 8. 7| is 2i times f of how many times li ? 
 
 9. A farmer having in his employ an equal number 
 of men and boys; to each boy he gave $4, to each 
 man $8; and to them all he gave $84 : how many 
 men were there ? 
 
 10. Two men hired a pasture for $35 ; one put in 3 
 cows, and the other put in 4 ; how much ought each 
 to pay ? 
 
 11. A man sold an equal number of ducks and 
 turkeys for 20 dimes ; the ducks, at 2 dimes each, and 
 the turkeys, at 3 dimes each ; how many did he sell 
 in all? 
 
 12. A farmer sold an equal number of ducks and 
 turkeys ; the ducks, at 4 dimes eacn, the turkeys, at 
 7 dimes each ; and for the turkeys he received $3 
 more than for the ducks ; how many of each kind did 
 he sell ? 
 
 13. There are two baskets, containing 37 apples; 
 in one of which there are 17 more than in the other; 
 how many apples are there in each ? 
 
 14. Charles and Henry together have 49 marbles, 
 and Charles has 7 more than twice as many as Henry : 
 how many has each ? 
 
 15. Philip has 20 apples more than Philo ; and to¬ 
 gether they have 92 ; how many has each ? 
 
 16. Three boys have 47 lemons; the first has 3 
 more than the second, and the second has 7 more 
 than the third ; how many has each ? 
 
 17. A boy was hired for 20 days, on this con¬ 
 dition ; that for every day he labored, he should re¬ 
 ceive 3 dimes, and for every day he was idle, he 
 should pay 2 dimes for his board. At the expiration 
 
ALGEBRAIC QUESTIONS. 
 
 125 
 
 » of the time he received only $1. How many days 
 was he idle ? 
 
 18. A boy bought a whistle, a whip, and a drum 
 for *70 cents. For the whip he gave twice as much as 
 for the drum, and for the drum, twice as much as for 
 the whistle ; how much did he give for each ? 
 
 19. The sum of three numbers is 54. The first is 
 twice, and the third 3 times the second ; what are 
 those numbers? 
 
 20. Sarah’s age is § of Susan’s, and the sum of their 
 ages is 24 ; what is the age of each? 
 
 21. f of an army were killed, f of the remainder 
 » taken prisoners, and 400 escaped. How many were 
 
 there in the army ? 
 
 •--—■<-*« » »•*- •>- -- 
 
 LESSON VIII. 
 
 1. A fishing rod, the length of which was 14 feet, 
 was broken into two pieces. The shorter piece was £ 
 of the length of the longer. What was the length of 
 each piece ? 
 
 Solution.-—! of the length of the longer piece, which is the 
 length of the shorter, + £, (the length of the longer) =J of the 
 length of the longer, which is the length of both, or 14 feet. 
 If £ of the longer is 14 feet, J- is 4 of 14 feet, which is 2 feet, 
 and £ (which is the length of the longer) are 4 times 2 feet, or 8 
 feet. 14—8 = 6 feet, the length of the shorter piece. 
 
 2. A pole, tlie length, of which is 20 feet, is in the 
 air and water, of the length in the air equals the 
 length in the water ; what is the length in the air and 
 water respectively ? 
 
 3. If in 2 days a man traveled 160 miles, and f of 
 the distance he traveled the first day, equals the dis¬ 
 tance he traveled the second day ; how far did he 
 travel each day ? 
 
 11* 
 
126 
 
 ALGEBRAIC QUESTIONS. 
 
 4. B and C together have 40 marbles; how many 
 has each, provided f of B’s number is equal to C’s ? 
 
 5. From New York City to Redhook is 100 miles, 
 and i of the distance from New York to Rhinebeck, 
 equals the distance from Rhinebeck to Redhook. How 
 far from Rhinebeck to New York, and how far from 
 Rhinebeck to Redhook ? 
 
 6. If a horse and a colt were worth $90, and the 
 horse was worth H times as much as the colt; what 
 was the value of each ? 
 
 7. A boy paid 70 cents for a slate and a book; how 
 much did he pay for each, provided the book cost 1£ 
 times as much as the slate ? 
 
 8. If a traveler pay $1.20 for his breakfast and 
 dinner; how much did he pay for each, provided 
 his dinner cost f as much as his breakfast ? 
 
 9. A pole, the length of which is 67 feet, is in the 
 air and water; § of the length in the air + 7 feet 
 equals the length in the water. Required the length 
 in the air, and in the water ? 
 
 10. Divide the number 108 into two such parts, 
 that j of the first -f- 8 shall equal the second. 
 
 11. Divide the number 97 into two such parts, that 
 £ of the first + 7 shall equal the second? 
 
 12. There is a fish the length of which is 18 feet; 
 its tail is 4 feet, and § the length of the body, equals 
 the length of the head. What is the length of the 
 head and body respectively ? 
 
 13. There is a fish the weight of which is 11 
 pounds, and i of the weight of the head + 8 pounds 
 equals the weight of the body ; what is the weight of 
 each ? 
 
 14. A sliip-mast 51 feet in length, was broken off 
 in a storm, and § of the length broken off, equaled £ 
 of the length remaining; how much was broken off, 
 and how much remained ? 
 
 15. A boy being asked how many apples and 
 

 ALGEBRAIC QUESTIONS. 
 
 127 
 
 oranges he had, answered, in all I have 36, and, § of 
 the number of apples, equals \ ot the number ol 
 oranges ; how many of each hind had lie^ 
 
 lg b 2 0 f one number equals f ot another, and their 
 
 sum is 57 ; what are the two numbers ? 
 
 17. A farmer has 290 sheep in two different fields; 
 and £ of the number in the first field, equals f of the 
 number in the second; how many are there in each 
 
 field? 
 
 18. A market woman was requested to buy 33 
 fowls, consisting of two kinds; £ of the number of the 
 first kind, was to equal § of the number ot the second ; 
 how many of each kind must she buy ? 
 
 19. A person, being asked the time of day, said, the 
 time past noon is £ of the time past midnight; what 
 was the hour ? 
 
 Remark. —Since the time past noon is 1 of the time past 
 midnight, the time from midnight to noon, which is 12 hours, 
 must be £ ot the time past midnight. 
 
 20. A person, being asked the hour of the day, said, 
 the time past noon, is £ of the time past midnight; 
 
 what was the hour ? ., 
 
 21. A person, being asked the hour of the day, said, 
 the time past noon, is £ of the time from now to mid¬ 
 night \ what is the hour ? 
 
 Solution.— From now to midnight is §, and l added (the time 
 past noon) is \. Consequently from noon to midnight (winch is 
 12 hours) is £ of the time it lacked of being midnight; and ‘ ot 
 the time, is £ of 12, which is 3 hours, the time past noon. 
 
 22. What is the time of day, provided £ of the time 
 from now to midnight equals the time past noon ? 
 
 23. A man, being asked the hour of the day, said, 
 | of the time past noon, equals f of the time from now 
 to midnight; what was the time ? 
 
 24. A pole the length of which was ^ 68 feet was m 
 the air and water; £ of the length in the air, equaled 
 
 11 
 
128 
 
 ALGEBRAIC QUESTIONS. 
 
 | of the length in the water. What was the length in 
 the air, and in the water respectively ? 
 
 25. The sum of two numbers is 1T6, and f of the 
 first + 4. equals § of the second ; required the numbers ? 
 
 26. A person, being asked the time of day, said, ■} 
 of the time past midnight equals T 3 F of the time from 
 now to midnight again ; what o’clock is it ? 
 
 27. Provided the time past 10 o’clock, A. M., equals 
 f of the time to midnight; what o’clock is it ? 
 
 28. Says A to B, f of my age + 4 years equals | 
 of yours, and the sum of our ages is 74 years. What 
 is each of their ages ? 
 
 29. A person, being asked the hour of the day, re¬ 
 plied, | of the time past noon, equals | of the time 
 from now to midnight + 2§ hours ; what was the time ? 
 
 30. A pole, the length of which is 78 feet, is in the 
 air and water ; f of the length in the air +12 feet, 
 equals times the length in the water. What is the 
 length in the air and water respectively ? 
 
 - » . ♦ ■» - 
 
 LESSON IX. 
 
 1. There is a fish the head of which is 4 inches 
 long, and whose tail is as long as its head + \ of its 
 body, and whose body is as long as its head and tail; 
 what is the length of the fish ? 
 
 Solution.— By a condition of the question, £ of the length 
 of body + 4 inches, is the length of tail; to which add 4 
 inches, (the length of the head), and we have i of the length of 
 the body + 8 inches = or the length of the body. There¬ 
 fore, -f — or ^ of the length of the body, equals 8 inches; and 
 f, or twice the length of the body, which is the length of the 
 fish, equals 4 times 8 inches, or 32 inches. 
 
 2. The head of a fish is 6 inches long, its tail is as 
 long as its head + \ of its body, and the body is as 
 
ALGEBRAIC QUESTIONS. 129 
 
 long as the head and tail together; what is the length 
 of the fish ? 
 
 3. The head of a fish is 12 inches long, the tail is as 
 long as the head + | of the body, and the body is as 
 long as the head and tail; what is the length of the 
 fish ? 
 
 4. The head of a fish weighs 10 pounds, the tail 
 weighs as much as the head +1- as much as the body 5 
 and the body weighs as much as the head and tail; 
 w T hat is the weight of the tail ? 
 
 5. -f of a certain number equals f of the same num¬ 
 ber + 10 ; what is that number ? 
 
 G. A boy, being asked his age, replied, f of my 
 age exceeded of my age by 4 years ; how old was 
 he ? 
 
 V. James, being asked how many arithmetical ques¬ 
 tions he had answered correctly during the week, re¬ 
 plied, f of the number is 3 more than f of the num¬ 
 ber*, how many questions had he answered ? 
 
 8. A farmer after selling §• of 1-| times as much 
 grain as he had, had 80 bushels remaining ; how much 
 had he at first ? 
 
 9. An individual, after spending f of all his money, 
 and | of what then remained, had only $12| remain¬ 
 ing ; how much had he at first ? 
 
 "lO. If 4 of a ship be worth f of her cargo which 
 is valued at 300 eagles ; what is the value of the 
 ship ? 
 
 11 . Dick being asked how much money he had, 
 said, its \ exceeded its f by $2 ; how much had lie? 
 
 12 . A tree by falling, was broken into three pieces; 
 the top part was 10 feet long, the bottom part was as 
 long as the top -f f of the middle, and the middle 
 part was as long as the other two; what was the length 
 of the tree, and of each piece ? 
 
 13. A man bought a hat, a coat, and a watch; the hat 
 cost $6, the watch cost as much as the hat + § of the 
 
130 ALGEBRAIC QUESTIONS. 
 
 cost of the coat, and the coat cost as much as the hat 
 and watch ; what was the cost of each, and of all ? 
 
 14. | of f is how many times § of T 5 ¥ ? 
 
 15. If f of a ton of hay cost f of an eagle, how 
 many dollars will \ of a ton cost? 
 
 16. A third and \ of a third of 10 is f of what 
 number ? 
 
 17. If from a certain number you take its | and its 
 i, the remainder will he 13|, what is that number ? 
 
 18. After spending § of my money, I earned f as 
 much as I spent, and then had only $20 less than what 
 I had at first; how much had I at first ? 
 
