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■■i 
 
 * ii\ 
 
 AN 
 
REVISED EDITION, 
 
 THE 
 
 AMERICAN 
 
 INTIIIIJCTIIAL 
 
 DESIUNED FOR 
 
 SCHOOLS AND ACADEMIES i 
 
 CONTAINING 
 
 AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS, 
 WITH CONCISE AND ORIGINAL METHODS OF SOLU- 
 TION, WHICH SIMPLIFY MANY OF THE 
 MOST IMPORTANT RULES IN 
 WRITTEN ARITHMETIC. 
 
 BY JOHN F. STODDARD, A.M., 
 
 AUTHOE OF TKE " NOEMAL aiATHElIATICAL SEEIES," ETC. 
 
 TORONTO : 
 ADAM MILLER, 62 KING ST. EAST. 
 
 1865. 
 
nu 
 
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 ne- 
 cessity of a more extended and systematic Intel- 
 lectual Arithmetic for the younger, as well as 
 more advanced 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 prepa- 
 ration is to tell but one thing at a time, and that 
 in its proper place. 
 
 ^ It would be laborious to point out all the par- 
 ticulars in which this work differs from others 
 of a similar character ; I shall, therefore, give 
 only a brief exposition of its general plan, leaving 
 the other differences (which, doubtless, 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, Mul- 
 
IV 
 
 PREFACE. 
 
 liplication, and Division of simple numbers ; 
 each of which is rendered familiar by an exten- 
 sive collection of practical questions. The last 
 Lesson in Chapter Second^ consists of questions 
 which combine Addition and Subtraction, the 
 last Lesson in Chaptti^ Third^ of (juestions com- 
 bining Addition, Subtraction, and Multiplication. 
 Thus, an intimate connection between Lessons 
 and even Chapters is kept up through the entire 
 work, with the exception of Chapter Fifths 
 which contains a few of the most important 
 tables of Weights and Measures ; each of which 
 is illustrated with appropriate questions. 
 
 Chapter Sixth is devoted to the subject of 
 Fractions, and contains twenty lessons, in which 
 many original combinations and concise solu- 
 tions 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,) 
 v/hen thoroughly understood, will be of incal- 
 culable benefit to those who are studying, or 
 intend to study Algebra. 
 
 Chapter Eighth includes Interest, Discount, 
 and per cent, of every description, in their vari- 
 ous modifications. The method of treating these 
 subjects is original ; and renders the rules in 
 Written Arithmetics, under these heads (which 
 are often incomprehensible to pupils) perfectly 
 intelligible by reducing the whole to one con- 
 tinued train of reasoning. 
 
PREFACE. 
 
 imbers ; 
 n exten- 
 The last 
 Liestions 
 tion, the 
 ns com- 
 lication. 
 Lossons 
 le entire 
 r Fifth, 
 iportant 
 )f which 
 
 bject of 
 n which 
 se solu- 
 
 and in- 
 L require 
 3 of the 
 7-hich, it 
 r work,) 
 if incal- 
 ^ing, or 
 
 r* is believed that this Chapter, if thoroughly- 
 taught, can not fail to quicken, strengthen, and 
 develope 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 Seventhy it 
 must of necessity cause the pupil to acquire the 
 habit of systematically classifying his know- 
 ledge, that he may, at any time, be able to call 
 to his aid, such portions of it as will assist him 
 in illustrating or demonstrating the subject 
 under consideration. 
 
 The mind is composed of a variety of faculties 
 which require for their development appropriate 
 and constant exercise. That Intellectual Arith- 
 metic, when properly taught, is better calculat- 
 ed, than any other study, to invigorate and 
 develope these faculties, ta produce accurate 
 and close discrimination, and, to enable the 
 pupil to acquire a knowledge of the Higher 
 Mathematics with greater ease, can not for a 
 moment admit of a doubt. 
 
 J. F. STODDARD. 
 
 New York, August 1, 1860. 
 
 iscount, 
 eir vari- 
 ng these 
 rules in 
 (which 
 )erfectlv 
 ne con- 
 
Suggestions to Teachers. 
 
 «.atVht%olif' "' *"'' -'^o^o experience i, limited, I 
 
 the I upj required to repeat and analvze it without nter 
 rnption, unless it be to .nake a „eoe.a.y critieil'l: cot 
 
 noHn'i7i''*r".^''^'^"'^^ upon promiscuously and 
 not in rotation, to take part in the recitation 
 
 Care should be taken that the language they use b. 
 strictly correct a. to construction and IrtifuIatZ. 
 If not carefully guarded, pupik, i„ their hurried solu 
 
 luteJlectual Arithmetic is a practical lesson in elocution 
 givl^foTCS ^"r*"".*'-* ^l^^ P-«cular forms ' 
 
imited, I 
 the most 
 )ranch of 
 
 Nation, to 
 ion ; the 
 exercise, 
 
 tly, and 
 Lit inter- 
 1 or cor • 
 
 sly and 
 
 use be 
 
 d solu- 
 . For 
 ivhich, 
 V pro- 
 
 !, v^en, 
 
 son in 
 ution, 
 in the 
 
 forms 
 inless 
 S. 
 
 ARITHMETIC. 
 
 I 
 
 
 
 CHAPTER I. 
 
 • 
 
 
 
 Lesson 
 
 I. 
 
 1. 
 
 2 
 
 and 
 
 1 
 
 are 
 
 how 
 
 Solution, - 
 
 —Two and one are 3. 
 
 
 2. 
 
 2 
 
 and 
 
 ^ 
 
 are 
 
 how 
 
 3. 
 
 2 
 
 and 
 
 3 
 
 are 
 
 how 
 
 4. 
 
 2 
 
 and 
 
 4 
 
 are 
 
 how 
 
 5. 
 
 2 
 
 and 
 
 5 
 
 are 
 
 how 
 
 6. 
 
 o 
 
 and 
 
 6 
 
 are 
 
 how 
 
 7. 
 
 2 
 
 and 
 
 7 
 
 are 
 
 how 
 
 8. 
 
 2 
 
 and 
 
 8 
 
 ar3 
 
 how 
 
 9. 
 
 2 
 
 and 
 
 9 
 
 are 
 
 how 
 
 10. 
 
 3 
 
 and 
 
 2 
 
 are 
 
 how 
 
 11. 
 
 3 
 
 and 
 
 3 
 
 are 
 
 how 
 
 12. 
 
 3 
 
 and 
 
 4 
 
 are 
 
 how 
 
 13. 
 
 3 
 
 and 
 
 5 
 
 are 
 
 how 
 
 14. 
 
 3 
 
 and 
 
 6 
 
 are 
 
 how 
 
 15. 
 
 3 
 
 and 
 
 7 
 
 are 
 
 how 
 
 16. 
 
 3 
 
 and 
 
 8 
 
 are 
 
 how 
 
 17. 
 
 3 
 
 and 
 
 9 
 
 are 
 
 how 
 
 18. 
 
 4 
 
 and 
 
 3 
 
 are 
 
 how 
 
 19. 
 
 4 
 
 and 
 
 4 
 
 are 
 
 how 
 
 20. 
 
 4 
 
 and 
 
 5 
 
 are 
 
 how 
 
 21. 
 
 4 
 
 and 
 
 6 
 
 are 
 
 how 
 
 22. 
 
 4 
 
 and 
 
 7 
 
 are 
 
 how 
 
 23. 
 
 4 
 
 and 
 
 8 
 
 are 
 
 how 
 
 24. 
 
 4 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 many ? 
 many? 
 many ? 
 many? 
 many ? 
 many ? 
 many? 
 many ? 
 many? 
 many ? 
 many ? 
 many ? 
 many? 
 many ? 
 many? 
 many ? 
 many ? 
 many? 
 many ? 
 many ? 
 many? 
 many ? 
 
8 
 
 ADDITION. 
 
 did'LhTm p'"'^' - "'■«" '""' J"'- 1 = how many 
 ^^^T^Sr^^^^^ ^l l^^Jo,n , ...y eogotbcr 
 
 how many cents did both receive ?" ° ^"'"^ ' 
 
 3 |L^"rwirCd'UL^'; "-"'^^ ^- ''^'" 
 
 w n.a^;:ow':ti a;"/ "^ '"-^^''-^ ^ -- > 
 
 motL™H!!f!:''\S"'' ''''" 2 oranges, and his 
 31 PMo di o*"" "'ry ^'^ te receive in all ? 
 
 how'malfCd h Jrht', '"''''' -^ "-«•'* « -- . 
 
 -Jt Sran^haVhrtfe:'?"^ ^^^ «- ■'^ ^ 
 Jny h'adtfe' ' "PP^-- -" I S-e hin. 3 ; how 
 
 ^.Srhoir^t^rdtdT^^^^^^^^^^^ 
 
 39. EalnhitT '^°'^, Many barrels did he buv C 
 hot"n.^c&brcostT'^' """^ " P'"-PP'e cost 8 ; 
 
 a 
 n 
 
 5 
 
 u 
 a] 
 
 P' 
 
 di 
 
 i 
 i 
 
ADDITION. 
 
 9 
 
 ow 
 
 many 
 
 jy together 
 Harvey j 
 jave him 
 gave me 
 
 5 more ; 
 
 and his 
 B in all 1 
 ler gave 
 
 ;ave me 
 
 ) more ; 
 
 bim2 
 
 3 J how 
 
 4 cents 
 ' both ? 
 nts for 
 
 and 6 
 
 > buy ? 
 vhat is 
 
 lost 8 ; 
 
 -, and 
 
 I 
 
 42. If it take 4 yards of cloth for a coat, and 3 for 
 a vest, how many yards will it take for both ? 
 
 43. Samuel bought 4 marbles, and found 4 ; liow 
 many had he then ? 
 
 44. Isaac bought 4 sheets of paper, and I gave him 
 5 ; how many had he then ? 
 
 45. A man 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 ; bow "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. 
 
 I. 
 
 5 
 
 and 
 
 4 
 
 are 
 
 how 
 
 2. 
 
 5 
 
 and 
 
 5 
 
 are 
 
 how 
 
 3. 
 
 5 
 
 and 
 
 6 
 
 are 
 
 how 
 
 4. 
 
 5 
 
 and 
 
 7 
 
 are 
 
 how 
 
 6. 
 
 5 
 
 and 
 
 8 
 
 are 
 
 how 
 
 6. 
 
 5 
 
 and 
 
 9 
 
 are 
 
 how 
 
 7. 
 
 6 
 
 and 
 
 5 
 
 are 
 
 how 
 
 8. 
 
 G 
 
 and 
 
 G 
 
 are 
 
 how 
 
 9. 
 
 6 
 
 and 
 
 7 
 
 are 
 
 how 
 
 10. 
 
 6 
 
 and 
 
 8 
 
 are 
 
 how 
 
 11. 
 
 6 
 
 and 
 
 9 
 
 are 
 
 how 
 
 12. 
 
 7 
 
 and 
 
 6 
 
 are 
 
 how 
 
 13. 
 
 7 
 
 and 
 
 7 
 
 are 
 
 how 
 
 14. 
 
 7 
 
 and 
 
 8 
 
 are 
 
 how 
 
 15. 
 
 7 
 
 and 
 
 9 
 
 are 
 
 how 
 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 mauv ? 
 
 ft/ 
 
 many .'* 
 mauv ? 
 many ? 
 many ? 
 many ? 
 many ? 
 mauv ? 
 many ? 
 many ? 
 
10 
 
 ADDITION. 
 