 19. The head of a fish is 8 inches long, the tail is 
 as long as the head and \ of the body + 10 inches, 
 and the body is as long as the head and tail; what is 
 the length of the fish ? 
 
 20. The head of a fish is 12 inches long; its tail is 
 10 inches longer than its head increased by | the length 
 of the body ; and its body is 20 inches longer than its 
 head and tail together. What is the length of the fish ? 
 
 -- < ' i » i ' - 
 
 LESSON X. 
 
 1. James is 20 years old, and John is 4 years old, 
 in how many years will James, who is now 5 times as 
 old as John, be only twice as old ? 
 
 Remark.— Four years ago James was 16, and in 16 years 
 more he will be twice as old as John. 
 
 2. Sarah is 10 years old, and Sally is 4 ; in how 
 many years will Sally be -i as old as Sarah ? 
 
 3. Jacob is 40 years old, and Alfred is 2 ; in how 
 many years will Alfred be \ as old as Jacob ? 
 
 4. If the third of 6 be 3, what will b of 20 be ? 
 
 5. If 3 be the third of 6, what will the } of 20 be ? 
 
 6. If | of 12 be 10, what will § of 10 be? 
 
ALGEBRAIC QUESTIONS. 131 
 
 Y. Divide the number 85 into two parts, that shall 
 be to each other as § to £. 
 
 8. When A was married, he was 3 times as old as 
 his wife, but when they had been married 15 years, he 
 was only twice as old as she; how old was each when 
 they were married ? 
 
 Remark. —The conditions of the above question give the fol¬ 
 lowing : 
 
 9. Three times a certain number +15 equals twice 
 the same number + 30 ; what is that number, and 
 what is 3 times the same number ? 
 
 10. Once a certain number + 15 equals § of the 
 same number + 30 ; what is that number, and what 
 is i of the same number ? 
 
 11. When I first met Mr. A, I was \ as old as he 
 was, and in 12 years after that, I was f as old as he 
 was; what was each of our ages when we first met ? 
 
 12. There are two numbers, one of which is 4 times 
 the other; but if to each 20 were added, one will be 
 double the other; wha* are these numbers ? 
 
 13. When B was married he was 3 times as old as 
 his wife; but after they had been married 60 years, 
 | of his age equaled hers ; what was the age of each 
 when they were married ? 
 
 14. A hound takes 3 leaps to a fox 4, and 3 of the 
 hound’s leaps are equal to 6 of the fox’s ; how many 
 leaps must the hound take to gain 1 on the fox ? 
 
 15. If the hound takes leaps to gain 1, on the 
 fox; how many must he take to gain 20 on the fox ? 
 
 16. A hare is 20 leaps before a hound, and takes 4 
 leaps to the hound 3 ; and 3 of the hound’s leaps are 
 equal to 6 of the hare’s. How many leaps must the 
 hou^d take to catch the hare ? 
 
 1/. A fox is 60 leaps before a hound, and takes 5 
 leaps tc the hound 2 ; and 4 of the hound’s leaps 
 equals 12 of the fox’s. How many leaps must the 
 hound take to catch the fox ? 
 
132 
 
 ALGEBUAIC QUESTIONS. 
 
 18. Alfred is 60 steps before Silas, and takes 9 steps 
 to Silas 0 ; and 3 of Silas’s steps equals 7 of Alfred’s. 
 IIow many steps, at this rate, will each take before 
 they will be together ? 
 
 Remark. — A box of glass contains 50 square feet , or as nearly 
 as may be. 
 
 19. How many panes of glass in a box, provided 
 they are 6, by 8 inches ? 
 
 Remark. —Find the area of a pane of glass by reducing the 
 inches to parts of a foot, and then multiply these parts together. 
 The area of a pane G by 8 inches is 4 of a square foot. The re¬ 
 mainder may be solved as follows: 
 
 Solution.— If to make | of a square foot it require 1 pane, 
 to make §, or 1 square foot, it will require 3 times 1, or 3 panes; 
 and to make 50 square feet (1 box,) it will require 50 times 3 
 panes, which are 150 panes. 
 
 20. IIow many panes of glass in a box, provided 
 they are 8, by 10 inches? 
 
 21. How many panes of glass in a box, provided 
 they are 10, by 12 inches? 
 
 22. How many panes of glass in a box, provided 
 they are 8, by 12 inches? 
 
 23. How many panes of glass in a box, provided 
 they are 12 by 15 inches? 
 
 
 LESSON XL 
 
 * 
 
 1. What number is that, to which if its a be added, 
 the sum will be 15 ? 
 
 2. What number is that, to which if its A be added, 
 the sum will be 24 ? 
 
 3. Wh&t number is that, to wdiich if its a be added, 
 the sum will be 40 ? 
 
 4. What number is that, to which if its a bf t .dded, 
 the sum will be 30 ? 
 
 5. What number is that, to which if its § be added, 
 the sum will be 88 ? 
 
ALGEBRAIC QUESTIONS. 
 
 133 
 
 6 . How old is that man, to whose age if you add 
 its i and its §, the sum will be 104 years? 
 
 V. What number is that, which being increased by 
 its J, its i and 18 more will be doubled? 
 
 8. A man, being asked his age, said, my age^ in¬ 
 creased by its f and 20 more, is double my age. What 
 was his age ? 
 
 9 . Suppose I buy a certain number of boxes of but¬ 
 ter, at $2 a box, and as many more at $4 a box ; and 
 sell them all, at $3 a box; do I gain or lose, and how 
 much ? 
 
 10. A boy, being asked how many oranges lie had, 
 replied, if my number were increased by its f, its f, 
 and 42 more, the sum would equal 3 times my num¬ 
 ber. How many had he ? 
 
 11. Suppose I buy a certain number of melons 5 
 some at 10 cents each, and as many more at 40 cents 
 each ] and sell them all, at 30 cents apiece *, Iioav 
 much do I gain on each melon ? 
 
 12 . If by selling 1 apple I lose ot a cent, how 
 many apples, at this rate, must I sell to lose 6 cents ? 
 
 13. A boy bought a certain number of lemons, at 2 
 cents apiece, and as many more, at 4 cents apiece ; 
 and sold them, at the rate of 3 for 5 cents : did he 
 gain or lose, and how much? 
 
 14. A woman bought a certain number ot apples, 
 at the rate of 2 for a cent, as many more, at the rate 
 of 3 for a cent ', and sold them all, at the rate ot 5 for 
 2 cents, and by so doing, lost 4 cents. How many of 
 each kind did she buy ? 
 
 15. A woman bought a certain number of eggs, at 
 the rate of 3 for a cent, and as many more, at 4 for a 
 cent; and sold them out, at the rate ot 8 for 3 cents, 
 and by so doing, gained 4 cents. How many eggs did 
 she buy ? 
 
 16. Three men agreed to share $510 in the propor¬ 
 tion of h h and 1 ; how much must each receive ? 
 
 12 
 
134 
 
 ALGEBRAIC QUESTIONS. 
 
 17. A’s fortune is to B’s as ^ to i ; and they to¬ 
 gether have 1100 ; how much has each ? 
 
 18. The difference of two numbers is 15, which is 
 | of twice as much as the smaller number; what are 
 these two numbers ? 
 
 19. A merchant bought a certain number of yards 
 of cloth, at the rate of 2 yards for $1, and as many 
 more, at the rate of 5, for $1 ; and sold them all, at 
 the rate of 10 yards for $3 ; and thereby lost $8. 
 How many yards did he buy ? 
 
 20. A man bought a certain number of melons, at 
 the rate of 4 for $1, and as many more, at the rate of 
 10 for $1 ; and sold them all, at the rate of 8 for $2, 
 and thereby gained $6. How many melons did he 
 buy ? 
 
 -■*-•> - 
 
 LESSON XII. 
 
 1. Mary has twice as many apples as Sarah, and 
 they together have 12 ; how many has each ? 
 
 Remark.— By the condition of the question Mary has 2 apples 
 as often as Sarah 1. Consequently Mary must have and 
 Sarah £ of the 12 apples. 
 
 2. Divide 18 into 2 such parts, that one shall be 
 twice the other? 
 
 3. Divide 21 oranges between two boys, so that one 
 may have twice as many as the other. 
 
 4. Franklin and Francis together have 15 quarts 
 of nuts, but Franklin has twice as many as Francis; 
 how many has each ? 
 
 5. Robert has twice as many cents as Harry, and 
 together they have 24 ; how many has each ? 
 
 6. Divide the number 27 into two parts, that shall 
 be to each other as 1 to 2. 
 
 7. Harriet is twice as old as Ellen, and the sum of 
 their ages in 30 years ; what is the age of each ? 
 
 8. A and B are 36 rods apart, and travel towards 
 
ALGEBRAIC QUESTIONS, 
 
 135 
 
 eacli other ; how far will each travel^before they meet, 
 
 provided A travels twice as fast as B ? _ e 
 
 9 . What number must be added to twice itseit, tiiat 
 
 the sum may be 57 ? . , „ •- 
 
 10 . A, after spending ‘ of all his money, and ^ ot 
 
 the remainder less $4, had only $14 remaining ; how 
 
 much had be at first ? < , 
 
 11. Divide the number 48 into two such parts, that 
 
 one shall be f of the other. 
 
 19 In a certain school, there are 3 times as many 
 boys'as girls, and in all there are 62 pupils; how 
 many boys and how many girls in the schoo 
 
 13. James and Jackson together have 45 marbles, 
 but James has only | as many as Jackson ; how many 
 
 T~| 0^0]l \ , 
 
 14 A man and his son together earned $280 m a 
 year : , how much does each earn, provided the boy 
 
 earns only i as much as his fathei ? 
 
 15. A boy bought a melon and a citron 101 $1 , 
 how much did each cost, provided the melon cost only 
 
 \ as much as the citron ? , . 
 
 16. A man bought a horse and a saddle ioi $120 , 
 
 the saddle cost only \ as much as the horse; what 
 was the cost of each ? 
 
 17. A man, being ashed the cost of his oxen, said, 
 my oxen and wagon together cost $240, and the oxen 
 cost twice as much as the wagon; what was the cost 
 
 18. A man bought a sheep, a hog, and cow for $42 , 
 for the hog, he gave twice as much as for the sheep, 
 and for the cow, 3 times as much as for the sheep. 
 
 How much did he give lor each ? . 1 
 
 19. A farmer and his two sons earned $560 m 1 
 year ; the father earned twice as much as his elder son, 
 and the elder son earned twice as much as the younger 
 
 son. How much did each earn \ 
 
 20 . A, B, and C together, in 1 day, can dig 10 a 
 
136 ALGEBRAIC QUESTIONS. 
 
 bushels of potatoes ; A digs \ as much as B, and B, ± 
 as much as C. How many bushels can each dig in a 
 day ? 
 
 21. A man bought three pieces of cloth for $160 ; 
 the first piece cost only i as much as the second, and 
 the second, only t as much as the third. IIow much 
 did each piece cost? 
 
 22. In an army consisting of 20,000 men; 3 times 
 as many were wounded as were killed, and 4 times 
 as many remained unhurt as were wounded. How 
 many were killed, wounded, and unhurt respect¬ 
 ively ? 
 
 23. i of A’s, + f of B’s money equals $5500 ; and 
 f- of B’s money is 4 times of A’s. How much 
 money has each ? 
 
 24. Herman and Byron together have 60 blocks; 
 and Byron owns | as many as Herman; how many 
 has each ? 
 
 25. Divide the number 60 into two parts, that shall 
 be to each other as \ to f ? 
 
 26. Adelia and Louisa arc to share 14 apples in 
 the proportion of 4 to 3 ; how many ought each to 
 receive ? 
 
 27. The sum of Mary and Hezekiah’s age is 25 
 years ; how old is each, provided Hezekiah is only § 
 as old as Mary ? 
 
 28. Henry and his father can thrash 35 bushels of 
 oats in a day ; how many does each thrash, if Henry 
 thrashes only | as much as his father ? 
 
 29. A pole, whose length is 70 feet, is in the air 
 and water ; how much is in the air and water respect¬ 
 ively, if | of the length in the air equals the length in 
 the water ? 
 
 30. Divide the number 36 into two parts, that shall 
 be to each other as 5 to 4. 
 
 31. Divide the number 45 into two parts, that shall 
 be to each other as 1 to f. 
 
ALGEBRAIC QUESTIONS. 137 
 
 32. A and B together own $480; but A owns only 
 | as much as B ; how much belongs to each? 
 
 33. A man died, and left $7200 to be divided be¬ 
 tween his son and daughter, in the proportion of 1 to 
 f. How much ought each to receive ? 
 
 34. In a mixture of tea consisting of 48 pounds, 
 there was | as much poor, as good tea : how much of 
 each kind was there? 
 
 35. A man bought a cow and a horse for $96 ; the 
 cow cost | as much as the horse ; how much was the 
 cost of each ? 
 
 36. Moses has only -f as many chestnuts as Aaron ; 
 and both have 40 quarts; how many belongs to 
 each ? 
 
 37. Divide the number 49, into two parts, that shall 
 be to each other as 1 to f. 
 
 38. A hound ran 60 rods before he caught a fox; 
 and | the distance the fox ran before he was caught, 
 equaled the distance he was ahead when they started. 
 How far did the fox run, and how far in advance of 
 the hound was he, when the chase commenced ? 
 
 39. The sum of two numbers is 140, and the larger 
 is to the smaller as 1 to £ ; what are the two num¬ 
 bers ? 
 
 40. A and B together owe $69, but B owes only li¬ 
 as much as A ; how much does each owe? 
 
 41. Thomas and Thornton found $240, but could 
 not agree about the division of it; they, therefore, 
 threw it on the floor and each got what he could ; it 
 so happened that Thomas got only f as much as 
 Thornton. How much did each get ? 
 
 42. In a certain school consisting of 48 pupils, there 
 are If times as many boys as girls ; how many boys, 
 and how many girls in the school ? 
 
 43. A gold and a silver watch were bought for $160; 
 the silver watch cost only | as much as the gold one; 
 how much was the cost of each ? 
 
 12 * 
 
138 
 
 ALGEBRAIC QUESTIONS. 
 
 44. Divide the number 17 into two parts, that shall 
 
 be to each other as § to j. . 
 
 45 A farmer had 180 sheep m two fields, and j ot 
 
 the number in the first field equaled } of the number 
 
 in the second ; how many in each field ■ 
 
 46. Divide 88 into two parts that shall be to each 
 
 other as | to f. , , , 
 
 47 Ji of the distance a hare ran after a hound started 
 
 in pursuit, equaled the distance she was before the 
 
 hound when they started; how far did the hare run 
 
 before she was caught, provided the hound ran 80 
 
 rods to overtake her ? • . . , 
 
 48. A and B started from the same point, and ran 
 
 in the same direction ; B ran 60 rods ; then T \ of t le 
 distance A had run equaled the distance A was ahead 
 of B. How much did A gain on B m running 60 
 
 rods ^ . 
 
 49 . A fishing-rod the length of which is 24 feet, is 
 
 in two parts; § of the longer part equals the length 
 of the shorter. How long is each part* 
 
 50 A hound ran 90 rods before he caught a deer; 
 the deer ran 44 times as far as it was ahead of the 
 hound when they started, before it was overtaken. How 
 far ahead of the hound was the deer when the chase 
 
 commenced ? _ , 
 
 51 of A’s number of sheep + f of Bs number, 
 
 equals 900 ; how many sheep has each, provided f of 
 B’s number is twice § of As number ? 
 
 
 LESSON XIII. 
 
 1 . A person had two silver cups, and only one cover 
 for both. The first cup weighed 6 oz. It the first 
 cup be covered, it will weigh twice as much as the 
 second, but if the second cup be covered it will weigh 
 
ALGEBRAIC QUESTIONS. 139 
 
 3 times as much as the first. What is the weight of 
 the second cup and cover? 
 
 Solution.— By the last condition of the question, 3 times 6 oz., 
 the weight of the first cup, or 18 ounces, equals the weight of 
 the second cup and cover. Consequently the two cups and 
 cover weigh 18+6 ounces, which are 24 ounces. And by the 
 first condition, the first cup and cover weigh twice as much as 
 the second cup. Therefore the 24 ounces must be divided into 
 two parts, which are to each other as 2 to 1. One of these parts 
 will be the weight of the second cup, and 2 the weight of the 
 first cup and cover, &c. 
 
 2 . A lady lias two silver cups, and only one cover 
 for both. The first cup weighs 8 ounces. The first 
 cup and cover weigh 3 times as much as the second 
 cup; and the second cup and cover 4 times as much 
 as the first cup. What is the weight of the second 
 cup and cover ? 
 
 3. A man bought a hat, a coat, and a vest for $40. 
 The hat cost $6; the hat and coat cost 9 times as 
 much as the vest. What was the cost of each ? 
 
 4. A boy bought a squirrel, a rabbit, and a bird. 
 The squirrel cost 15 cents. The squirrel and rabbit 
 cost twice as much as the bird ; and the rabbit and 
 bird cost 3 times as much as the squirrel. What was 
 the cost of the bird and rabbit respectively ? 
 
 5. A farmer bought a cow, an ox, and a horse; 
 the cow cost $20. The cow and ox together cost 3 
 times as much as the horse; the ox and horse 
 together cost 4 times as much as the gow. What was 
 the cost of the ox and horse respectively ? 
 
 6 . A man bought two horses and a saddle. The 
 younger horse cost $40. The saddle cost j as much 
 as both horses; and the younger horse cost as much 
 as the other horse and saddle together. What did the 
 saddle and older horse cost respectively ? 
 
 7. A man traveled three successive days. The 
 first day he traveled 30 miles, which was { of the dis¬ 
 tance he traveled the other two days ; and 4 times the 
 
140 
 
 ALGEBRAIC QUESTIONS. 
 
 distance lie traveled the second day equaled the dis¬ 
 tance lie traveled tlie first and third days. How fai 
 
 did he travel each day ? * 
 
 8. A is worth $1000, and B and C together are 
 worth 9 times as much as A ; and C is worth | as 
 much as A and B. How much is B and C worth 
 respectively ? 
 
 9. A’s coat cost $20, and his vest and hat together 
 cost 5 times as much as his coat ; and 3 times the cost 
 of his vest equaled the cost of both coat and hat. 
 What was the cost of his vest and hat respectively ? 
 
 10. B’s harness cost $120, which was ^ of the cost 
 of his horse and sleigh ; and the harness and horse 
 together cost twice as much as the sleigh. How much 
 did the horse and sleigh cost respectively ? 
 
 11. A tree in falling broke into three unequal 
 pieces. The top piece was 8 feet long, which was 
 of the length of the other two pieces; and 3 times the 
 length of the bottom piece, equals the length ot the 
 other two pieces. How long was the tree, and how 
 long was each piece? 
 
 12. Find the ages of A, B, and C, by knowing that 
 A is 20 years old, and that the sum of B and C s age 
 is 4 times A’s age ; and that C’s age is 4 of the sum 
 of A and B’s age. 
 
 13. Find the fortunes of A, B, C, I>, E, and F, by 
 knowing that A is worth $20, which is \ as much as 
 B and 0 are worth, and that C is worth 1 as much as 
 A and B ; and, also that if 19 times the sum of A, B, 
 and C’s fortune were divided in the proportion of f, 4, 
 and \ it would respectively give f of D’s, \ of E’s and 
 | of F’s fortune. 
 
 14. A and B dug a 100 rods of ditch for $100. A 
 
 received 10 shillings a rod and B 6 shillings a rod. 
 Flow many rods did each dig, provided each received 
 $50? Ans. A dug 62|- rods, and B 37£. 
 
 Note.-— Consider the above a Penn, or N. J. question. 
 
REDUCTION. 
 
 141 
 
 CHAPTER VIII. 
 LESSON I. 
 
 Remark.—I n our calculations on interest, we shall reckon 
 30 days to the month, and 12 months to the year. Althouo-h 
 tliis, mathematically speaking, will not produce a result strictly 
 
 accurate; yet it will be^ sufficiently correct , for all practical pur- 
 poses. 
 
 1. Reduce 2 years and 4 months to the fraction of 
 a year. 
 
 Solution.—4 months is what part of a year? There are 12 
 months in 1 year, therefore 1 month is -D 0 f a year . and 4 
 months are 4 times jL, which are T % or $ of a year. In 24 years 
 how many thirds ? In one there are f, therefore 3 times the 
 number of whole ones equal the number of thirds. 3 times 2 
 are 6, and added are years. 
 
 JST Remark .—Always reduce a fraction to its lowest terms 
 before perform ing any other operation with it. 
 
 Pupils may not be able, readily to discover the greatest num¬ 
 ber that will divide both numerator and denominator , without a 
 remainder. Consequently, the most expeditious way will be, to 
 continue to divide by the least number that is contained in both 
 numerator and denominator without a remainder, until the 
 fraction is reduced to its lowest terms. 
 
 2. Reduce 1 year and 3 months to the fraction of a 
 year. 
 
 3. Reduce 3 years and 5 months to the fraction of 
 a year. 
 
 4. Reduce 4 years and 10 months to the fraction of 
 a year. 
 
 5. Reduce 7 years and 9 months to the fraction of 
 a year. 
 
 G. Reduce 8 years and 8 months to the fraction of 
 a year. 
 
 7. Reduce 12 years and 7 months to the fraction 
 of a year. 
 
 8. Reduce 11 years and 11 months to the fraction 
 of a year. 
 
 -V**? 
 
 r 
 
142 
 
 KEDUCTION. 
 
 9. Reduce 6 years and 6 months to the fraction of 
 a year. 
 
 10. Reduce 9 years and 8 months to the fraction of 
 a year. 
 
 11. Reduce 2 years 4 months and 15 days to the 
 fraction of a year. 
 
 Solution. —15 days is what part of a month? There are 30 
 days in one month, therefore 1 day is of a month, and 15 
 days are 15 times ^ which are or £ of a month. 4^ months, 
 or | months, is what part of a year? There are 12 months in 
 1 year, therefore, 1 month is of a year, and \ of a month, is 
 \ of which is of a year; and if J of a month is of a 
 year, 9 halves are 9 times which are or § of a year. 2£ 
 years, equal J s - years. 
 