 16. 
 17. 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 ^ and 7 ire how 
 8 and 8 are how 
 
 S and 9 are L„.. 
 8 and 5 are how 
 
 ow 
 
 9 
 9 
 9 
 9 
 9 
 9 
 
 and 
 and 
 and 
 and 
 and 
 and 
 
 6 
 
 8 
 9 
 
 many 
 many 
 many: 
 many 
 
 are how many ? 
 are how many ? 
 are how many ? 
 
 10 are how many? 
 7 are how many ? 
 
 11 are how many? 
 ^b. Mary has answered 5 questions correctlv and 
 
 4 incorrectly ; .ow many questions was /he asked ^ 
 
 nn q ^k .f'^^'^^ ™^^ *'''^ ^°.^^^' 5 one gave him 5 cents' 
 and the o her gave him 6 cents ; hovv many cent' did 
 they togetder give him ? ^ ^ 
 
 h.!f ■ / '^^'' ?,''''^^^ ^^ ^^^ ^*^^' ^ doiiars, and a pair of 
 boots for 6 dollars ; how much was the cost of bothi 
 
 29. There are 9 boys on one bench and 8 on an- 
 
 frf \^^'T ^^^^^ ''^^'^ t^^^i-e on both ? 
 
 rfO. Maria gave her teacher 5 pinks and 7 rosea • 
 how many flowers did she give him P ' 
 
 >^ . i^w ^''^' 'i"?u^ ^ ^q^^'rrols, and Henry cauoht 
 « ; how many did both catch ? ^ ^au^at 
 
 o^ sball we learn m two weeks ? 
 fnr ?'.. rV""^^ ^ """^^^ ^^^ ^ ^^^ts., and an or.nae 
 M f ' u'^'VI^^^' ^^^'^ *^^^ ^^« ^ec^i^e for both '^ 
 
 how'ma^^ha'rhflL^^^^' ^^' '^^^^^^ ^^^ ^-^^ ^ ^ 
 
 hofA.P'''^ bought G candies, and Sarah bought 8 • 
 how many were bought hj both ? ^ ' 
 
 hot -^^^^^^^ ^^^ ,^ orangfis, and Catharine has 9 • 
 liow many oranges have both ? ' 
 
 h,'pf 6 ^^;°Jrt'?^^i* 7 applet and his father ^ave 
 "-i-i ^ , now rnniiy had he then ? 
 
 ■■* 
 
 I 
 
ADDITION. 
 
 11 
 
 ;^9. Minerva bought 7 yards of ribbon,and her mother 
 gave her 6 ; how many yards did she then have ? 
 
 40. There were 7 boys sitting on one bench, and 8 
 on another ; how many were on joth r 
 
 41. There were 7 hoys 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 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 raisius ; how many cents did these 
 cost her ? 
 
 48. (reorge shot 9 pigeons, and James shot 8 ; how 
 many did both shoot ? 
 
 49. Eussel caught 7 fish, and Robert caught 5 ; 
 how many did both catch ? 
 
 50. In ore 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 f 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 anH 62 ? 2 nnd 
 72 ? 2 and 82 ? 2 and 92 ? 
 
12 
 
 ADDITION. 
 
 3. How many are 3 and 3 ? 3 and 13 ? 3 and 23 ? 
 3and33] 3and43? 3 and 53 ? 3and63? 3and73? 
 
 3 and 83 ? 3 and 93 ? 90 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 man}^ 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 IG ? and 26 ? 
 
 6 and 36 ? 6 and 46 ? 6 and 56 ? 6 and 66 ? 6 and 
 
 76 1 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 81 8 and 18 ? S and 28 ?' 
 
 8 and 38 ? 8 and 48 ? 8 and 58 ? 8 and 68 ? 8 and 
 
 78 ? 8 and 88 1 8 and 98 ? 
 
 9. How many are 9 and 9 ? 9 and 19 ? 9 and 29 T 
 
 9 and 39 ? 9 and 49 ? 9 and 59 ? 9 and 69 1 9 and 
 
 79 ? 9 and 89 ? 9 and 99 1 
 
 10. How many are 10 and 11 ? 10 and 21 1 10 and 
 
 31 ? 10 and 41 ? 10 and 51 ? 10 and 61 1 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? 1184? 1194? 
 
 15. How many are 10 and 5 ? 10 and 15 ? 10 and 
 
 35 
 10 
 
 25 
 11 
 
 3i 
 3i 
 
 8i 
 8 
 
 7 
 7 
 
 8 
 8 
 
ADDITION. 
 
 13 
 
 35? 10 and 45? 10 and 55? 10 and 65 ? 10 and 75? 
 
 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 451 11 and 55? 11 and 65 r 
 
 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 and48? 3and 58? 3 and 68? 3and78 . 
 
 3 and 88? 3 and 98? ^ ,., o ^ o^ ? 
 
 18. How many are 8 and 4 ? 8 and 14 ? 8 and 24 ? 
 8and34?8and44? 8and54? 8and64? Sand 74? 
 
 8 and 84? 8 and 94? -..^.^ ao>7 7 
 
 19. How many are 7 and 7 ? 7 and 17 ? 7 and27 ? 
 7 and 37? 7 ond 47? 7 and 57 ? 7 and 67 ? 7 and 77? 
 
 7 and 87? 7 and 97 ? ..... ^op7 
 
 20 How many are 8 and 6 ? 8 and 16 ? 8 and 26 r 
 8and36? 8 and 46? 8 and 56? Sand 66? 8 and 76? 
 S and 86 ? 8 and 96 ? 
 
 Lesson VI. 
 
 i 
 
 1. 
 2. 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 10, 
 11. 
 12. 
 13. 
 14. 
 15. 
 
 8 and 
 11 and 
 
 10 and 
 7 and 
 6 and 
 and 
 
 11 and 
 
 15 and 
 14 and 
 
 16 and 
 21 and 
 
 24 and 
 
 25 and 
 27 and 
 23 and 
 
 9 are 
 7 are 
 9 are 
 14 are 
 12 are 
 1.5 are 
 18 are 
 
 12 are 
 
 13 are 
 
 14 are 
 
 12 are 
 lo are 
 
 15 are 
 
 13 are 
 17 are 
 
 how 
 now 
 now 
 how 
 how 
 how 
 how 
 how 
 how 
 how 
 how 
 how 
 how- 
 how 
 how 
 
 many ? 
 
 many? 
 
 manv? 
 
 many 
 
 many ? 
 
 many ? 
 
 many : 
 
 many ? 
 
 many ? 
 
 many ? 
 
 many ? 
 
 many ? 
 
 many ? 
 
 many ? 
 
 many ? 
 
14 
 
 ADDITION. 
 
 16. 
 17. 
 18. 
 19. 
 
 29 and 11 are how- many ? 
 
 30 and 20 are how many ? 
 34 and 15 are how many ? 
 32 and 18 are. how many? 
 
 1 dime ^^ ~ ^ '^'™''' '" '■^''^^^' 1« cents (J^ma^ 
 
 tJh!S''^"^"^'/*'.''^""^^^"•^'• ^nd clenotes that the qiiauti- 
 -r «!?.!? T^"'^ ^^' '^ f'^^^«^^^' ^'^ to be added. Thus^4 + 2 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 2i. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 33. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 38. 
 
 ^9. 
 
 40. 
 
 41. 
 
 42. 
 
 43. 
 
 33 + 44 are how many ? 
 35+^5 are how many ? 
 36 + 12 are how many ? 
 40 + 36 are how many ? 
 40+29 are how 7nany ? 
 
 44 + 20 are how many ? 
 48 + 32 are how many ? 
 
 45 + 35 are how many ? 
 4 + 8 + 6 are how many? 
 8 + 2 + 7 are how many ? 
 10 + 7 + 3 are how many ? 
 12 + 10 + 9 are how maiay ? 
 15 + 12 + 6 are how many ? 
 1 8 + 4 + 10 are how many ? 
 24 + 16 + 12 are how many ? 
 22 + 33 + 11 are how many? 
 15 + 16 + 2 are how many*? 
 28 + 12 + 15 are how many ? 
 46 + 24 + 19 are how many ? 
 12 + 8 + 6 + 4 are how many^ 
 24 + 10 + 6 + 12 are how many ? 
 22 + 32 + 6 — 10 are how many? 
 37 + 23 + 15 are how many ? 
 64 + 26+12-8 are how many? 
 
 J* 
 
ADDITION. 
 
 15 
 
 ? 
 f 
 
 nd wheo 
 i equal to 
 Qts equal 
 
 ! qnauti- 
 
 IS, 4 + 2- 
 our plus 
 
 t 
 I 
 
 Lesson V. 
 
 1. Three boys, 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. Give 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. Give 7 nuts to one boy, 6 to another, and 7 to 
 another ; how many nuts did the three boys receive ? 
 
 5. Eought 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 piiiks, 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. Eobert shot 9 birds, Eichard shot 11, and 
 James shot 12 ; how many did they shoot ? 
 
 11. A boy bought a pound of butter for 14 cents, 
 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 ^br 9 cents, a robin for 
 10 cents, and a squirrel for 11: cents ; how much did 
 all cost him ? 
 
 15. A lady bought some pins for 15 cents, some 
 
16 
 
 ADDITION. 
 
 thread for 10 cent?, and some lace for 18 cents ; bow 
 many cents did all these articles cost her ? 
 
 16. A gentleman bought a hat for 6 dollars, a vest 
 for 5 dollars, und 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 GO 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 manv 
 cents would you then have ? 
 
 22. A boy spent 12 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 travelled 17 miles one day, and 23 the 
 next ; 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 manv 
 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 pisreons on one tree, and 36 on 
 another ; how many did he see in all ? 
 
 28. In a certain recitation 21 questions were an- 
 swered corrpnflv- nn^ Q iiinnT'T'ooflv . h'\\^ 'v in- 
 
 tions were asked during the recitation ? 
 
ADDITION. 
 
 17 
 
 S ; bow 
 
 J, a vest 
 
 V many 
 
 a gold 
 dollars ; 
 s? 
 d23 to 
 
 a barrel 
 11 dol- 
 
 for 20 
 1 did all 
 
 ts, your 
 w manv 
 
 9 cents 
 mts did 
 
 irs, and 
 lars did 
 
 : 23 tbe 
 
 'ess for 
 tv many 
 
 i, and a 
 ;ive for 
 
 136 on 
 
 3re an- 
 
 Y ques- 
 
 'M 
 
 29. Gave 87 dollp"s for a cbaise, 2 dollars for a 
 wbip, and 11 dollars far a buffalo robe ; bow mucb 
 was given for all ? 
 
 30. If a borse is wortb 60 dollars, and a sleigh 75 
 dollars, wbat is tbe value of both ? 
 
 31. Mattbew is 15 years old, Morgan is 7, and 
 Martin is 10 ; wbat is the sum of their ages ? 
 
 62. 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 bis 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 ; bow much did the horse 
 and oxeu together cost him ? 
 
 35. John gave 11 candies to his brother, 9 to bis 
 sister, and kept 12 himself ; bow 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, 
 3«7 the next week, and 33 the following week ; bow 
 many barrels did he sell during the three weeks ? 
 
 38. A merchant sold a barrel of sugar for 25 dol- 
 lars, a barrel of rum for 15 dollars, and a hogshead of 
 molasses for 23 dollars ; how much did he receive for 
 all these articles ? 
 
 39. A man bought a firkin of butter for 9 doll'-'S, 
 a keg of molasses for 7 dollars, a box of cheese for 4 
 dollars, and a box of raisins for 5 dollars ; how much 
 wasthe entire cost ? 
 