 12. Reduce 4 years 7 months and 6 days to the 
 fraction of a year. 
 
 13. Reduce 5 years 9 months and 18 days to the 
 fraction of a year. 
 
 14. Reduce 1 year 7 months and 18 days to the 
 fraction of a year. 
 
 15. Reduce 2 years 7 months and C days to the 
 fraction of a year. 
 
 Remark. —Omitting the intermediate steps in the analysis we 
 have: 
 
 Solution.— 6 days is or \ pf a month. 1 4 months equal 
 iyi months. - 3 / months equal f of a year. 2| years equal -> 5 3 - 
 years. 
 
 16. Reduce 3 years o months and 6 days to the 
 fraction of a year. 
 
 17. Reduce 5 years 4 months and 24 days to the 
 fraction of a year. 
 
 18. Reduce 6 years 5 months and 18 days to the 
 fraction of a year. 
 
 19. Reduce 7 years 11 months and 6 days to the 
 fraction of a year. 
 
 20. Reduce 10 years 10 months and 12 days to 
 the fraction of a year. 
 
PERCENTAGE AND INTEREST. 143 
 
 LESSON Ii. 
 
 Remark.— Interest is money due for the use of money bor¬ 
 rowed ; and is estimated, at a certain rate per cent, per annum 
 which is regulated by law. ’ 
 
 The sum on which the interest is paid is called the Principal. 
 ine sum ot the principal and interest is called the Amount 
 
 By 6 per cent, is meant, 6 cents on 100 cents, $6 on $100, or 
 b on 100 whatever be the denomination. Hence, at 6 per cent, 
 ion or 3(r the principal equals the interest. 
 
 When no time is specified 1 year is understood. 
 
 1.. At 4 per cent., what part of the principal equals 
 the interest. 1 
 
 . Solution.— If the interest of 100 cents is 4 cents, of 1 cent it 
 is yfo of 4 cents which is T ~ or J, of a cent. Therefore, at 4 
 per cent., -Jj of the principal equals the interest. 
 
 2. At 2 per cent., what part of the principal equals 
 
 the interest ? 1 
 
 3. At 5 pci cent., what part of the principal equals 
 
 the interest ? 11 
 
 4. At G pci cent., what part of the principal equals 
 
 the interest ? 1 
 
 5. At 8 per cent., what part of the principal equals 
 
 the interest ? r ^ 
 
 G. At 10 per cent., what part of the cost equals the 
 gain ? 
 
 t . At 7 pei cent., what part of the principal equals 
 the interest ? 1 
 
 8. At 12 per cent., w r hat part of the cost equals the 
 gam ? 
 
 9.. At lb per cent., what part of the principal equals 
 the interest ? * 
 
 10. What is the interest of $80 for 1 year, at 15 
 per cent. ? 
 
 SoLunoN.-At 15 per cent. T ^, or ^ of the principal equals 
 the interest. £ s of $80 is $12, the interest. 
 
 11. What is the interest of $120 for 1 year, at 25 
 per cent. ? J 
 
144 
 
 PER CE NT. 
 
 12. What is the interest of $510 for 1 year, at 20 
 
 per cent. ? 
 
 13. What is the interest of $750 for 1 year, at 24 
 per cent. ? 
 
 14. A man paid $120 for a wagon and sold it, at a 
 gain of 30 per cent.; how much was his gain ? 
 
 Solution.— If he gained 30 per cent, he gained yhb, or T 3 ff of 
 the cost. t 3 o of $120 is $36, the gain. 
 
 15. A tailor sold a coat that cost him $25, at a gain 
 of 32 per cent.; how much did he gain ? 
 
 16. A man sold a quantity of goods that cost him 
 $840* at a gain of 75 per cent.; how much did he 
 gain ? 
 
 17. Edward spent 85 per cent, of $120 for a suit of 
 clothes. How much did his clothes cost him? 
 
 18. Henry’s watch cost $180, he sold it at a loss of 
 15 per cent.; how much did he receive for it? 
 
 19. A boy sold a quantity of candies that cost him 
 50 cents, at a gain of 120 per cent. ; how much did 
 he receive for them ? 
 
 20. Jacob sold a horse that cost him $240, at a loss of 
 25 per cent.; how much did he receive for the horse ? 
 
 -—♦ - 
 
 LESSON III. 
 
 Remark.— "When we say of the principal equals the in¬ 
 terest, it will be understood, that, a twentieth part of the princi¬ 
 pal, whatever be the denomination , will equal the interest. 
 
 4 1 . If _3_ 0 f the principal equals the interest, what is 
 
 the rate per cent. ? 
 
 Solution. —If the interest of 1 cent is of a cent, the in¬ 
 terest of 100 cents is 100 times or , or 6 cents. There¬ 
 fore, it is 6 per cent. 
 
 2. If J_ of the principal equals the interest, what is 
 the rate per cent. ? 
 
 3 . If _ 2 _ of the principal equals the interest, what is 
 the rate per cent.? 
 
PER CENT. 
 
 145 
 
 4= If °f the c °st equals the gain, what is the 
 rate per cent. ? 
 
 5* If o 3 5 ot the cost equals the gain, what is the 
 rate per cent. ? 
 
 6 - If 2V °f the principal equals the interest, what is 
 the rate per cent. ? 
 
 7. If T y of the cost equals the gain, what is the 
 rate per cent.? 
 
 8. If the interest of $44 for 1 year is $4, what is 
 the rate per cent. ? 
 
 Solution. —If the interest of $44 is $4, ¥ 4 T , or -J of the 
 principal equals the interest. If the interest of $1 is^-L the 
 interest on $100 is 100 times $y L i -, or -TP- 0 -, or $9—. Therefore, 
 $44 in 1 year will give $4 interest, at 9 T y per cent. 
 
 9. If the interest of $72 for 1 year is $6, what is 
 the rate per cent. ? 
 
 10. If the interest of $96 for 1 year is $12, what is 
 the rate per cent. ? 
 
 11. B bought a horse for $100 and sold it for $109, 
 how much did he gain per cent. ? 
 
 12. A woman bought a quantity of oranges for 75 
 cents and sold them for 84 cents 5 how much did she 
 gain per cent. ? 
 
 13. A merchant bought a quantity of books for $200, 
 and sold them for $228; how much did he rrain per 
 cent. ? 
 
 14. Thornton bought a boat for $50 and sold it for 
 $80 ; what was his gain per cent. ? 
 
 15. Harvey bought a hogshead of molasses for $25 
 and sold it for $314 • bow much did he gain per cent. ? 
 
 16. Bought a knife for 37 cents and sold it for 574 
 cents ; what was the gain per cent. ? 
 
 17. A stationer sold a quantity of paper for f of 
 what it cost him; how much did he gain per cent. 4 ? 
 
 _ 18* James received for his horse f of what it cost 
 him ; how much did he gain per cent. ? 
 
 13 
 
146 
 
 PEE CENT. 
 
 19. A man sold a barrel of pork for of what it 
 cost him ; how much did he gain per cent. ? 
 
 20. The interest of $500 for 4 years is $240 ; what 
 is the rate per cent. ? 
 
 Solution.— If the interest of $500 for 4 years is $240, for 1 
 year it is } of $240, or $60. Therefore, or YS of the P rin ' 
 cipal equals the interest. If the interest of $1 for 1 year is 
 $# 5 , the interest of $100 is 100 times or or $ 12 * 
 Therefore, it is 12 per cent. 
 
 21. A man, being asked, at what per cent, his money 
 was on interest, replied, I receive $120 interest in 10 
 years for $240 ; what was his rate per cent. ? 
 
 22. A bought a horse for $150 and sold it for $180; 
 what was liis gain per cent.? 
 
 23. Elisha bought 10 horses for $800, and sold 8 
 of them for what they all cost; what was his gain per 
 cent. ? 
 
 24. Jg- of the money C paid for books, is £ of what 
 he gained by selling them. How much did he gain 
 per cent. ? 
 
 25. ¥ j of the money I have on interest, is 4 times 
 the yearly interest received. What is the rate per 
 cent. ? 
 
 26. if of the cost of A’s merchandise, is f of what 
 he gained when he sold it. What was his gain per 
 cent. ? 
 
 27. of the cost of B’s wagon, is f of what ho 
 gained by selling it. What did he gain per cent, ? 
 
 28. A book was sold for f of f of what it cost. 
 What was the loss per cent. ? 
 
 29. | of | of the cost of a sleigh, was what it was 
 sold for. What was the gain per cent. ? 
 
 30. A merchant bought a quantity of goods for 
 $860 and sold them for $1075 ; how much did he gain 
 per cent. ? 
 
 V 
 
PERCENTAGE, 
 
 147 
 
 * > 
 
 LESSON IV. 
 
 !• At 5 per cent, for 4 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 Solution.—I f the interest of $1 for 1 year is 5 cents, for 4 
 years it is 4 times 5 cents, or 20 cents. Therefore, T ^° 0 , or £ of 
 the principal equals the interest. 
 
 2. At 6 per cent, for 5 years, what part of the prin¬ 
 cipal equals the interest? 
 
 3. At 3 per cent, for 2 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 4. At 4 per cent, for 3 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 5. At 6 per cent, for 3 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 6. At 4 per cent, for 3 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 7. At 9 per cent, for 6 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 8. At 8 per cent, for 5 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 9. At 4 per cent, for 6 years, what part of the prin¬ 
 cipal equals the interest ? 
 
 10. At 6 per cent, for 8 years, what part of the 
 principal equals the interest ? 
 
 11. At 10 per cent for 5 years, what part of the 
 principal equals the interest ? 
 
 12. At G per cent, for 4 years and 8 months, what 
 part of the principal equals the interest ? 
 
 Remark.—I t is expected that pupils thoroughly understand 
 every lesson they have been over; and are, therefore, prepared 
 to arrive at results, understandingly, without giving the entire 
 analysis of all parts of the question. 
 
 Solution.—8 months is or § of a year. 4§ years equal 
 J a 4 - years. If the interest of $l for 1 year is 6 cents, for 
 years it is ’A times 6 cents, or 28 cents. Therefore, or 
 23 of the principal equals the interest. 
 
148 
 
 INTEREST. 
 
 13. At 4 per cent, for 6 years and 6 months, what 
 part of the principal equals the interest? 
 
 14. At 6 per cent, for 5 years and 4 months, what 
 part of the principal equals the interest? 
 
 15. At 10A per cent, for 1 year and G months, what 
 part of the principal equals the interest? 
 
 16. At 4| per cent, for 9 years, what part of the 
 principal equals the interest ? 
 
 17. At 3f per cent, for 2 years and 2 months, what 
 part of the principal equals the interest ? 
 
 18. At 6| per cent, for 4 months and 24 days, what 
 part of the principal equals the interest $ 
 
 19. At 7 a per cent, for 10 months, what part of the 
 principal equals the interest ? 
 
 20. At 3 T \ per cent, for 2 years, 4 months and 15 
 days, what part of the principal equals the interest ? 
 
 LESSON V. 
 
 1. What is the interest of $50 for 4 years, at G per 
 cent. ? 
 
 Solution. —If the interest of $1 for 1 year is 6 cents, for 4 
 years it is 4 times 6 cents, or 24 cents. Therefore, T ~A, or -A 
 of the principal equals the interest. A of $50 is $12,'the in¬ 
 terest. 
 
 2.. What is the interest of $10 for 2 years, at 5 per 
 cent. ? 
 
 3. What is the interest of $48 for G years, at 5 per 
 cent. ? 
 
 4. What is the interest of #70 for 7 years, at 5 per 
 lent. ? 
 
 5. What is the interest of $G8 for 5 years, at 6 per 
 cent. ? 
 
 G. W hat is the interest ol $70 for 2 years, at 5 per 
 cent. ? 
 
 A What is the interest of $75 for o years, at 3 per 
 cent. ? 
 
INTEREST. 
 
 149 
 
 $ 
 
 8. What is the interest of $120 for 8 years, at 5 
 per cent. ? 
 
 9. What is the interest of $100 for 10 years, at 6 
 per cent. ? 
 
 10. What is the interest of $140 for 12 years, at 5 
 per cent. ? 
 
 11. What is the interest of $150 for 5 years, at 3 
 per cent. ? 
 
 12. AVhat is the interest of $145 for 6 years, at 5 
 per cent. ? 
 
 13. What is the interest of $200 for 10 years, 8 
 per cent. ? 
 
 14. What is the interest of $250 for 3 years, at 8 
 per cent. ? 
 
 15. AVhat is the interest of $220 for 11 years, at 10 
 per cent. ? • 
 
 16. AVhat is the interest of $500 for 9 years, at 8 
 per cent. ? 
 
 17. What is the interest of $250 for 12 years, at 6 
 per cent. ? 
 
 18. AVhat is the interest of $500 for 8 years, at 12 
 per cent. ? 
 
 19. What is the interest of $200 for 9 years, at 3 
 per cent. ? 
 
 20. AVhat is the interest of $405 for 10 years, at 8 
 per cent. ? 
 
 21. AVhat is the interest of $50 for 2 years and 2 
 months, at 6 per cent. ? 
 
 Solution.—2 months is of a year. 21 years equals 
 years. If the interest of $1 for 1 year is 6 cents, for yt years 
 it is times 6 cents, or 13 cents. Therefore, T yh of the prin¬ 
 cipal equals the interest. ^ 0 f $50 is or $6.50, the in¬ 
 terest. 
 
 22. AVhat is the interest of $25 for 4 years and 3 
 months, at 4 per cent. ? 
 
 23. What is the interest of $80 for 5 years and 5 
 months, at G per cent. ? 
 
 13 * 
 
150 
 
 INTEREST. 
 
 24. What is the interest of $60 for 8 years and 6 
 months, at 6 per cent. ? 
 
 25. What is the interest of $240 for 3 years and 9 
 months, at 6 per cent. ? 
 
 26. What is the interest of $75 for 4 years and 8 
 months, at 9 per cent. ? 
 
 27. What is the interest of $50 for 2 years and 9 
 months, at 6 per cent. ? 
 
 28. What is the interest of $80 for 12 years and 10 
 months, at 6 per cent. ? 
 
 29. What is the interest of $69 for 8 years and 4 
 months, at 2 per cent. ? 
 
 30. What is the interest of $60 for 4 years and 8 
 months, at 3 per cent. ? 
 
 31. What is the interest of $600 for 2 years 4 
 months and 15 days, at 4 per cent. ? 
 
 Solution'. —15 days is J of a month. 4J months equals 9 
 months. months equals or | of a year. years equal 
 y 1 - years. If the interest of $1 for 1 year is 4 cents, for -y 9 - 
 years it is -\ 9 - times 4 cents, or -V- cents. Therefore, of the 
 
 principal equals the interest. -J/o $600 is $57, the interest. 
 
 32. What is the interest of $300 for 5 years 9 
 months and 18 days, at 5 per cent. ? 
 
 33. What is the interest of $550 for 4 years 7 
 months and 6 days, at 10 per cent.? 
 
 34. What is the interest of $500 for 1 year 7 
 months and 18 days, at 6 per cent,? 
 
 35. What is the interest of $250 for 3 years 7 
 months and 6 days, at 4 per cent. ? 
 
 36. What is the interest of $250 for 3 years 3 
 months and 6 days, at 6 per cent. ? 
 
 37. What is the interest of $50 for 6 years 4 months 
 and 24 days, at 5 per cent.? 
 
 38. What is the interest of $75 for 2 years 11 
 months and 6 days, at 15 per cent. ? 
 
 39. What is the interest of $150 for 2 years 6 
 months and 12 days, at 15 per cent. ? 
 
INTEREST. 
 
 151 
 
 40. What is the interest of $300 for 2 years 9 
 months and 18 days, at If per cent.? 
 
 --»♦« ■ » > . »■- 
 
 LESSON VI. 
 
 1. What is the amount of $75 for 2 years, at 6 per 
 cent ? 
 
 Solution. — If the interest of $1 for 1 year is 6 cents, for 2 
 years it is 2 times 6 cents, or 12 cents. Therefore, -J/ ¥ , or qt of 
 the principal equals the interest, of $15 is $9, the interest; 
 to which add $75, the principal, and we have $84, the amount. 
 
 2. What is the amount of $90 for 3 years, at 7 per 
 cent. ? 
 
 3. What is the amount of $100 for 4 years, at 5 per 
 cent. ? 
 
 4. What is the amount of $160 for 10 years, at 5 
 per cent. ? 
 
 5. What is the amount of $160 for 8 years, at 5 per 
 cent. ? 
 
 6. What is the amount of $200 for 12 years, at 5 
 per cent. ? 
 
 7. What is the amount of $210 for 2 years and 6 
 months, at 4 per cent.? 
 
 8. What is the amount of $250 for 4 years and 3 
 months, at 8 per cent. ? 
 
 9. What is the amount of $240 for 4 years and 3 
 months, at 3 per cent. ? 
 
 10. What is the amount of $500 for 3 years 3 
 months and 6 days, at 6 per cent.? 
 
 11. What is the amount of $200 for 5 years 4 
 months and 24 days, at 5 per cent, ? 
 
 •- »>«•» » « »■- 
 
 LESSON VII. 
 
 1. What principal will in 4 years, at 6 per cent., 
 give $12 interest? 
 
 Solution. —If the interest of $1 for 1 year is 6 cents, for 4 
 
152 
 
 INTEREST. 
 
 years it is 4 times 6- cents, or 24 cents. Therefore, y ( 4 q, or ~^ of 
 the principal equals the interest, which is $12. If ^ of the 
 principal is $12, of the principal is £ of $12, or $2; and If 
 or the principal, is 25 times $2, or $50. 
 
 2. What principal will in 6 years, at 4 per cent., 
 give $36 interest ? 
 
 3. What principal will in 4 years, at 5 per cent., 
 give $30 interest ? 
 
 4. What principal will in 8 years, at 7 per cent., 
 give $42 interest? 
 
 5. What principal will in 10 years, at 7 per cent., 
 give $140 interest? 
 
 6. What principal will in 4 years and 6 months, at 
 6 per cent., give $54 interest ? 
 
 7. What principal will in 4 years and 3 months, at 
 
 5 per cent., give $102 interest? 
 
 8. What principal will in 4 years, and 3 months, at 
 8 per cent., give $51 interest ? 
 
 9. How much money has that man on interest, who, 
 at the expiration of 4 years and 4 months, at 6 per 
 cent., receives $260 interest? 
 
 10. At the expiration of 2 years and 4 months, at 
 
 6 per cent., a man received $49 interest. How much 
 money had he on interest ? 
 
 11. A is worth twice as much as B, and the in¬ 
 terest of their united fortunes for 4 years and 2 
 months, at 6 per cent., is $600. How much is each 
 worth ? 
 
 12. The interest on the cost of B’s store and house, 
 for 1 year and 6 months, at 4 per cent., would he $270. 
 What was the cost of each, provided the store cost y 
 as much as the house? 
 
 13. If the money B paid for a sheep, a cow, and 
 horse, was put on interest for 4 years and 6 months, 
 at 4 "per cent., it would give $18 interest. What was 
 the cost of all, and of each respectively, provided the 
 sheep cost y as much as the cow, and the cow, 4 as 
 much as the horse ? 
 
INTEREST. 
 
 153 
 
 LESSON VIII. 
 
 1. What principal will in 4 years, at 5 per cent., 
 amount to $360 ? 
 
 Solution. —If the interest of $1 for 1 year is 5 cents, for 4 
 years it is 4 times 5 cents, or 20 cents. Therefore, T 2 ^° ff , or 4 of 
 the principal equals the interest; to which add |, the principal, 
 and we have | of the principal equal to the amount, $360. If 
 4 of the principal is $360, 4 of the principal is 4 of $360, which 
 is $60, and j (the principal), is 5 times $60, which are $300. 
 
 2. What principal will in 3 years, at 6 per cent., 
 amount to $118 ? 
 
 3. What principal will in 6 years, at 10 per cent., 
 amount to $120 ? 
 
 4. What principal will in 10 years, at 7 per cent., 
 amount to $1V0? 
 
 5. What principal will in 4 years, at 5 per cent., 
 amount to $660 ? 
 
 6. A is worth 4 as much as B; and the interest on 
 their united fortunes for 2 years, at 5 per cent., is $880. 
 What is each of their fortunes? . 
 
 V. A merchant sold a quantity of cloth for $214, 
 and thereby gained V per cent. What did the cloth 
 cost him ? 
 
 8. What principal will in 2 years, at V per cent., 
 amount to $1140 ? 
 
 9. What principal will in 10 years and 8 months, 
 at 9 per cent., amount to $490 ? 
 
 10. The amount due on a note, which had been on 
 interest 6 years and 2 months, at 6 per cent, was 
 $274. What was the face of the note? 
 
 11. What principal will in 12 years and 9 months, 
 at 4 per cent., amount to $302 ? 
 
 12. If 4 of A’s fortune for 4 years and 6 months, at 
 6 per cent., amounts to $127; what is his whole for¬ 
 tune ? 
 
 13. If | of B’s fortune, being put on interest for 3 
 
154 
 
 INTEREST. 
 
 years 3 months and 6 days, at 15 per cent., amount to 
 $149 ; what is his whole fortune ? 
 
 14 . Mary, being asked how much money she had on 
 interest, and at what per cent., replied; the principal 
 and rate per cent, are such that in 5 years the amount 
 would be $750, and in 7 years, $810. What was the 
 
 principal and the rate per cent. ? 
 
 15. A man sold two horses for $240, losing on the 
 first 20 per cent., gaining on the other 20 per cent.; 
 what was the value of each horse, provided he received 
 for the second 3 times as much as for the first ? 
 
 16. The amount of Robert’s capital for a certain 
 time,’at 4 per cent, is $360, and for the same time, at 
 7 per cent, it is $405 ; required his capital and the 
 
 time. 
 
 
 LESSON IX. 
 