 40. A lady bought a silk dress for 18 dollars, a mr-f 
 for 11 dollars, a shawl for 17 dollars, and a pair of 
 gloves for 1 dollar ; the entire cost is required. 
 
18 
 
 SUBTRACTION, 
 
 CHAPTER 1 1. 
 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 shall 
 have remaining the difference between 3 and 1 which is 2 
 apples. 
 
 2. William had 4 chesnuts, and gave 1 to his 
 brother ; 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 gave 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 
 oif 4 of them ; how many remained on the bush ? 
 
 12. How many are 4 less 2 ? 
 
 13. How many are 5 less 3? 
 
 14. How many are 6 less 3? 
 
 15. How many are 9 less 4? 
 
 f 
 
 th( 
 on 
 fr< 
 
 IG. How 
 
 many are 9 less 3? 
 
SUBTRACTION. 
 
 19 
 
 to Bic bi- 
 rd, I shall 
 hich is 2 
 
 L to his 
 
 ) school, 
 
 brother ; 
 
 m; how 
 
 zabeth j 
 
 of them 
 
 w many 
 
 jsterday 
 I she re- 
 
 w many 
 
 picked 
 
 :sh? 
 
 4 
 I 
 
 17. 
 18. 
 19. 
 20. 
 21. 
 22. 
 28. 
 24. 
 25. 
 26. 
 27. 
 28. 
 29. 
 80. 
 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 
 are 9 
 are 6 
 are 11 
 are 10 
 are 11 
 are 14 
 are 8 
 are 13 
 are 14 
 are 17 
 are 15 
 are 13 
 are 23 
 are 27 
 
 less 
 less 
 less 
 less 
 less 
 less 
 less 
 less 
 less 
 less 
 less 
 
 7? 
 5? 
 4? 
 4? 
 5? 
 4? 
 6? 
 3? 
 5? 
 7? 
 5? 
 
 less 10? 
 less 3? 
 
 less 7? 
 
 Remark. — The symbol— , is called mijitfs; and denotes that 
 the quantity on the right of it is to be taken from the quantity 
 on the left. Thus, 6—4 = shows that 4 is to be subtracted 
 from 6 ;— and ia read, 6 tninus 4 equal 2. 
 
 .•?f< 
 
 31. 8 — 5 are how 
 
 32. 9 — 7 are how 
 
 33. 10—8 are how 
 
 34. 11 — 8 are how 
 
 35. 12—6 are how 
 
 36. 13—8 are how 
 
 37. 14 — 8 are how 
 
 38. 18—8 are how 
 
 39. 22—12 are how 
 
 40. 24 — 14 are how 
 
 41. 12 — 4 are how 
 
 42. 28 — 8 are how 
 
 43. 20—5 are how 
 
 44. 20 — 8 are how 
 
 45. 20—9 are how 
 
 46. 20—7 are how 
 
 47. 20—10 are how 
 
 48. 20 — lo are how 
 
 49. 24—10 are how 
 
 many : 
 many? 
 many ? 
 many ? 
 many? 
 many? 
 many? 
 many? 
 many ? 
 many? 
 many? 
 many? 
 many? 
 many? 
 many? 
 many? 
 many ? 
 many ? 
 many ? 
 
^ 
 
 i 
 
 20 
 
 SUBTRACTION 
 
 50. 
 51. 
 
 52. 
 
 53. 
 
 54. 
 
 55. 
 
 66. 
 
 57. 
 
 58. 
 
 59. 
 
 60. 
 
 61. 
 
 62. 
 
 03. 
 
 64. 
 
 65. 
 
 66. 
 
 67. 
 
 68. 
 
 69. 
 
 70. 
 
 71. 
 
 72. 
 
 73. 
 
 74. 
 
 75. 
 
 76. 
 
 77. 
 
 78. 
 
 25—10 + 5 are 
 
 26—10 + 4 are 
 
 28—10 + 5 are 
 
 27—10 + 5 are 
 
 29—10 + 6 are 
 
 32—10 + 8 are 
 
 34—10 + 7 are 
 
 36—10 + 8 are 
 
 35-10+4 are 
 
 37—^0 + 7 are 
 
 38—10 + 8 are 
 
 39—10 + 9 are 
 
 47—10 + 6 are 
 
 40—12 + 9 are 
 
 42—20 + 7 are 
 
 45—20 + 5 are 
 
 45—20 + 6 are 
 
 47— 20 + S are 
 
 47 + 37 + 4 are 
 
 49—19 + 9 are 
 
 52—22 + 10 are 
 
 54 — 34 + 11 are 
 
 26—46 + 22 are 
 
 57—27 + 14 are 
 
 58—48 + 9 are 
 
 how 
 how 
 liow 
 how 
 how 
 
 many : 
 many ? 
 many '! 
 many ? 
 many ? 
 
 liow many ? 
 
 how many ? 
 many 
 many 
 many 
 many 
 many 
 many 
 many 
 
 how many 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how 
 ]iow 
 liow 
 how 
 how 
 liow 
 how 
 
 many 
 
 62- 
 55- 
 68- 
 
 how 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many 
 
 -30+10 are how many 
 
 -40 + 15 are how many 
 
 -48 + 16 are how many 
 are 
 
 74 — 34 + 15 are how many f 
 
 79. Gave 7 cents for a spool of thread, and 4 cents 
 for a lemon ; how much more did the thread coat 
 than 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 ? 
 
 i 
 
 ..ii 
 
SUBTRACTION. 
 
 21 
 
 
 82. Sold a quantity of wool for 27 dollars, aud re- 
 ceived ill payment a barrel of flour worth 5 dollars ; 
 how many dollars remain duo ? 
 
 83. James has 27 mar])les, and John has 17 ; how 
 many more has James than John ? 
 
 84. Harry is 15 years old, and Henry is 9 years 
 old ; how many years older is Harry than Henry ? 
 
 85. A teacher being asked how many pupils he 
 had, answered that he usually had 37, but at present 
 he had only 27 ; how many were absent ? 
 
 8G. 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. A has 9-1 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 answered correctly ? 
 
 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 4G dollars ; how much did he gain ? 
 
 93. A cow was bought for 25 dollars and sold for 
 19 dollars ; how much Avas 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 loose ? 
 
 95. Frcm a vessel containing 57 gallons, 27 gallons 
 leaked out ; how much remained in it ? 
 
 i 96. A merchant bought a quantity of silk for 47 
 
 1 dollars, and sold it for 67 dollars ; how much did he 
 ^ gain by the bargain ? 
 
22 
 
 ADDITION AND SUBTRACTION. 
 
 97. A butcher has 57 sheep, and 4 4 lambs ; how 
 many more sheep has he than lambs ? 
 
 98. Paid 97 dollars for a quantity of sugar, and 43 
 dollffrs for some molasses ; how much more did the 
 sugar cost than the molasses . 
 
 iK 
 
 Lesson II. 
 
 CHAPTER FIRST COMDINED WITH THE PRECEDINO LESSON. 
 
 1. A boy has 7 chesnuts 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 s mrrel 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 kf - of 
 cheese for 5 dollars, and received in payment a bnixel 
 of flc \r worth 6 dollars ; how much remains duo / 
 
 7. James gave 12 cents for oranges, 15 cents for 
 cake, and had 13 cents remaining ; how much had he 
 at first ? 
 
 8. Mary b<H ght a comb for 10 cents, a spool of 
 thread for 12 - ?ntB, und a paper of needles for 8 
 cents ; she i■iimd^d the c^erk 37 cents ; how r.iuch 
 change ought she to receive ? 
 
 ^ 
 vfi 
 
 
ADDITION AND SUBTRACTION. 
 
 23 
 
 bs ; how 
 
 r, and 43 
 I (lid the 
 
 ESSON. 
 
 4 in the 
 I than in 
 
 nd some 
 the fish 
 of both ? 
 rs for a 
 ow than 
 )th? 
 
 ', and 25 
 i cost of 
 e other ? 
 6 dollars 
 of both ; 
 le flour ? 
 a kf , cS 
 a b;:in.. ; 
 due/ 
 ents for 
 [i had he 
 
 spool of 
 es for 8 
 
 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 waggon worth 17 dollars ; how muca 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 
 G, and then had only 8 remaining ; how many had he 
 atOrst? 
 
 12. Sampson having 9 apples, gave 4 to his mother, 
 and 3 to his sister j — 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 G3 dollars, and 
 exchanged it for a yoke of oxen,— these he 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 loose, 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 ? 
 
 y S. A drover bought some sheep for 40 dollars, 
 some cattle for 180 dollars, and sold them all for 
 200 dollars ; how much was his gain ? 
 
 19. A jeweler bought a watch for 20 dollars, a chain 
 for 40 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 
 
 aj:)ditiox and subtraction. 
 
 22. 14 + 16 + 11 are how mnny ? 
 
 23. 36 + 9 — 12 are how inauy? 
 
 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 manv? 
 
 28. 27 + 1^3— 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 ^ain 4 ? 
 
 32. A merchant bought a hogshead of molasses for 
 47 dollars, and paid 3 dollars fov cartage; for how 
 much must lie sell it to gain 12 dollars ? 
 
 83. 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 '-ought 24, of another 8, and of another 22, : he 
 then sold 20 of them ; haw many remained unsold ? 
 
 35. A watch cost 40 dollars ; how must it be sold 
 to gain 13 dollars ? 
 
 36. Pour boys bought a melon ; 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. Mattheu- 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 fanner had 25 sheep in one field and 15 in 
 another, — he then bought enough more tomake h is 
 number 6G ; how many did he buy ? 
 
 40. John has 34 marbles, and Albert 25 ; how 
 many have they both ; and how many more has Jonu 
 than Albert ? 
 
 
"^(Si 
 
 MULTIPLICATION. 
 
 25 
 
 CHAPTEE III. 
 
 Lesson I. 
 
 ow much 
 
 iasses for 
 for how 
 
 ugar for 
 18 dol- 
 
 one man 
 22,: he 
 msold ? 
 b be sold 
 
 3 cents, 
 Quch did 
 
 nd 13 at 
 im ; how 
 
 LO more, 
 ber 39 ; 
 
 d 15 in 
 
 lake h is 
 
 5 ; how 
 as Jonn 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 
 6. Two 
 
 7. Two 
 
 8. Two 
 
 9. Two 
 10. Two 
 
 Two times 
 
 Two times 
 
 Two times 
 
 Two times 
 
 Two times 
 
 times 
 times 
 times 
 times 
 times 
 
 1 
 2 
 3 
 
 4 
 5 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11. Two times 11 
 
 12. Two times 12 
 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 
 how many? 
 
 many- 
 
 how 
 
 how many ? 
 
 how many ? 
 
 how many I 
 
 how many ? 
 
 how 
 
 many 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 mk 13. What will 2 oranges cost at 3 cents a piece ? 
 
 Solution. — If one 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 cv>st, at 8 cents a piece ? 
 
 17. What will 2 pounds of meat cost, at 5 uenta 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 coat, 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 ? 
 
 25. Three times 4 are how many ? 
 
 fesr.lfL'^:*''-^;^**^- 
 
m, 
 
 2(6 
 
 MULTIPLICATION. 
 