 1 . In what time will $40, at 6 per cent., give $12 
 interest ? 
 
 Solution. —If the interest of $40 is $12, or T 3 ^ of the 
 principal equals the interest. If the interest of $1 for 1 year is 
 \ of a dollar, of $100, it is 100 times $ T 3 o, or $30. If it require 
 1 year for $100 to give $6 interest, to give $30 interest it will 
 require as many years as $6 is contained times in $30, or 5 
 years. 
 
 2 . In what time will $60, at 5 per cent., give $18 
 interest ? 
 
 3 . In what time will $90, at 7 per cent., give $27 
 interest ? 
 
 4 . In what time will $100, at 6 per cent., give $10 
 interest ? 
 
 5 . In what time will $120, at 10 per cent., give 
 $120 interest? 
 
 6 . In what time will $250, at 6 per cent., give $20 
 interest ? 
 
PER CENT. 
 
 155 
 
 V. In what time will $40, at I per cent., give $8.40 
 interest ? 
 
 8. In what time, at 8 per cent., will $30 give $9.60 
 interest ? 
 
 9. In what time, at 6 per cent., will $10 give $2.40 
 interest ? 
 
 10. In what time, at 4 per cent., will $20 give 
 $5.60 interest ? 
 
 --- 
 
 LESSON X. 
 
 1. At what per cent., will $50, in 1 year and 6 
 months, or (li years), give $6 interest? 
 
 Solution.— If the interest of $50 for 1J, or % years is $6, for 
 i °f a year it is £ of $6, or $2; and for f, or 1 year, it is 2 times 
 $2, or $4. Therefore, or ^ of the , principal equals the 
 annual interest. If the interest of$l for 1 year is $ A, of $100, 
 it is 100 times $A> or $8. Therefore, it is 8 percent. 
 
 2 r At what per cent., will $40 annually give $2 
 interest ? 
 
 3. At what per cent., will $80 annually give $3.20 
 interest ? 
 
 4. At what per cent., will $120 annually give $12 
 interest ? 
 
 5. At what per cent., will $120 in 4 years, give $20 
 interest ? 
 
 6. At what per cent., will $100 in 3 years, give $30 
 interest ? 
 
 V. At what per cent., will $5 in 14 years, give $7 
 interest ? 
 
 8. At what per cent., will $25 in 1 year and 9 
 months, give $3.50 interest ? 
 
 9. At what per cent., will $80 in 5 years and 8 
 months, give $34 interest? 
 
 10. At what per cent., will $500 in 7 years and 6 
 months, give $15 interest? 
 
156 
 
 PER CENT. 
 
 11. At what per cent., will $600 in 2 years 4 months 
 and 15 days, give $57 interest? 
 
 
 LESSON XI. 
 
 1. At what per cent., will $10 in 4 years, amount to 
 
 $ 12 ? 
 
 Remark —From the amount subtract the principal, and the 
 rematadm Will be the interest. Them proceed as m the pre- 
 ceding lesson. 
 
 2. At what per cent., will $12 in 3 years, amount to 
 
 what per cent, will $20 in 6 years, amount 
 
 t0 4 12 At what per cent., will $24 in 10 years, amount 
 
 t0 5 3 At what per cent., will $30 in 7 years, amount to 
 
 * 3 6. 3 At what per cent., will $50 in 10 years, amount to 
 
 S7 7. ? At what per cent., will $36 in 5 years, amount 
 
 t0 If At what per cent, will a given principal double 
 itself, in 20 years ? 
 
 Solution—A given principal ^ 
 
 100 per cent.; and in 20 years, at * of 100 pel cent., or 
 
 per cent. . . . , , , 
 
 9. At what per cent, will a given principal double 
 
 ^lO.'At what per cent, will a given principal double 
 itself, inji yeiws^ ^ ^ ^ ^ principa l double 
 
 ' tS ^L2. 1 At what per cent, will $80 in 7 years give $80 
 interest ? 
 
PER CENT. 
 
 157 
 
 13. At what per cent., will $640 in 6 years give 
 $640 interest ? 
 
 14. At what per cent., will 25 cents in 8 years give 
 25 cents interest? 
 
 15. At what per, cent., will $97 in 9 years give $97 
 interest ? 
 
 16. At what per cent., will $372 in 25 years give 
 $372 interest? 
 
 1*7. At what per cent., will $1 in 30 years give $1 
 interest ? 
 
 18. At what per cent., will $15 in 124- years give 
 $15 interest? 
 
 19. At what per cent., will $42 in 144 years give 
 $42 interest ? 
 
 20. At what per cent., will 5 cents in 16|- years give 
 5 cents interest ? 
 
 ---» ’ «< » «■»■- 
 
 LESSON XII. 
 
 1. In what time will a given principal double itself 
 at 5 per cent. ? 
 
 Solution.—A given principal will double itself in 100 years, 
 at 1 per cent., and, at 5 per cent., in V of 100 years, which is 20 
 years. 
 
 2. In w r hat time will a given principal double itself, 
 at 4 per cent. ? 
 
 3. In what time will $25, at 3 per cent., give $25 
 
 interest ? 1 ’ b 
 
 . 4 * In w Lat time will $275, at 6 per cent., give $275 
 interest ? 
 
 5. In what time will a given principal double itself, 
 at 2 per cent. ? 
 
 6. In what time will $4, at 7 per cent., give $4 in¬ 
 terest ? 1 ’ b 
 
 . w ^at time will $94, at 9 per cent., give $94 
 
 interest ? & 
 
 14 
 
158 
 
 pee cent. 
 
 8. In what time will 5 cents, at 8 per cent., give 5 
 
 cents interest • . djo*? 
 
 9. In what time will $3§ at 10 per cent., give $3-^ 
 
 interest? • 
 
 10. In what time will 1 dime, at 12 { per cent., gne 
 
 1 dime interest ? 
 
 LESSON XIII. * 
 
 1. Bought a bushel of grass-seed, for $5 and sold it 
 for $7 ; what was the gain per cent, ? 
 
 Solution.— Since it was bought for $5 and sold for $7, the 
 gain must* have been $7-$5 which is $2 Therefore j of the 
 lost equals the gain. If on $1 I gam $f, on $100 I will gam 
 100 times $f ? or $40. Therefore, the gam is 40 per cent. 
 
 2. A hook was bought for $2, and sold lor $3 ; what 
 
 was the gain per cent. ? „ . ^ 
 
 3. A shawl cost $5, and was sold for $8; what was 
 
 the gain per cent. ? . - * 0fS . 
 
 4» A cow was bought for $20, and sold oi $i.o , 
 
 what was the gain per cent. \ 
 
 5 A merchant bought a hogshead of molasses tor 
 
 $80, and sold it for $95; what did he gam per‘cent. . 
 
 6. A barrel of pork cost $12, and was sold ioi $11, 
 
 what was the loss per cent. ? ., * . 
 
 7. A horse was bought for $140, and sold lor $ , 
 
 what was the loss per cent . j . 
 
 8. Bought an orange for 4 cents, and sold it lor o 
 
 cents ; what was the gain per cent. ? . » 
 
 9. Bought a melon for 15 cents, and sold it lor 
 
 cents; what was the gain per cent. ? . « Q 
 
 10. Bought a hook for 5 dimes, and sold it lor 8 
 
 dimes: what was the gain per cent.? 
 
 11. Bought a quantity of silk for $120, and sold it 
 
 for $200 ; what was the gain per cent. ? 
 
 12. A boy sold melons, at the rate of 10 cent* 
 
PERCENTAGE. 
 
 159 
 
 apiece, A of which equaled his gain; how much would 
 he have gained per cent., if he had sold them, at 12 
 cents apiece ? 
 
 13. A merchant sold sugar, for $80 a hogshead, 
 and thereby cleared T l w of his money ; if he had sold 
 it, at $92 a hogshead, what would he have gained per 
 cent. ? 
 
 14. A quantity of cloth was bought for $36, and 
 sold for $43 ; what was the gain per cent. ? 
 
 15. A horse was bought for $100, and sold for $95 ; 
 what was the loss per cent. ? 
 
 16. A man sold a horse for $120, and thereby 
 cleared a of its cost; how much would he have lost 
 per cent., if he had sold him for $80 ? 
 
 17. What per cent, of a is a ? Of § is a ? Of § is 
 A* of I is f? Off is f? Of 2i is f ? Of 3i is 2 t V? 
 
 18. | of $6 is what per cent, of i of $100 ? 
 
 19. -f of $28 is | of what per cent, of f of $300 ? 
 
 20. Walter sold a horse for $120, and thereby 
 cleared i of its cost; what would he have lost per 
 cent, by selling it for $80 ? 
 
 -4 M4 - » ♦»- 
 
 LESSON XIV. 
 
 1. A man bought a cow for $20 ; for what must he 
 sell her, to gain 5 per cent, on the cost ? 
 
 Solution.—I f he gains 5 per cent, he gains or ^ of the 
 cost. of $ 20 is $1» the gain. Therefore, to gain 5 per cent, 
 he must sell the cow for $20 + $1, or $21. 
 
 2. A man bought a yoke of oxen for $100; how 
 must he sell them, to gain 6 per cent, on the cost ? 
 
 3. A man bought a barrel of rum for $10 ; for what, 
 must be sell it, to gain 10 per cent, on the cost? 
 
 4. A gallon of wine was bought for 20 dimes; how 
 must it be sold a pint, to gain 20 per cent, on the 
 cost? 
 
160 
 
 DISCOUNT. 
 
 5. A hogshead of molasses cost $20; for what 
 ought it to be sold a gallon, to gain 40 per cent, on the 
 cost ? 
 
 6. B bought a horse for $80, and by selling it, lost 
 5 per cent, on the cost; for what did he sell it ? • 
 
 V. A wagon cost $140, and was sold for 5 per cent, 
 less than it cost; for what was it sold ? 
 
 8. A merchant, by selling 40 yards of cloth for 
 $164, lost 20 per cent, on the cost. What did it cost 
 per yard ? 
 
 9. If a quart of brandy cost 50 cents, how must it 
 be sold a gill, to lose 4 per cent. ? 
 
 10. B lost 5 per cent, by selling a gallon of rum, 
 which cost 80 cents; for what did he sell it a gallon ? 
 
 •--»* »♦ - 
 
 LESSON XV. 
 
 1. What principal will, in 4 years, at 5 per cent., 
 amount to $60 ? 
 
 Solution.— If the interest of $1 for 1 year is 5 cents, for 4 
 years it is 4 times 5 cents, or 20 cents. Therefore, y 2 ^, or £ 
 of the principal equals the interest; to which add f, the prin¬ 
 cipal, and we have £ of the principal equal to the amount, or 
 $60. If j of the principal is $60, of the principal is 4 °f $60? 
 which is $10; and (the principal), is 5 times $10, which are 
 $50. 
 
 2. What principal will, in 3 years, at 6 per cent., 
 amount to $118 ? 
 
 3. What principal will, in 5 years, at 6 per cent., 
 amount to $130. 
 
 4. What principal will, in 7 years, at 5 per cent., 
 amount to $81 ? 
 
 5. What principal will, in 9 years, at 8 per cent., 
 amount to $86 ? 
 
 6. What principal will, in 3£ years, at 8 per cent., 
 amount to $260 ? 
 
DISCOUNT. 
 
 161 
 
 V. What principal will, in 4| years, at 6 per cent., 
 amount to $640 ? 
 
 8. Wliat principal will, in 5^ years, at 7 per cent., 
 amount to $42 ? 
 
 9. What principal will, in 6^ years, at 7 per cent., 
 amount to $87 ? 
 
 10. What principal will, in 8§ years, at 6 per cent., 
 amount to $76 ? 
 
 Remark. —The present worth of a debt payable at some future 
 time, without interest, is such a sum, as will, in the given time, 
 and at the given rate per cent., amount to the debt. Hence, the 
 present worth of any sum of money, payable at some future time 
 without interest, may be found in the same way that we found 
 the principal , when we had given the amount, time, and rate 
 per cent. 
 
 See the above solution. 
 
 11..What is the present worth of $26, due 5 years 
 hence, at 6 per cent. ? Ans. $20. 
 
 12. What is the present worth of $14, due 8 years 
 hence, at 5 per cent. ? 
 
 13. What is the present worth of $110, due 5 years 
 hence, at 5 per cent. ? 
 
 14. What is the present worth of $86, due 8 years 
 hence, at 9 per cent. ? 
 
 15. What is the present worth of $102, due 9 years 
 hence, at 4 per cent.? 
 
 16. What is the present worth of $72, due 4 years 
 hence, at 5 per cent. ? 
 
 17. VV hat is the discount on $46, due 3 years hence, 
 at 5 per cent. ? 
 
 Remark. —The discount equals the amount minus the present 
 worth. 
 
 18. What is the discount on $54, due 5 years hence, 
 at 7 per cent. ? 
 
 19. What is the discount on $65, due 5 years hence, 
 at 6 per cent. ? 
 
 20. What is the discount on $93, due 3 years hence, 
 at 8 per cent. ? 
 
 14 * 
 
162 
 
 PERCENTAGE. 
 
 21. What is the present worth of $186, due 4f 
 years hence, at 5 per cent. ? 
 
 22. What is the present worth of $66, due 5^ years 
 hence, at 6 per cent. ? 
 
 23. What is the present worth of $128, due 4§ 
 years hence, at 6 per cent. ? 
 
 • - ^ » > ^ >« <> »- 
 
 LESSON XVI. 
 
 1. If I sell cloth, at $2.50 a yard, and thereby gain 
 25 per cent. ; what did it cost a yard ? 
 
 Solution.— If I gain 25 per cent. I gain \ of the cost; to 
 which add £, the cost, and I have f of the cost equal to $2.50. 
 If | of what I gave for it, is $2.50, ^ of the cost is £ of $2.50, 
 or 50 cents; and f (the cost) is 4 times 50 cents, which are 200 
 cents, or $2. 
 
 2. A horse was sold for $38, which was at a loss 
 of 5 per cent. What did the horse cost ? 
 
 3. If I sell cloth, at $2.50 a yard, and thereby 
 gain 25 per cent., how must I sell it a yard, to lose 20 
 per cent.? 
 
 4. If I sell cloth, at $4.40 a yard, and thereby gain 
 10 per cent., how ought I to sell it, to lose 25 per 
 cent. ? 
 
 5. If by selling a piece of cloth for $46, I gain 15 
 per cent., how ought I to have sold it, to have lost 30 
 per cent. ? 
 
 6. A sold his horse for $105, and thereby gained 5 
 per cent, on the cost; for what ought he to have sold 
 it, to have lost 10 per cent. ? 
 
 7. A farm was sold for $495, which was 10 per cent, 
 less than what it was worth ; for what ought it to have 
 been sold, to have received 40 per cent, more than its 
 value ? 
 
 8. A mechanic lost 20 per cent, on the cost of a 
 wagon, by selling it for $40 ; for what ought it to have 
 been sold, to have gained 30 per cent. ? 
 
PERCENTAGE. 
 
 163 
 
 9. A horse was sold for $90, which was 10 percent, 
 less than its value ; what would have been the gain 
 per cent., if it had been sold for $120? 
 
 10. A farm was sold for $690, which was 8 per 
 cent, less than its value; what would have been the 
 gain per cent., if it had been sold for $850 ? 
 
 11. A book was sold for 90 cents, which was 10 
 per cent, less than its value; what would have been 
 the gain per cent., if it had been sold for $1.50? 
 
 12. A man sold two watches, at $12 each; on one 
 he gained 50 per cent., and on the other he lost 50 per 
 cent. Did he gain or lose by the bargain, and how 
 much ? 
 
 13. An individual sold two gold pencils, at $6 
 apiece; on one he gained 20 per cent., and on the 
 other he lost 20 per cent. Did he gain or lose, and 
 how much ? 
 
 14. A farmer sold two horses at $210 apiece ; for 
 one he received 25 per cent, more than its value, and 
 for the other 25 per cent, less than its value. Did he 
 gain or lose by the bargain, and how much ? 
 
 15. A merchant sold a quantity of cloth for $280, 
 and by so doing lost 60 per cent.; he then sold an¬ 
 other quantity for $80, and thereby gained 60 per 
 cent. Did he gain or lose by the operation and how 
 much ? 
 
 —-——-■ 
 
 LESSON XVII. 
 
 1. An individual was ordered to collect $190, and 
 his own fee, which is to be 5 per cent, on all the 
 money collected. How much should he receive ? 
 
 Solution.— He is to receive 5 per cent, or T | 7 or of all 
 he collects. |£, all he collects, minus A, his f® e , equals 4,y of 
 all he collects, or $190, the amount he is to pay his employer. 
 If of what he collects equals $19-0, is -fg of $190, which 
 
164 MISCELLANEOUS QUESTIONS. 
 
 is $10; and (what lie collects) is 20 times $10, or $200. 
 Therefore he must receive $200 —$190 = $10. 
 
 2. How much ought xk to receive for collecting $90 
 and his own fee, of 10 per cent, on all he collects ? 
 
 3. What amount ot money will be sufficient to pay 
 a debt of $38 and the collector’s fee, which is 5 per 
 
 • cent, on all the money collected ? 
 
 4. IIow much cider must that man mate to bring 
 away 15 barrels, after the o'wner of the mill receives 
 16| per cent, of all he has made? 
 
 5. How much grain must a farmer take to mill, that 
 he may bring away the flour of 1 bushel, after the mil¬ 
 ler has taken 10 per cent, of all he took there ? 
 
 -< »» 4 n »- 
 
 MISCELLANEOUS QUESTIONS. 
 
 1. At 5 per cent, for 4 years, what part of the prin¬ 
 cipal equals the interest? 
 
 2. In how many years, at 4 per cent., will a given 
 principal amount to the same, as it would in 8 years, 
 at 6 per cent. ? 
 
 3. At what per cent, will a given principal, in 14 
 years, amount to the same, as it would in 12 years, at 
 7 per cent. ? 
 
 4. If aV °f U le principal equals the interest, what is 
 the rate per cent. ? 
 
 5. The rent of B’s farm, for 8 years amounted to 
 
 of its value. What per cent, did he annually re¬ 
 ceive on the value of his farm?. 
 
 6. What is the interest of $75, for 5f years, at 6 
 per cent. ? 
 
 7. What principal will, in 7^ years at 8 per cent., 
 give $24 interest ? 
 
 8. What principal will, in 4 j years, at 5 per cent., 
 amount to $155 ? 
 
 . 
 
MISCELLANEOUS QUESTIONS. 165 
 
 9. At what per cent., will a given principal double 
 itself, in 12-1 years ? 
 
 10. The interest of A’s and B’s fortune, for 8 years, 
 at 5 per cent., is $420. What is the fortune of each, 
 provided A’s fortune is twice B’s ? 
 
 11. The interest of of A’s and £ of B’s fortune, 
 for 7 years at 5 per cent., is $2100. What is each of 
 their fortunes, provided § of A’s fortune equals f of 
 B’s? 
 
 12. B sold his horse, for -i of l-i times what it cost; 
 what did he lose per cent. ? 
 
 13. What is the interest of $540 for 4 years, at 5 
 per cent. ? 
 
 14. What is the interest of $180, for 5 years and 9 
 months, at 6| per cent. ? 
 
 15. What principal will in 4 years 7 months and 
 6 days, at 6| per cent., amount to $412 ? 
 
 16. The interest of the cost of B’s horse, sleigh and 
 wagon, for 6 years, at 5 per cent., is $69. What is 
 the cost of each, provided their prices are to each 
 other respectively, as -I, § and f ? 
 
 17. What principal will, in-8 years and 8 months, 
 at 7j per cent., amount to $419 ? 
 
 18. What principal will, in 5 years 9 months and 
 18 days at 10 per cent., give $116 interest ? 
 
 19. In what time, will $420, at 5 per cent., give 
 $147 interest? 
 
 20. If the interest of $200, for 1 year and 6 months, 
 is $18, what is the rate per cent. ? 
 
 21. At what per cent., will $500, in 4 years and 9 
 months, give $190 interest? 
 
 22. At what per cent., will $500, in 22 years and 6 
 days, amount to $1821 ? 
 
 23. At what per cent, will a given principal double 
 itself, in 20 years ? 
 
 24. In what time will a given principal double 
 itself, at 12| per cent. ? 
 
166 MISCELLANEOUS QUESTIONS. 
 
 25. At wliat per cent, will a given principal double 
 itself, in 6 years and 8 months ? 
 
 26. A horse was bought for $60, and sold for $90 ; 
 what was the gain per cent.? 
 
 27. A basket containing 39 oranges, cost $1.20; how 
 must they be sold apiece to gain 30 per cent.? 
 
 28. If 1 quart of champagne cost 40 cents, how 
 must it be sold a gill to gain 20 per cent. ? 
 
 29. What is the present worth of $68, due 10 
 years hence, at 7 per cent. ? 
 
 30. What is the discount on $162, due 10 years 
 and 4 months hence, at 6 per cent. ? 
 
 31. What is the present worth of $87, due 3| years 
 hence, at 5 per cent. ? 
 
 32. If a hogshead of molasses containing 84 gallons 
 cost $30 ; how must it be sold a gallon, to gain 40 per 
 cent. ? 
 
 33. The money I have on interest, in 9 years, at 
 10 per cent., amounts to $190 ; what is the prin¬ 
 cipal ? 
 
 34. When money was worth 6 per cent., I bought 
 
 $400 worth of goods ; 6 months afterwards I sold them, 
 and gained 10 per cent, on the cost. How much did 
 I gain ? Ans. $28. 
 
 3 5. A speculator bought a horse for $36, and 
 sold it for 25 per cent., more than he gave for it; 
 which, however, was 10 per cent., less than what he 
 asked for it. How much did he ask for the horse ? 
 
 36. A gentleman being asked how much money he 
 had on interest, replied, that it instead of 6 per cent, 
 he should receive 10 per cent., he would receive $268 
 interest more than he then did. How much money 
 had he on interest? 
 
 37. A merchant bought broadcloth for $1.20 a yard 
 and sold it for 33 t per cent, more than he gave for it; 
 which, however, was 33^ per cent, less than his marked 
 price for it. How much was his marked price per 
 yard ? 
 