 26. Three times 5 
 
 27. Three times 6 
 
 28. Three times 7 
 
 29. Three times 8 
 
 30. Three times 9 
 
 31. Three times 10 
 
 32. Three times 11 
 
 33. Three times 12 
 
 34!. Four 
 
 35. Tour 
 
 36. Four 
 
 37. Four 
 
 38. Tour 
 
 39. Four 
 
 40. Four 
 
 41. Four 
 
 42. Four 
 
 43. Four 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 11 
 
 times 12 
 
 3 
 4 
 5 
 6 
 
 7 
 
 8 
 
 
 
 10 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 how 
 how 
 how 
 how 
 
 many ? 
 many ? 
 many ? 
 many " 
 
 how many ? 
 how many ? 
 
 how 
 how 
 how 
 how 
 how 
 how 
 how 
 how- 
 how 
 how 
 how 
 how 
 
 many r 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 many ? 
 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. Whatwill 3 yards of ribbon cost, at 7 centsayd.? 
 
 48. What will 4 quarts of chestnuts cost, at 6 
 cents a quart ? 
 
 49. W hat will 4 yards of edging coat, 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, ouccb ' 
 
 M 
 
 54. What will 3 yards of calico cost, at H cents a 
 
 yaxd? 
 
MULTIPLICATION. 
 
 27 
 
 r 9 
 •? 
 
 •? 
 
 '? 
 
 ^? 
 ■? 
 
 ? 
 
 •P 
 
 P 
 9 
 ? 
 
 * 
 
 ? 
 ? 
 
 ■ 
 
 ? 
 
 ■ 
 ■ 
 
 it 6 cents 
 
 s a piece ? 
 
 4 cents a 
 
 sntsayd.? 
 ost, at 6 
 
 5 cents a 
 t 8 cents 
 at 7 cents 
 i 10 cents 
 it 8 cents 
 .1 cents a 
 
 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 centa 
 
 a pound ? 
 
 58. What will 4 candlesticks cost at, llcts. 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. Pive times 6 are how many? 
 
 are 
 
 62. Five times 
 
 63. Five times 
 
 64. Five times 
 Pive times 
 Five times 
 Five times 
 Five times 
 Six 
 
 65. 
 6Q. 
 67. 
 
 68. 
 69. 
 
 70. 
 71. 
 
 72. 
 73. 
 74. 
 75. 
 
 Six 
 Six 
 Six 
 Six 
 Six 
 Six 
 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 
 7 
 8 
 5 
 
 10 
 
 9 
 
 12 
 
 11 
 
 6 
 
 8 
 
 7 
 
 10 
 
 9 
 
 12 
 
 11 
 
 76. Seven times 
 
 77. Seven times 
 
 78. Seven times 
 
 79. Seven times 
 
 80. Seven times 
 81. 
 82. 
 
 Seven times 
 Seven times 
 
 6 
 
 8 
 
 7 
 
 10 
 
 9 
 
 12 
 
 11 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 how many ? 
 
 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 ? 
 
 uO. 
 
 ..,^11 ft Vio««/^la /^f flqVi nnqf of. 7 finWaTS a 
 
 barrel ? 
 
*%■ 
 
 28 
 
 MULTIPLICATION. 
 
 a po J^ ""^^ ^ P'"^^^ ^^ "^^^*<^^ ^ost, at 7 cents 
 a hLT?^"^ "^'^^ ^ ^''^'^^ ^^ ^^g^^ ^°^*> ^* 12 dollars 
 centaTo" ' ^°"^'^ °^ ^^^^'^^^ -«^' «^ 10 
 oenTsaTo'undf ' ^^^"'^ ^^ ^^-^^« -«^' ^^ 12 
 
 92* mft li/l r^''''!f °^/°^'^ ^°«^' ^^ ^10 a bbl.? 
 
 93 What w . P°^^^' "^/^"^^^^^ ^^^^' ^^ ^^- ^ lb.? 
 qt wf . • 5 f°^*' ^ost, at 9 dollars a piece '^ 
 
 piece> '''^^ ^ handkerchiefs cost, at 11 Lnts'a 
 
 96* wtl 7'U ^ i^^'*"^^^ '''^' ^* S ^^^*« a piece ? 
 
 97 Wh^ • I ^T^' '''^^ ^^ ^ ^i^^« a piece ? 
 
 98 wtl • ^P^^'^' "°'<^» ^* 8 dollars a piece ? 
 99* Wha :; 7 ^''-'^ '^ ?P^ ^°^^> ^ 1^ ^- - box ? 
 
 a qui;e? ^ ^^'''' ^^P^P^^ ^°«*' ^^ H cents 
 
 ^. m What will 7 letter-folders cost, at 11 cents a 
 
 101. Eight times 8 
 
 ino' J^S'bt times 10 
 
 103. jNme times 8 
 
 104. Eight times 7 
 
 105. Nine times 9 
 
 106. Eight times 9 
 
 107. Nine times 11 
 
 108. Eiglit times 12 
 
 109. Nine times 10 
 
 110. Eight times 11 
 
 111. Nine times 12 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 are 
 
 liow many ? 
 
 bow many ? 
 
 bow many ? 
 
 bow many ? 
 
 bow many ? 
 
 bow many ? 
 how many ? 
 bow many ? 
 bow many ? 
 bow many ? 
 bow many ? 
 
 a bunoh^''''* "'^^ ^ ^'""'^'' "^"^''^ ^S'9 cents 
 
 lu Vbattl^r^'^T' T'' "' ^2 cts.a piece? 
 c»nft: wi*. ^ ''""«''^* of grapes cost, at 12 
 
 a 
 
 a 
 

 MULTIPLICATION. 
 
 29 
 
 at 7 cents 
 
 12 dollars 
 
 )st, at 10 
 
 )st, at 12 
 
 Oabbl.? 
 :9c. alb.? 
 a piece ? 
 
 I cents a 
 
 i a piece ? 
 piece ? 
 L piece ? 
 5. a box ? 
 
 II cents 
 
 L cents a 
 
 ? 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 > 
 
 9 cents 
 
 I piece? 
 at 12 
 
 115. What will 11 yards of calico cost, at 11 cents 
 a yard ? 
 
 116. What will 19 balls 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. 
 
 CHAPTEE3 FIEST AND SECOND COMBINED WITH THE PEECEDING 
 
 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, 
 bow 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 come to ? 
 
 9. The fair by railroad from Albany to Boston is 
 5 dollars for 1 person ; how much will it be for a 
 family of 9 persons ? 
 
so 
 
 MULTIPLICATION. 
 
 10. Helen had 8 rose bushes, and there were 7 
 roses on each ; how many roses had she in all ? 
 
 11. At 3 dl-^es 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 traveller 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 i 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 jBeld 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 f 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 a dime a piece, how much will 4 handker- 
 chiefs cost? 6 ? 8 ? 10 ? 12 ? 11 .? 14 .? 16 ^ 
 
 24. At 6 dimes a 'niece how 
 cost? 4? 5? 8? 10? 12? 9? 7? 
 
 
3 were 7 
 ill? 
 allons of 
 
 ard, and 
 3re iu the 
 
 > to each 
 ive to all 
 
 I paid for 
 rd i how 
 10 cloth? 
 
 3 butter 
 
 iws, and 
 field? 
 cents a 
 
 dimes a 
 
 hat will 
 lucks ? 
 at is the 
 ons .? of 
 
 4 books 
 Doks ? 7 
 
 be the 
 
 ►st how 
 
 mdker- 
 
 2 geese 
 
 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 ? 6 ? 9 ? 10 ? 12 ? 
 
 27. At 7 cents a yard, how murh will 5 yards of 
 ribbon cost ? 6 yards ? 8 yards ? 9 yards ? 10 yards ? 
 12 yards ? 
 
 2*8. 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 
 csnts 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 candy 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 ? at 8 dollars a box ? 
 
 41. How much will 12 1 ^rrels of pork cost at 5 
 dollars 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 ? 
 
 4 
 
32 
 
 ADDITION, SUBTRACTIOX. 
 
 43. James ia 9 years old, and his father is 4 times 
 as old as he ,s ; how old is his father ? 
 
 44. Jane's froct contains 7 yards of silk, worth 8 
 dimes a yard i what was the value of the silk ? Pro- 
 
 c" st' f tdt:'. ""'' ' •^""'"^^ ' "- ■"-" -« the 
 
 hot'ioStl'il -rLfve'r^al'? ^^-^^ '' -"^^ « '^»^'' 
 
 46. If I earn 12 dollars in a month and spend 8 
 how much shall I have at the end of 12 montC ? ' 
 
 47. If I earn 12 dollars a month and pay 25 cents 
 a week for washing, and 2 dollars a week for board 
 
 moIthT)"? "'" ^ '^"'■^ ''^ '^' '"^ °f ^"^ ^««M10 
 
 »plf fi /' ^ '"^^i^ *?"?? °^ '"'^' "' 1- ^o"'"'s a ton, and 
 tons at 10 f ,/^ "^"^ "= ", *°"' '""1 '"^^ 3 remaining 
 tr;ptatlit ""'''"' tow much shall I gain b^ 
 
 yard ■ h7t^ ^ V'"''' f broadcloth, at 4 dollars a 
 yard, but, bemg damaged, I was obliged to lose 18 
 ddlars by the sale of it ? how much Si I receive for 
 
 Sn bf sfiofng ? '"-^ ''' """"^ '>°- »-'^ ^"^^U I 
 
 51. A man bought a horse for 80 dollars, mid 2 
 dollars a week for his keeping, and received 4 dXs 
 a week for his work ;-at the expiration of 10 weeks 
 
 thVotttlfon'T '° '"'''''' ■' '°- --^ ''' ^^ ^^t 
 
 52. For how much must I sell 4 barrels of wheat 
 which cost me 8 dollars a barrel, to gain 8 dol W 
 
 each ? " ^" '"'* °^ ^ '°'''' ** 25 dollars 
 
 54. Provided a hunter should kill 5 pigeons and 
 wound 4 at every shot ; how manv wonlL!, V°» ."? 
 wound respectively, by shooting 8 times ? ' """ 
 
AND MULTIPLICATION. 
 
 33 
 
 i 4 times 
 
 worth 8 
 c? Pro- 
 was the 
 
 8 days, 
 
 spend 8, 
 ths? 
 25 cents 
 c board, 
 leks (10 
 
 OD, and 
 maining 
 s^aiu by 
 
 lollars a 
 lose 18 
 eive for 
 
 i a bar- 
 shall I 
 
 paid 2 
 dollars 
 ' weeks 
 jain by 
 
 wheat 
 
 irs? 
 
 dollars 
 
 IS and 
 
 ill artrl 
 
 55. If a man travel 29 miles in a day, how many 
 miles will he travel in 6 days ? 
 
 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 ap art will they 
 be at the end of 8 hours ? 
 
 63. Two men are 50 miles apart, and approach each 
 other " ^t the rate of 2 miles an hour, the other, 
 3 miles. . iv ; how far apart will they be at the 
 end of 5 ^ 
 
 64. If 1 Oiange 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 1 
 
 * 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, 
 
 •i 
 
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 ? 
 
 bS. 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 
 
 havTboth ? '' '"'"''^ ^'' ^^""'^'^ ""^ ^°^ '^^"^ 
 
 70 Albert has 9 marbles, Aaron 3 times as many, 
 
 less 7, and Amos has twice as many as both, less 8 : 
 
 etleiT^ ^''''^' ^""^ ^""^ "^^""^ ^^""^ ^^^y *°- 
 
 71. Perry worked for Elisha 4 days, at 6 dimes a 
 day ;---±^li8ha gave him 7 bushels of corn, at 3 dimes 
 a Dusnel ; 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 centos a pound, 
 and the remaining 10 pounds, at 4 cents a pound 
 how much did he gain by so doing ? 
 