MISCELLANEOUS QUESTIONS. 167 
 
 38. A merchant sold a quantity of cloth for $120, 
 and by so doing gained 50 per cent. He then sold 
 another quantity, for $120, and thereby lost 50 per 
 cent. Did he gain or lose by the bargain, and how 
 much ? 
 
 39. B sold a horse for $60, and gained 20 per cent. 
 He then sold another horse for $60, and lost 60 per 
 cent. Did he gain or lose, and how much ? 
 
 40. The interest on li times A’s, and f of B’s for¬ 
 tune, for 8 years, at 5 per cent., is $520. What is the 
 fortune of each, provided li times A’s fortune, equals 
 f of B’s ? 
 
 41. | of D’s fortune added to f of E’s, which is 3 
 times | of D’s, being put on interest for 8 years, at 5 
 per cent., gives $800 interest. What is the fortune of 
 each ? 
 
 42. The interest of A’s, B’s, and C’s fortune, for 5 
 years, at 8 per cent., is $1040. What is the fortune of 
 each, provided they are to each other as and £ ? 
 
 43. The interest, of A’s, B’s, and C’s fortune, for 5± 
 years, at 6 per cent, is $800. W hat is each of their 
 fortunes, provided B’s, is twice A’s ; and B’s and C’s 
 are equal? 
 
 44. A’s fortune added to |- of B’s, which is to A’s 
 as 2 to 3, being put on interest for 6 years, at 4 per 
 cent., amounts to $124. What is the fortune of 
 each ? 
 
 45. D’s money added to 4 times E’s, which is equal 
 to D’s, being on interest for 10 years, at 5 per cent., 
 amounts to $3000. What was each of their fortunes ? 
 
 46. The sum of f of A’s 4- } of B’s money, being 
 on interest for 8 years, at 5 per cent., amounts to 
 $2100. Provided \ of B’s money is twice f of A’s ; 
 how much money has each ? 
 
 47. | of the cost of C’s house, increased by § of the 
 cost of bis farm, being placed on interest for 10 years, 
 at 7 per cent., amounts to $17000. What is the cost 
 
168 MISCELLANEOUS QUESTIONS. 
 
 of each, if | of the cost of the house is only i of f 
 of the cost of the farm ?. 
 
 48. If f of A’s fortune ip 2 years and 4 months, at 
 6 per cent., amounts to $570 ; what is his whole 
 fortune ? 
 
 49. The sum of A’s, and B’s fortune in 4 years and 
 8 months, at 6 per cent., amounts to $256. What 
 was each of their fortunes, provided § of A’s fortune 
 equals B’s ? 
 
 50. The interest for 5 years, at 6 per cent., on § of 
 the money Morgan owes is $180; and the interest for 
 the same time and rate per cent., on § of the money 
 due him is $120. IIow much has Morgan after pay¬ 
 ing his debts ? 
 
 51. The money John paid for a sheep, a cow, and a 
 horse, in 8 years, at 10 per cent., would give such an 
 interest, as would in f as long, at -i as great a per cent., 
 amount to $104 ; how much did he pay for each, pro¬ 
 vided the sheep cost \ as much as the cow, and the 
 cow ± as much as the horse? 
 
 52. The interest of the sum of \ of Simpson’s, f of 
 Eyer’s, and ^ of Homer’s fortune for 3 years 7 months 
 and 6 days, at 10 per cent, is such as will in the same 
 time, at \ the rate per cent, amount to $531. What 
 is the fortune of each, provided times Homer’s part 
 of the principal equals £ of Eyer’s, and T 7 ^ of Eyer’s 
 part of the principal equals | of Simpson’s ? 
 
 53. The interest of the sum of i of A’s, and | of 
 B’s fortune, for a certain time, at 2 per cent., was to 
 this sum as 9 to 250. And the amount of this interest 
 for 25 times as long, at 10 times as great a per cent., 
 was $180. What was each of their fortunes, provided, 
 A’s fortune was to B’s as 1 to 3 ? And how long was 
 the first on interest ? 
 
 Remark. —Since the interest was to the principal as 9 to 250, 
 
 of the principal equals the interest. Hence, 1 year 9 months 
 and 18 days is the time required, 
 
QUESTIONS, QUERIES, AND PUZZLES, 
 
 FOB 
 
 PUPILS AT HOME. 
 
 «*■ 
 
 1 . A hound is in pursuit of a fox that is 10 rods ahead of him, 
 and while the hound runs 10 rods the fox runs 1 rod, (i e. 
 while the hound runs a certain distance, the fox runs one-tenth 
 of that distance.) Will the hound overtake the fox ? The con¬ 
 ditions remaining the same, what is the greatest distance they 
 can run ? 
 
 2 . A hound is in pursuit of a fox that is 10 rods ahead of 
 him, and while the fox runs 1 rod the hound runs 10 rods. How 
 far will the hound run before he overtakes the fox ? 
 
 3. Place four 5’s in such a position that they shall equal 6J. 
 
 4. A boy was sent to a spring with a 5, and a 3 quart meas¬ 
 ure to procure exactly 4 quarts of water. How did he measure 
 it? 
 
 6 . What is the difference between twice 25, and twice 5 and 
 20 ? 
 
 6 . A man had 9 pigs and put them in four pens, with an odd 
 number of pigs in each pen. How did he divide them ? 
 
 7. Two men have an 8 gallon cask full of wine, which they 
 desire to divide equally between them. How can they effect this 
 division, provided the only measures they have are a 5 gallon 
 cask and a 3 gallon cask? 
 
 8 . Place four 2’s in such a manner that they shall exactly 
 equal 23. 
 
 9. Place 9 apples in 10 rows so that each row shall contain 
 3 apples. 
 
 10. A squirrel finding 9 ears of corn in a box, took from it 
 daily, 3 ears ; how many days was he in removing the corn from 
 the box ? 
 
 11. If from six you take IX, and from IX you take ten ; and 
 if fifty from forty be taken, there will then just half a dozen 
 remain. 
 
 15 
 
170 QUESTIONS AND PUZZLES. 
 
 12. Edward, Maria, and their mother went to market. Ed¬ 
 ward had 60 apples and sold them, at 2 for 1 cent ; Maria had 
 60 apples and sold them, at 3 for 1 cent. Their mother had 
 120 apples and sold them, at the rate of 5 for 2 cents. Which 
 received the most, the children or the mother, and why ? 
 
 13. A gentleman desiring to see an inmate of a prison, was 
 asked by the keeper whether he was related to the culprit, re¬ 
 plied : “ brothers and sisters have I none, but his father is my 
 father’s son.” What relation was the gentleman to the prisoner ? 
 
 14. A man having a fox, a goose, and a peck of corn, was 
 desirous of crossing a river. He could take only one across at 
 a time, and if he left the fox and goose, while he took the com 
 over, the fox would kill the goose; but if he left the goose and 
 corn, the goose would eat the corn. How shall he get them all 
 safely across the river ? 
 
 15. A snail wants to get up a wall 20 feet in height, during 
 the day it climbs 5 feet, but slips back 4 feet every night; how 
 many days would it take to reach the top ? 
 
 16. A man purchased a hat for $5, and handed the mer¬ 
 chant a $50 bill to pay for it; the merchant being unable to 
 make the change, sent the bill to a broker, got it changed, and 
 then gave the man who bought the hat $45. The broker, after 
 the purchaser of the hat had gone, discovered that the bill was 
 counterfeit and, therefore, returned it to the merchant and re¬ 
 ceived $50 good money. How much did the merchant lose by 
 the operation ? 
 
 17. Place ten pennies in a row, then carry one over two, 
 leaving it upon the third, and continue doing this until the ten 
 pennies occupy only live places with two in each place. 
 
 18. Two boys laid a wager as to which could lift the most 
 One lifted ninety-nine pounds, and the other a hundred, and 
 icon. How many pounds did both lift ? 
 
 19. A frog, at the bottom of a well 10 feet deep, ascends 3 
 feet every jump. How many jumps must he take to get out ? 
 
 20. A drover being asked how many horses he had replied, 
 “ my horses together have twenty fore legs how many horses 
 had he ? 
 
 21. Write 12 in such a manner, that you can show its half to 
 be 7. 
 
 22 . “I am constrained to plant a grove 
 To please the lady that I love, 
 
 This ample grove is to compose, 
 
 Nineteen trees in nine straight rows; 
 
 Five trees in each row I must place. 
 
 Or I shall never see her face.” 
 
QUESTIONS AND PUZZLES. l7l 
 
 23. Do the waters of the Mississippi river flow up hill? 
 
 24. If a man should start from the city of New York, at 
 12 o’clock on Monday, and travel directly west for 24 hours, at 
 the rate of 15 degrees an hour, it is evident he would then have 
 reached New York again. It was Monday 12 o’clock when he 
 started, and has been midday to him during his journey; (the 
 sun being in his meridian,) on his return to New York City it is 
 Tuesday, 12 o’clock; at what point on his journey did it change 
 from Monday to Tuesday noon ? 
 
 25. Arrange in a square the numbers from 1 to 16, in such a 
 manner that they shall amount to the 
 same in each column, whether added 
 perpendicularly, horizontally, diagonally, 
 or taking any four of the numbers in 
 the form of a square. 
 
 1 
 
 12 
 
 6 
 
 15 
 
 5 
 
 13 
 
 3 
 
 10 
 
 11 
 
 2 
 
 16 
 
 5 
 
 14 
 
 7 
 
 9 
 
 4 
 
 Magic Squares—An East India Puzzle. 
 Puzzle. —Take any odd number whatever—square it. 
 
 and 
 
 write the series of figures from one to the square of the number 
 taken, in a square whose side is indicated by the number taken, 
 in such a manner that the figures added horizontally, perpen¬ 
 dicularly, or diagonally, shall equal the same sum. 
 
 Example. —Take the number 5,—its square is 25,—write the 
 figures from 1 to 25 in a square made up of twenty-five smaller 
 squares in such a manner that, added perpendicularly, horizon¬ 
 tally, or diagonally, the sum shall be the same, that is, one-fifth 
 of the sum of the series of numbers, 1 to 25 ; —and so of the 
 numbers 7, 9, 11, etc. 
 
 Pule.—B egin by placing 1 in the middle square at the top, 
 then, in filling up, observe these directions according to the posi¬ 
 tion of the square just filled, viz.: Proceed diagonally upward 
 to the right, or if you can not do this go to the square on the 
 opposite side of the parallelogram in the next line at the right, 
 or next line above; or if you can not do this, take the square 
 immediately below. 
 
 These figures can be varied in 
 at least four different ways. If 
 the number 7 be taken, they can 
 be varied six different ways; if 
 9 be taken, they can be varied 
 eight different ways, perhaps 
 more, 
 
 17 
 
 24 
 
 1 
 
 8 
 
 15 
 
 23 
 
 5 
 
 7 
 
 14 
 
 • 16 
 
 4 
 
 6 
 
 13 
 
 20 
 
 22 
 
 10 
 
 12 
 
 19 
 
 21 
 
 3 
 
 11 
 
 18 
 
 25 
 
 2 
 
 9 
 
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