 73. tf the interest on i dollar for a year is 6 cents, 
 
 pound 7^^^ ''''" ^^ ^°''''^' °^ ^®^^ ''°'*' ^* ^ ^®^*' ^ 
 
 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- 
 
 oIIIa TVI ^^''' ^^*^""'^ ^g^ + 1^ years. Ee'^ 
 quired, the father's age. 
 
 m.lt ^^J"" °''^°^^ ''^'^^ ^^^^^'^ lemon twice as 
 much, and a melon 4 tunes as much as the orange and 
 
 '^^^^F 
 

 DIVISION. 
 
 35 
 
 low many 
 
 >st? 
 
 Is, and 3 
 )y8 in the 
 ler? 
 
 times as 
 low many 
 
 as many, 
 3, less 8 J 
 they to- 
 
 dimes a 
 ; 3 dimes 
 
 r for 125 
 
 a pound, 
 
 pound ; 
 
 6 cents, 
 he same 
 
 I cents a 
 
 pork 9 
 irk cost 
 
 her way 
 
 ;s ; how 
 
 ; and 5 
 a num- 
 3. Ee- 
 
 vice as 
 ige and 
 
 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? 
 
 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 ? 
 
 CHAPTER IV. 
 
 Lesson I. 
 
 1. 8 are how many times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 3 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times 2 ? 
 
 times ^ I 
 
 times 4 ? 
 
 SOLUTION.- 
 
 -8 are as many times 2 as 2 
 
 8, which are 
 
 4 times. 
 
 
 
 2. 
 
 6 
 
 are 
 
 how 
 
 many 
 
 3. 
 
 4 
 
 are 
 
 how 
 
 many 
 
 4. 
 
 ,10 
 
 are 
 
 how 
 
 many 
 
 5. 
 
 12 
 
 are 
 
 how 
 
 many 
 
 6. 
 
 14 
 
 are 
 
 how 
 
 many 
 
 7. 
 
 6 
 
 are 
 
 how 
 
 many 
 
 8. 
 
 9 
 
 are 
 
 how 
 
 many 
 
 9. 
 
 12 
 
 are 
 
 how 
 
 many 
 
 10. 
 
 15 
 
 aia 
 
 how 
 
 many 
 
 11. 
 
 18 
 
 are 
 
 how 
 
 many 
 
 12. 
 
 21 
 
 are 
 
 how 
 
 many 
 
 13. 
 
 24 
 
 are 
 
 how 
 
 many 
 
 14. 
 
 16 
 
 are 
 
 how 
 
 many 
 
 15. 
 
 18 
 
 are 
 
 how 
 
 many 
 
 16. 
 
 20 
 
 are 
 
 bow 
 
 many 
 
 17. 
 
 22 
 
 are 
 
 how 
 
 many 
 
 18. 
 
 24 
 
 are 
 
 how 
 
 many 
 
 19. 
 
 26 
 
 are 
 
 how 
 
 many 
 
 20. 
 
 28 
 
 are 
 
 how 
 
 many 
 
36 
 
 DIVISION. 
 
 ^^i::z;^X LTi: lr„.^^ istt tSiT 
 
 SoLUTioN.-If for 2 cents I cnn buy 1 apple, for 1 cent T „„„ 
 b.y_|^of an app.e , «„„ f„, 4 eeots, /timc's'^^Wci ^ '/or S 
 
 buy fcA- c/nt? " ''''''• '■"^ """^ "■■""e^^ «"■> I 
 boughtlw's ::„!;?"""' '"" """^ P^""^^' "- ''« 
 can te toughir iVd"!^^ "■''"^- ^"'^^ "^ -''- 
 
 bollnVoTelT""'' ''°" ""'"^ '«"°- -^ b^ 
 
 be tugt fo/io c^en'tf?' '°" """^ ''''' °' '"?« "^ 
 
 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 ? • 
 
 a b?si.e?°e:nTLS\VLr P ''^''"^^' ^* ^ "=^"'^ 
 
 be'L.^aTs'dSraVarT?"''"^ ^"'^ °' "'"''' "- 
 ol. For 18 apples; how many oranges can ha 
 bought at the rate of 2 apples for 1 oranle ? 
 
 rafeantl"7t S d°fllts"' ^* ' '"'"' '' "^ 
 
 34. For 22 dollars; how many sheen mav h^ 
 
 bought, at 2 dollars a piece ? ^ ^ ^ ^^ 
 
 3 dtes^'a pie'ceT "'''"' "'^ ^' '^^ ^^^ '' ^™««' ^* 
 
DIVISION. 
 
 37 
 
 I can jou 
 
 Bents I can 
 fiich are 2, 
 
 he above. 
 
 cent I can 
 are ^ or 2 
 
 !S can I 
 
 s can be 
 
 •f calico 
 
 can be 
 
 ;ape can 
 
 ihels of 
 
 imes a 
 
 3 cents 
 
 >th can 
 
 jan be 
 
 can be 
 
 a bar- 
 
 iy be 
 
 teS; at 
 
 36. At 8 cents a piece, how many tops may be had 
 for cents ? 
 
 37. If 1 peck of beana coat 3 dimes, how many 
 pecks can be bought foi 21 dimea ? 
 
 38. At 3 cents a mile, how many miles can I rid© 
 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 dimea ? 
 
 41. 8 are how many times 4 ? 
 
 42. 12 are how many times 4 ? 
 
 43. IG are how many times 4? 
 
 44. 10 are how many times 5 ? 
 
 45. 15 are how many times 5 ? 
 
 46. 20 are how mauy times 6 ? 
 
 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 ? Q? Z? 2? 
 
 58. 54 contains 2 how many times .^ 3 .^ 9 .? 
 
 59. 75 contains 3 how many times ? 5 .? 15 ? 
 
 60. 63 contains 2 how many times ? 4 ? 
 
 61. At 5 dimes each, how many turkeys can be 
 had for 25 dimea ? 
 
 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 I'Z dimes, if he icceive 4 dimes a day ? 
 
 D 
 
38 
 
 DIVISION. 
 
 64. If a boy spends 5 cents a day, how many days 
 will it take him to spend 15 cents ? 
 
 65. A boy had 20 marbles, and divided them 
 equally among his 5 brothers ; how many did each 
 receive ? 
 
 QQ. A boy divided 28 cents equally among 4 poor 
 women ; how many cents did each receive ? 
 
 67. A farmer gave 4 of his laborers 32 bushels of 
 corn ; how many bushels did each receive ? 
 
 68. If 5 quarts of molasses cost 30 cents, what will 
 1 quart cost ? 
 
 69. At 5 cents a yard, how many yards of ribbon 
 may be had for 35 cents P how many for 50 cents ^ 
 
 70. How 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, how many 
 miles does he travel in I hour ? 
 
 72. If a man travel 5 miles in an hour, how 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 ; how many rows are 
 there in the orchard ? 
 
 75. "Fov 56 dollars, how many barrels of pork can 
 be bought, at 8 dollars a barrel) 
 
 76. If a man can travel 6 miles in an hour, how 
 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 P 
 
many days 
 
 ided them 
 ly did each 
 
 ong 4 poor 
 
 bushels of 
 
 * 
 
 I, what will 
 
 i of ribbon 
 )0 cents ^ 
 ich, can be 
 
 how many 
 
 how many 
 
 iirs a yard, 
 
 >s standing 
 ly rows are 
 
 ' pork can 
 
 hour, how 
 
 irs a yard, 
 
 it the rate 
 le buy ? 
 3 of flour ; 
 
 \ miles, at 
 
 DIVISION. 
 
 Lesson II. 
 
 39 
 
 1. 20 are how many times 2? 4if 10 / 
 
 2. 22 are how many times 1 i ? 
 
 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 5* 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 re- 
 maining ? 
 
 Remark— Whenever there is a remainder, it may be men- 
 tioned simply as a remainder. 
 
 23. 7 are how many times 2 ? 
 
 24. 17 are how many times 4 ? 2 ? 5 ? 
 
 25. 18 are how many times 6 ? 4 ? 2 ? 
 
 26. 34 are how many times 4? 6? 5? 2? 
 
 27. 25 are how many times 5 ? 4 ? 2 ? 3 ? 
 
 28. 16 are how many times 9? 4? 8? 7? 
 
 29. 32 are how many times 7 ? 5 ? 6 ? 
 
 30. 63 are how many times 9 ? 4 ? 6 ? 6 ? 
 
 31. 74 are how many times 2 ? 4? 6? 7? 
 
40 
 
 DIVISION. 
 
 32. 80arehowmanytimes2?3?4?5?6? 788? 
 
 33. 84 are how mauy times 2 ? 3 ? 4 ? 5 ? 6? 7 ? 8 ? 
 
 34. 15 are how many times 4?6?7?*8? 
 
 35. 29 are how many times 2?3?4?5?6972 
 
 36. 90 are how many times 2?4?6?8?9?11? 
 
 37. 144 are how many times 2 ? 4 ? 6 ? 8 ? 12 ?" 
 
 Lesson III. 
 
 for\4'^c*entsf *' '''^' ^""^ many lemons can you buy 
 SoLUTioN.~If 1 lemon cost 2 cents, for 14 cenU T n«« u 
 
 as many lemons as 2 is contained times in 14 which areT ^ 
 Another SoLUTioN.-If for 2 cents I can buy 1 lemon for i 
 
 cent, lean buy 1 half of a lemon, and for 14 cYnts UrL 1 
 
 half, which are 14 halves, or 7 lemons. ' ""^^^ ^ 
 
 2. How mauy boxes of cheese, at 4 dollars a hnr- 
 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 ? ""w lar 
 
 6. If 10 men accomplish a certain piece of work in 
 2 days how long wil it take 1 man to do the samel 
 
 7. It 3 yards of cloth make one coat, how manv 
 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 travelled 7 miles in one hour, at the same 
 rate how long would it take him to travel 63 mT,' 
 
 ^e\'Jol eZZs'' '-''''' '^^^ ''^'^y -- -^ 
 
 11. How manv noriH ^an ■''•'^p ^"■~ ^ — '^'^ • •« - 
 
 pen cost 3 cents ^ ' 
 
MULTIPLICATION AND DIVISION. 
 
 41 
 
 ) ? 6 ? 7 ? 8 ? 
 
 5?6?7?8? 
 ?8? 
 
 ?5?6?7? 
 8?9?11? 
 3?8?12? 
 
 m you buy 
 
 ts I can buy 
 h are 7. 
 lemon, for 1 
 , 14 times 1 
 
 lars a box, 
 
 >nars, how 
 
 rsons one 
 ^eeks ; 
 , how far 
 
 f work ju 
 he same ? 
 low many 
 
 > ytar, in 
 Qterest ? 
 the same 
 33 miles ? 
 !Ows may 
 
 mid, if i 
 
 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 88 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 110 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 brrrels 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 64 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 ; how many boys were tbere, provided each bov 
 received 2 marbles ? *^ 
 
 30. How many pounds of butter, at 14 cents a 
 P°o? \?^' ^^ ^-^^Sbt for 28 apples, at 3 cents each ? 
 
 31. At 7 cents a bottle, how many bottles of ink c- 
 
 you buy for 14 sheets of paper, at 2 cents a sheet ? ' 
 
 62. 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 b men m 3 days I 
 
 34. In how many days can 4 men earn as much as 
 8 men m 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 m 5 months ? 
 
 37. How many men can in 7 days earn as much as 
 28 men m 4 days ? 
 
 38. In 10 days 6 men will earn as much as how 
 many men m 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 ]3 barrels of flour, worth 4 dol- 
 lars a barrel, for 26 yards of cloth; how much was 
 the cloth a yard ? 
 
 1^ 
 « 
 
 Lesson IV. 
 
 CnAPTERS FIRST, SECOND, THIRD, AND FOURTH COMBINED. 
 
 1. 4 times 6 are how many times 2 ? 
 
 2. 4 times 9 are how many tim^es 8 ? 
 
 3. 4 times 8 are how many times 2 ? 
 

 IN, 
 
 M 
 
 FUNDAMENTAL RULES. 
 
 43 
 
 3d each boy 
 
 4. 
 
 
 5. 
 
 14 cents a 
 
 6. 
 
 cents each ? 
 
 7. 
 
 IS of ink c; . 
 
 8. 
 
 1 a sheet ? 
 
 9. 
 
 3 much as 7 
 
 10. 
 
 
 11. 
 
 much work 
 
 12. 
 
 
 13. 
 
 as much as 
 
 14. 
 
 
 15. 
 
 ■n as much 
 
 16. 
 
 
 17. 
 
 at as much 
 
 18. 
 
 
 19. 
 
 as much as 
 
 20. 
 
 
 21. 
 
 ch as how 
 
 22. 
 
 
 ^ 23. 
 
 irs a yard. 
 
 m ^^' 
 
 rs a set ? 
 
 m 25. 
 
 orth 4 dol- 
 
 W 26. 
 
 much was 
 
 27 
 
 
 28. 
 
 
 29. 
 
 
 30. 
 
 
 31. 
 
 
 32. 
 
 
 33. 
 
 )MBINED. 
 
 34. 
 
 
 35. 
 
 
 36. 
 
 Therefore) 
 
 37. 
 
 
 ^B 38. 
 
 
 Jl 39. 
 
 
 WtM 40. 
 
 4 times 10 are how many times 5 ? 
 4 times 12 are how many times 6 ? 
 
 4 times 14 are how mauy times 7 ? 
 
 5 times 9 are how many times 15 ? 
 
 6 times 8 are how mauy times 4? 
 
 5 times 12 are how many times 15 ? 6 ? 
 
 6 times 7 are how many times 2 ? 
 
 6 times 8 are how many times 12 ? 3 ? 
 
 4 times 6 are how many tim'^s 8 ? 
 
 7 times 15 are how many times 5 ? 
 12 times 7 are how many times 21 ? 
 
 8 times 7 are how many times 4 ? 
 How many times 12 are 9 times 4 ? 
 How many times 20 are 5 times 4 ? 
 How many times 9 are 3 times 21, + 9 ? 
 How many times 5 are 7 times 15, + 10 — 5 ? 
 How many times 9 are 3 times 36, — 2 + 11 ? 
 How many times 12 are 9 times 4, + 24— 12 ? 
 How many times 21 are 9 times 14,-! 42 1 
 How many times 7 are 3 times 14, + 21 — 14 ? 
 How many times 5 are 8 times 10, + 5 — 15 ? 
 How many times 5 are 10 times 6,+ 15 + 5 ? 
 How many times 5 are G times 1 5, + 10 + 15 ? 
 
 10 times 4, + 2 are how many times 7 ? 2 ? 
 
 8 times 9, — 2 are how many times 5 ? 
 12 times 8, — 8 are how mnny times 2 ? 
 26 times 11, — 6 are how many times 28 ? 
 7 times 8, + 4 are how many times 12 ^ 
 
 6 times 7, + 4 are how many times 2 ? 
 
 5 times 8, + 8 are how many times 6 ? 
 4 times 9, — 4 are how mauy times 8 ? 
 
 9 times 5, — 3 are how many times 7 ? 
 
 7 times 12, — 14 + 5 are how many times 5 ? 
 4 times 15, + 7—3 are how many times 8 ? 
 
 6 times 7, + 14 — 2 are how many times 9 ? 
 
 11 times 13, + 11 — 14 are how many times 7 1 
 11 times 1 5,-10 + 15 are how many times 17 ? 
 
44 
 
 
 ♦I 
 
 SIMPLE PROPORTION. 
 
 Lesson V. 
 
 PBAOIIOAI, Q0IST.ONS OOMBZKr.VG OHAPTra, THIRD AND FOURTH. 
 
 cos^t ?^''^ "^^'"^ "™* * "'''*'' '"''" """=•' ^'U 3 apples 
 
 cost 8 times 2oe;,s;;th "e'e^'L^^^r' ' ""•" ' "PP'^'"'" 
 2. If 2 pears cost 16c., how much w , pears cost ? 
 quL"ets?r" *="' '^ •=^"*^' '^^ ■"-'^ ^^ 
 oratge's cosu"^'' "°'* '' "'''''' ''"^ '""<'•' ^"1 9 
 pefches" cLrr'^'' '"^^ '' '=^''*^' '^"^ ■"«<=>> will 9 
 lemlYcostr""' "°^* '* •'^"*=' ''°^ ""»<='' will 7 
 6 /ard^f 2u ' "^ ^''P^ '=°^* 18 cents, how much will 
 
 wilteUSuSir 2« <^--' '"- "--y cents 
 -ill V'y'aKstt """^"'' '=°^* ^'^^ <=«"'«' •>»- »uch 
 7 bo^oWsu"''' '""*^* '^''"''' '"'"' "^y oe^te will 
 
 12* If 10 t»:f' ""'''■,"'"* ^^ •=""*'■ what will 2 cost ? 
 be|eSjr7fetor2ro?a^^^^^^ 
 cost 45^dimeTr'' "" '' ^'"^^ of silk cost/if 5 yards 
 
 thillfY " ""^J *?^'' 15 "''«» i" 3 tours, how far at 
 this rate can he travel in 9 hours ? 5 hours 2 7 hours 
 
 4 dollars how A '^' f/.i?*^ "^ P'^^^r 20 miles cos 
 nouars, how far could it be carried for 12 dollarq ? 
 
 21 yard^oT clTh^ T.' "' ?""'*'?"»' <=- >- -fou of 
 ZfJ,^!.. °* ??^^' 't 3 pair can be cut out nf a - 
 -I ""o isarae Kind of cloth ? 
 
 .# 
 
 '-•A 
 
 "^ J ITS, -^.U^ 
 
r 
 
 SIMPLE PROPORTION. 
 
 45 
 
 IND FOURTH. 
 
 U 3 apples 
 
 ^ostihalfof 
 apples will 
 
 3ars cost ? 
 Lch will 3 
 
 ch will 9 
 
 ch will 9 
 
 5li will 7 
 
 mch wi]l 
 
 ny cents 
 
 ►w much 
 
 mts will 
 
 ! 2 cost ? 
 uch will 
 
 5 yards 
 
 ^ far, at 
 hours ? 
 es cost 
 liars ? 
 out of 
 
 7 l.Ti Vl^J 
 
 17. How much 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 clota 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 ciJer 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 
 vard ; how manv vards did he receive ? 
 
 32. A merchant having 15 yards of cloth worth 75 
 
46 
 
 SIMPLE PROPORTION. 
 
 +1 
 
 
 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 
 "f shels were given for 15 yards of cloth • how 
 much did the cloth cost .a yard ? ' 
 
 34 If 35 yards of cloth iost 140 dollars, how much 
 will 95 yards of the same cloth cost ? 
 
 36. How many boxes will be required to contain 
 56 bushels, provided each box contains 8 bushelsT 
 
 d7. How many barrels of onions, at 3 dollars a bar- 
 r^,^must be given for 21 boxes of raisins, at 2 dolts 
 
 38 A farmer bought 9 yards of cloth, at 4 dollars 
 a yard, and paid for it with dder, at 3 del ars a barM 
 how many barrels did he take ? ' 
 
 rdu "^^Y ^"""^ "^^^^^ '^ *^^« a man to lay up 24 
 dollars, if he save two dollars a week ? ^ ^P -^^ 
 
 him p f if^'^'f ^'''^ ^ ^^^'"'^'^ ^"d agreed to give 
 Inm 6 dollars lor every 3 days' .-ork ; how much did 
 he receive a week, allowing 6 working days in a 
 
 Tofth ?'" ""'' ' "°"*'' '"^--^^ ^ weZto the 
 
 41. If 4 oranges are worth 12 cents, how manv 
 
 42. How many yards of cloth, at 2 dollars a vard 
 can^be bought for 4 reams of paper, at 5 ddilrTa 
 
 43 6 men bought a horse for 80 dollars, and paid 
 
 Ittll "" ''■'f} l<^'^'^i»"S l.im ;-at the end of 10 
 
 eTefmanw' "" '°" '' "''""^^^ l«>w much did 
 
 ..^..eo nre woilli j. orange, and 2 oranges 
 
TABLES AND REDUCTION. 
 
 47 
 
 10 dollars a 
 
 1 45 dimes, 
 3loth ; how 
 
 , how much 
 
 th running 
 ains on the 
 inutes will 
 
 to contain 
 bushels ? 
 liars a bar- 
 fc 2 dollars 
 
 b 4 dollars 
 s a barrel j 
 
 lay up 24 
 
 3d to give 
 much did 
 lays in a 
 >ks to the 
 
 3w many 
 kvorth 12 
 
 s a yard, 
 dollars a 
 
 and paid 
 ud of 10 
 luch did 
 
 are worth 1 lemon ; how many lemons can be 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 abound, 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 iirkins of butter for 35 dollars ; for 
 what must I sell it to gain 10 dollars ? what is the gain 
 on each firkin i 
 
 CHAPTER V. 
 Lesson I. 
 
 Table oi? United States Cuerency. 
 
 10 Mills (w.) 
 10 Cents 
 10 Dimes 
 10 Dolfavs 
 
 make 1 Cent, 
 " 1 Dime, 
 " 1 Dollar, 
 « 1 Eagle, 
 
 marked c. 
 d. 
 
 1. How many mills in 4 ceuts? 
 
 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 RKDUCTIOW. 
 
 J.^IIo^ many dimes in 1 eagle and HI In 2 eagle: 
 
 7. How many dollara in 80 dimes ' 
 Solution. — Thoro .,.. m j- . 
 the number of dbe,eoual^t'' 'J *'' "'"^fore, 1 tenth of 
 
 InVceTtsr^'''''"^^'"^" «-*«? ' In 70 cents? 
 yards can be bought for 1 donfrf ''' ^°" ""y 
 
 ^ -I V ' "^^^^^^^^^^^^ ^^" ^°" ^"^ '•- 
 
 1^ eaglS^^ToTouCs If Z^olStsf ^''^ ""^ ^^ 
 
 
 Lesson II. 
 
 Table of English I^^onet 
 aOShilliDgg ., ,i|'""'"g, '^ ,. 
 
 LS,-rr''^''^"^=^^^«Miings. 
 
 the «umC-ofXds;o„lHt""°«V'' ' ^- "-'f-e 20 time, 
 In'e^t" many shillings in'l£ ? ''in'st^g 3^ , 
 
TABLES AND REDUCTION. 
 
 49 
 
 In $3? In 
 In 2 eaglcc 
 ru$3? In 
 
 re, 1 tenth of 
 • 1 tenth of 
 
 70 cents ? 
 >00 centa ? 
 
 Qts? 
 
 ho^ - many 
 •u buy ibr 
 u buy for 
 
 
 20 times 
 20 times 
 
 4. How many pence in 2£ 10 shilliDgs 5 pence ? 
 
 5. How many pounds iu 60 shillirgs ? In 8O5. ? 
 In I2O5. ? 
 
 6. How many pounds in 480 pence ? In 720f/. ? 
 
 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 shillJngs ? 
 
 Lesson III. 
 
 Table op teoy Weight. 
 
 24 Grains (gr) make 1 Pennyweight, marked dwi. 
 20 Pennyweight ** 1 Ounce, " oz. 
 
 12 Ounces " 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 f In 70 ? 
 
 6. If 7 grains of gold cost 168 dimes, how much 
 will 10 pennyweights cost ? 
 
 7. What will 1 pennyweight of gold cost, if 2 
 gi'ains cost 18 dimes ? 
 
 8. How many pennyweights in 4 ounces and 6 
 pennyweights ? 
 
 ?. How many pounds in 480 pennyweights ? 
 10. How many grains in 2 oz., 2 dwt., and 2 gr. 
 
TABLES AND REDUCTION. 
 
 Xiesson IV. 
 
 Taule OP AvoiHDurois Weioht. 
 io Drams, (dr ) r«„i , /> 
 
 lOOcnoor •' ^koIOuno^, marked o.. 
 
 25 Pounds ., 'P™-'!. » 4: 
 
 pounds ? In coo pound, ? Tr. ??nr"'"^" • !'» 400 
 
 4. How many prunds in /^ '^OOpounda? 
 qrs. ? -^ P""""^ « 3 qra. ? In 2 qrs. ? In 7 
 
 ^ 7. ifsoirofh^jTosTn,-!;""''*'^ ^^■■s'>'? 
 
 ters cost? will 1 cwf ? w II 2 .^^f' '':^'^' ^'" ^ guar- 
 
 8. What will 2 (•!;„<. i • "'^'- """^ ^V-^ 
 dime? ' ^ *°»« °f "-"I cost, if 1 ]b cost 1 
 
 io.lttt!it 'r ftr ' 1 ^ '^'-^ =* ^r. ? 
 
 pound ? at 5 cents a^und? « "'"'' "* * *'''»« « 
 
 ,*t; 
 
 •I 
 
 12 Inches (m) 
 3 Feet 
 
 5^ards.orl6|feet 
 
 8 Furlongs, or 320 rods, ' 
 3 Miles „ 
 
 69i Miles 
 860 Degrees 
 
 Lesson V. 
 
 Table of Long Mbasuee. 
 
 make 1 Foot, 
 " 1 Yard, 
 " 1 Rod, 
 1 FurloDff, 
 1 Mile, 
 1 League, 
 1 Degree, 
 
 1 Circle of the Earth. 
 
 marked ft. 
 
 " k 
 
 u -fr- 
 mt. 
 
 lea. 
 
 deg. or «> 
 
 1 TT . * ^^^c^e of the Earth " 
 
 In'5f?rirxST^^-l«-^In2ft.Tl.fe.P 
 
TABLES AND REDUCTION. 
 
 51 
 
 arked oz. 
 " lb. 
 gr. 
 t* cwt. 
 " T. 
 
 In 10 oz ? 
 ?In81bs? 
 ? In 400 
 da? 
 
 [rs. ? In 7 
 
 ight ? 
 
 ght? 
 
 ill 3 quar- 
 
 Ib cost 1 
 
 Desaqr. ? 
 * dime a 
 
 ■d /If. 
 yd. 
 
 rd. 
 fur. 
 mi. 
 lea. 
 deg. or o. 
 
 1 4 ft. ? 
 
 ,4^ 
 
 2. Haw niftny feet in 2 yds. ? In G yds. ? In 5 yds. ? 
 In 12 yds. ? 
 
 3. How many yards in 2 rods ? In 4 rds. ? In 8 
 rds.? Ill 10 rds.'? 
 
 4. How many furlongs in 4 miles ? In 6 mi. ? In 
 mi. ? 
 
 5. How many inches in 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 ? 
 
 Lesson VI. 
 
 Table o¥ Cloth Measuee- 
 
 2^ 
 
 4 
 
 4 
 
 3 
 
 5 
 
 6 
 
 Inches 
 
 Nails 
 
 Quarters 
 
 Quarters 
 
 Quarters 
 
 Quarters 
 
 4i 
 <( 
 
 make 1 Nail, tnarkod na. 
 
 1 Quarter of a yard, " qr. 
 
 1 Yard, " yd. 
 
 « 1 Ell Flemish, " E. Ft. 
 
 " 1 Ell English, " E. E. 
 
 " lEU French, " 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 yds. and quarters ? 
 
 6. In 3 Ella French, how many yds. and quarters '^ 
 
 7. In 4 Ells Fr., and 8 Ells FL, how many ya rds ? 
 
 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 ? 
 
52 
 
 TABLES AMD REDUCTION. 
 
 Lesson VII. 
 
 Table of Land or Sqfaeb Measuee. 
 
 '1 I^Te Je^er ' ^''' *'«•> ^^^^ J i'l-e foot. .,.^, 
 
 30i Square yards « i 1^^'® ^^/''' '9.id' 
 
 40 Square rods u ] 1^"^ '°^' ^' P^^«' ^' 
 
 640 Acres . /^^°''^' ., A. 
 
 - „ 1 Square mile, sq.m. 
 
 sq. ;d?7 "^'"^ '^"'^^ ^^^^- ^^ ^ «5- y<i^. ? In 8 
 
 2. How many poles in 4 roods ? In 6 roods ? 
 
 3. How many acres in 40 roods ? In 160 roods ? 
 ^^4.^ How many square yards in 81 sq. ft. ? Z'loS 
 
 5. How many square yards in 1 rood 10 rods ? 
 
 
 Lesson VIII. 
 
 Table op Cubic Measure. 
 
 24J Cubio feet „ ] S"*"? y*'"''' ««■ V. 
 
 16 Cubic feet „ ^ P«''f of stoue, jo,;^: 
 
 8 Cord feet, or ) 1 Cord foot, c.//- 
 
 128 Cubic feet J- " 1 Cord of wood, O. 
 
 1. How many cubio feet in 4 cubic yards 1- 
 3. How many cubic feet in 4 perch olatoL , 
 3. How ™any cords in 96 cord feet "fo*?,/ ft P 
 
 In'e 0^:?""""^ '"'^ '■*«" '" ^ «ords ? In 6 cords ? 
 
TABLES AND REDUCTION. 
 
 63 
 
 or pole, P. 
 R. 
 A. 
 sq.m. 
 
 ds.? In 8 
 
 oods 1 
 >0 roods ? 
 ? lulOS 
 
 ' rods ? 
 
 cu.ft. 
 cu. yd. 
 > pch. 
 eft' 
 
 C. 
 
 le? 
 
 J c. ft. ? 
 '4 cubic 
 
 cords ? 
 
 
 Lesson 
 
 IX. 
 
 
 
 
 Table op 
 
 Wine Measube. 
 
 
 
 4 Gills (^0 
 
 
 make 1 Pint, 
 
 marked 
 
 Pt. 
 
 2 Pints 
 
 
 i( 
 
 1 Quart, 
 
 ii 
 
 qU 
 
 4 Quarts 
 
 
 i( 
 
 1 Gallon, 
 
 K 
 
 gal. 
 
 42 Gcallons 
 
 
 {( 
 
 1 Tierce, 
 
 t( 
 
 Her. 
 
 8H GalloDs 
 
 
 u 
 
 1 Barrel, 
 
 <( 
 
 bar. 
 
 2 Bar. or 63 Gallons 
 
 (( 
 
 1 Hogshead. 
 
 (i 
 
 hhd. 
 
 2 Hogsheads 
 
 
 li 
 
 1 Pipe, 
 
 U 
 
 pi. 
 
 2 Pipes 
 
 
 l< 
 
 1 Tun, 
 
 4( 
 
 tun. 
 
 1. How many gills in *i pints 1 In 4 pints ? 
 
 2. In 3 qts., how 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 f 
 
 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 1 
 
 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 op Dbt Measuee. 
 
 2 Pints 
 8 Quarts 
 4 Pecks 
 
 make 1 Quart, 
 " 1 Peck, 
 « 1 Bushel, 
 
 marked qt. 
 pk. 
 bu. 
 
 
 1. In 1 peck how many pints ? 
 
 2. 2 pecks will fill how" naany pint measures ? 
 
 3. In 3 pecks and 3 quarts how many pints? 
 
 E 
 
"»»*-,. 
 
 h4 
 
 TABLES AND REDUCTION. 
 
 S.' lu ? bir ? ''"''''' ''°" "^y quarts . 
 pints ? '""'"'' '^°»' "'"=7 quarts? low many 
 
 cost at'thi'i^t?';^;'^, ""' '' -"*'' -i-^' will 3 necfa 
 how much did she gal P ""' '*' ^ "^"'^ » Pw* i 
 
 at lo^riTnS Ltt:„t ' p^ V --^^. 
 
 .ooseberHes.^., . eenfs 7^^?^' Inll tit 
 
 9- What will 5 nnartq nf „i, j. 
 cost 128 cents ? ^ "* "^^'"^ cost, if 1 bushel 
 
 10. A farmer sold 1 l^n q i 
 seed, at 040 cents a bushel and in"'"' ^ P'" °^«^°^e^- 
 1 bu., 2 pk. and 3 quartrnf t " Payment received 
 bushel ; Lw much Suf dlz^r''''' "* "'^ "^^'^ " 
 
 ♦I" 
 ,1' 
 
 60 Soconda (wc.) 
 
 60 Minutes ^ 
 
 24 Hours 
 VDays 
 
 4 Weeks 
 
 12 ^lendar months 
 62 Weeks 
 866 Days 
 366 Days 
 100 Years 
 
 Lesson XL 
 
 Tablk of Time. 
 
 make 1 Minute, 
 1 Hour, 
 1 Day, 
 1 Week, 
 1 Month, 
 1 Year, 
 1 Year, 
 
 1 Common Year, 
 1 Leap Year, 
 
 (i 
 
 marked m. 
 
 <( 
 (( 
 (( 
 
 « 
 
 « 
 
 hr. 
 d. 
 
 tc. 
 
 mo. 
 
 yr. 
 
 yr, 
 
 yr. 
 
 yr. 
 
 C. 
 
 Ti.^^71 . 1 Century, « w 
 
 7^^':^t^^Vt\l^\^^^ the divisions of th„ 
 
 ixi each 
 
 ana the number 
 
 of day 
 
 s 
 
""M r, 
 
 TABLES AND REDUCTION. 
 
 55 
 
 quarts ? 
 iiow many 
 
 will 3 pecks 
 
 f strawber- 
 nts a pint ; 
 
 ►f currants, 
 1 bushel of 
 h remains 
 
 f 1 bushel 
 
 of clover- 
 fc received 
 20 ceats a 
 
 d m. 
 hr. 
 d. 
 to. 
 mo. 
 yr. 
 
 yr, 
 yr. 
 yr, 
 c. 
 
 of the 
 fdays 
 
 Ist month, January, 
 2d " February, 
 
 3d *' March, 
 4th " April, 
 5th " May, 
 
 June 
 July, 
 August, 
 
 September, 
 
 October, 
 
 November, 
 
 Jth " December, 
 
 « 
 
 
 has 
 
 (( 
 
 << 
 
 (( 
 (( 
 
 81 days. 
 
 28, in leap year 29. 
 
 31 days. 
 
 30 " 
 
 31 " 
 
 30 " 
 
 31 " 
 81 " 
 
 SO 
 81 
 30 
 
 31 
 
 «( 
 
 (( 
 
 The following lines will help to remember the num- 
 ber of days in each month : 
 
 " Thirty days hath September, 
 April, June and N^overaber ; 
 All the rest have thirty-one, 
 Except February alone. 
 Which hath but twenty-eight in fine, 
 Till leap year gives it twenty-nine." 
 
 JJ^" In our calculations on interest we shall reckon 80 days 
 to the months and 12 months to the year, although not strictly 
 accurate* 
 
 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 1 
 
 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 ? 
 
56 
 
 TRACTIONS. 
 
 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 dajs ? 
 
 Lesson XII. 
 
 Miscellaneous Table. 
 
 12 Units 
 12 Dozen 
 12 Gross 
 20 Units 
 
 24 Sheets of Paper 
 20 Quires 
 56 Pounds 
 60 Pounds 
 196 Pounds 
 
 200 Pounds 
 
 make 
 
 
 u 
 «f 
 
 «{ 
 
 « 
 
 r 
 
 1 Dozen. 
 1 Gross. 
 
 Great Gross. 
 
 Score. 
 
 Quire. 
 
 Ream. 
 
 Bushel of Corn. 
 
 Bushel of Wheat. 
 
 Barrel of Flour. 
 
 Barrel of Beef, 
 
 Pork, or Fish. 
 
 ai> T^^^ ^^^^ ^ ^^^^^ of paper cost, at 15 cents a 
 
 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 I 
 
 CHAPTER VI. 
 Lesson I. 
 
 1. John has 6 nuts, and Joel 1 half as many : how 
 many has he ? j > ^^ 
 
 mSrh^riir^n.^ 3 nut'"""' ' >"'«--»y. j«.i 
 
FRACTIONS. 
 
 57 
 
 2. Mary had 4 dresses, and Kachel 1 half as many ; 
 
 how many had she ? . ^ ■, . -, ^ ^e ^A 
 
 3. Jacob is 8 years old, and John is 1 half as old ; 
 
 how old is John ? ^^ ^e cj.\, 4. 
 
 4. Moses having 2 marbles, gave 1 half ot 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 1 
 
 6. What is 1 half of 6 ? 
 
 7. How many halves in 1 ? i -, v li* 
 
 8. If an orange cost 8 cents, and a peach 1 halt as 
 much, what is the cost of the peach \ 
 
 9. James had 12 cakes, and John 1 half as many ; 
 
 how many had John 1 4. ^ a «nT.f a 
 
 10. If 3 apples cost 6 cents, what part of 6 cents 
 
 will one apple cost ? 
 
 11. What is 1 third of 6 ? 
 
 12. What is 1 half of 8 ? 10 ? 12 ^U ? 16 U8? 
 
 20 f 
 
 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 f 
 4 pounds 1 5 pounds ? 6 pounds ? 
 
 16 What is 1 fourth of 8 ? of 12 ? of 16 ? of 20? 
 i?: What is 1 fifth of 15 I of 10 ^ of 20 , of 30? 
 18 If 1 fifth of 15 is 3, what is 2 fifths of 15 ? d 
 
 fifths ? 4 fifths I 6 fifths ? 8 fifths ? 
 
 19. AVhat is 1 sixth of 12 ? ^ 
 
 20. If 1 sixth of 12 is 2, what is 2 sixths of 1^ ? ^ 
 sixths 1 4 sixths 1 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 1 8 sevenths ? 4 seventnsY o sevuutuB i ^ «8tx...vIi^ . 
 
 23. If 1 pound of candies cost 12 cents, what part 
 
58 
 
 FRACTIONS. 
 
 .¥ 
 
 f<^^;L7IZYlJ%iT. ^ ^- ^ -ts . for 
 
 cents ' ,/l [ZZoZu^l r*'' ^"""'r' "f 36 
 
 twelfths? iVtwemt? '^""^'^ 9 twelfths? 10 
 
 30. y\ aat uo you understand by 1 third ? 2 thirds' 
 
 are called 2 tUrds '"^' ^""^ '"» "^ "'ese plrts 
 
 q?" wl!''J "^j" "°" understand by 1 half ? 
 fourftsTslouHh jr ""'^'^"'='"'' "y 1 f-'tb 1 2 
 
 3 lfttsT4lfth7?''" ""^'''''"'^ ^' "■ fi^* • 2 fifths? 
 34. How many thirds make a whole one ? 
 ds. Jlow many fourths in 1 « 
 
 sevenths MseveLhsr5:rv'enthsY ' "''''*''^ ' ^ 
 rfS. ±low many sixths in 1 ? 
 89. How many ninths in 1 ? 
 
 40. How many eighths in 1 ? 
 
 41. How many sevenths in 1 ? 
 4J. How many tenths in 1 ? 
 
 
 XT 
 
 ow 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 1 
 
 SoLunox -Tf James Ims 9 marbles, and Jacob 2 thirds as 
 
 46. Mary bought 12 candies and Sarah bought 2 
 thirds as many ; how many did S^f ^^uy ? 
 
 47. Eachel has 12 primers, Mary ^ 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 
 
 aa old : how old is be .^ . r. k 
 
 49 Augustus has 40 cents, and Augusta has 5 
 
 eighths as^many ; how many has she ? 
 
 50. Morgan had 36 marbles, and gave 4 s^«»8 »' 
 them to Martin ; how many did he give to Martin, 
 
 ■'I^Zrha^li fo-ferackers, and Nathan has 7 
 ^ Sn L'rceXand Mrtlhew had 5 ninths 
 
 " sTLLbr i^sTyett o'ld! and his father is 9 fifths 
 
 as old ■ what is his father's age 1 
 
 54 A farmer had 84 sheep and a wolf killed I 
 third of them ; how many had he remaining 1 
 
 55 In a certain school there are 12 girls, and 7 
 four'ths'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 ] , anellin^ 
 
 ^7 4 fifths of all the words given out in a spe^im^ 
 57. 4 Wtas 01 ^^ .Q,„^^tlv, and 8 were misspelled ; 
 lesson w«ru ispciivv. ^^^----- -J' '„i. i 
 
 of how many worde did the lesson consist ? 
 
60 
 
 inf.; 
 
 J.I' 
 
 part 
 
 FRACTIONS. 
 
 flfth^fthSr -tol'' \ ^''' -'-'«' for 7 
 
 60. A received «Mnr T.""^ "»« *•>« gam ? 
 
 1 fifth of It for boirS? L^ '"''l!^' '''''°^' """Ipaid 
 week ? '"'^'^'' * ^°'' "'"ch did he save each 
 
 61. How many are 4, fifths of 75 ? 
 
 l^er age e,u,,s i^T^t ^ht^ ^S at' f"' ' ^'^'"'"^ "^ 
 
 4 sixths ^5 -ths'r^lS /oTe -LV°"^'''«^ 
 
 eiSs?7^eighZ re UZif^ f ^3?tLths . 5 
 
 . 66. 3 nintlfs of 27 4e^tw ^ "^,*.^ ' ^ tWrds ? 
 
 ninths; 8 ninths ? 2 thirds r ^°^ ^ "'"*''«' ^ 
 
 »r 18. Is'areVrtits'sf* '' '' ""^ ' ""'^'"^ -« 3 time, 6, 
 
 70. 9 thid of 1 st 1''°^ """"y «"^« 6 ? 
 
 71. 4 fifths of 25 Cl.*'"'" ""^V times 3 ? 
 
 72. 6 n nths of IS »! 7 """"y *'»«« 2 ? 
 
 73. 7 S» of qo r ^^ """"y *'•»«« 6 ? 
 
 75. 15 seventeenth nf .7 """^^ ''««» 2 ? 
 
 76. Hc/manrtime?17 a «^^^^ «mes6? 
 
 77. Jlaw many times 8 aril 9 H •^?'''"*« "^ 36? 
 
 78. How many t mea 5 ar« in *'';'''^^°"'« "f 26 ? 
 7q tt« ^ «^iuit;s o are JO thirds nf Qft ? 
 
 79. How many times 4 are 2 thirds of 97 o , 
 «0. How many times 6 nra q t i „ '' ~ 2 ? 
 
 how manv Ld h« .4.-^- ^ -^ ^ °^*^^"^ *« ano^iier • 
 »^. A had $120 • 1 fhi^A r.ff vi 
 
 1 third of It he spent for a watcb, 
 
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 ? 
 
 S4. 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. Bequired the cost of the 
 farm. 
 
 92. 5 eighths of 72, -] l3, 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 1 
 
 94. What will 2 thirds of 12 pounds of coffee cost, 
 at 13 cents a pound ? 
 
 95. What will 3 fourths of a gallon of alcohol cost, 
 at 9 cents a pint ? 
 
 96. What will 1 sixteenth of a bushel of flax-seed 
 cost, at 6 cents a pint ? 
 
, M t 
 
 FRACTIONS. 
 
 97. How 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 be 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 
 23 any times 7 ? 
 
 lOi?. 2 thirds of 30, +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 ? 
 
 10'^ 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. How 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 11. 
 
 1. If 1 third of an orange cost 2 cents, what will 
 1 orange cost ? 
 
 Solution.— If 1 third of an orange cost 2 cents; 3 thirds, or 
 1 orange, will cost 3 times 2 cents, which are 6 cent?. 
 
FRACTIONS. 
 
 63 
 
 2. If 1 half of a pound of raisins cost 8 cfjnls, 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 I 
 
 4. If one third of a pound of pork cost 5 cents, how 
 much will 2 pounds cost ? 
 
 5. 2 is 1 third of what number ? 
 
 Solution.— If 1 third of some Dumber is 2, 8 thirds, which is 
 that number, are 3 times 2, or 6. 
 
 6. 5 is 1 half of what number ? 
 
 7. If 1 fourth of a lemon cost 2 cents, what will 1 
 
 8. If 1 fourth of a lemon coat 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 ? 
 
 13. What will 4 fifths 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 ? . n *. 
 
 15. If 1 sixth of a gallon of vinegar cost 2 cents, 
 
 what will 1 gallon cost ? , ^ , . , . j 
 
 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? , . , , • v i, 
 
 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 of a yard of cloth for 4 dimes J 
 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 ? .«^ *• i.i. v 
 
 20. AVhat wi'll 1 yard of cloth cost, if 1 ninth ot a 
 
 yard cost 5 cents ? 
 
 ■« 
 
 ii 
 
 ^1 
 
64 
 
 FRACTIONS. 
 
 »!• 
 
 eAy:i:i:,tft''°^ -w. cos, if x 
 
 euLI^ri "'",'"' *''^, '°'' °^2 cords of wood, if 1 
 
 wfit I "• *"'^'^"' "^ ""^ distance from Albmv to 
 
 ^5™9Ts rten"? '"f "^' '^ ""^ entire dine" P*° 
 o« T r ! *'""'^ "^^ ^''•"'t number ? 
 
 07 IP 1' r«<.T''*o°"; "^ ^^l^at number .^ 
 28. 12 IS 1 fifth of G times what number ? 
 qn 1 Q !' J V^^ "^ ^ *™«^ "-hat number ' 
 31. 10 ,s 1 eighth of 20 times what number 1 
 
 34 lo 1 1 tl^Tfr ^? "■"«« ^bat number 
 is required. ^^^^ °^ ^^® '^o^'se 
 
 wafi t^StCf I s (rntuK f r- T'?-'"^ 
 
 cost bi „Hat was thrst^^hl^ajL f'"* 
 
 l^^elfth of 3 times^his^'-':!' X^S^l^^l 
 
 3 tlmeelhe To'st oVi' "''.'* *"' ^1"'='' ^"^ ^ *«"«" of 
 her dress? "" ''^^^^ ^ ^^at was the cost of 
 
 your a/eiYSuh'^r/:'- "'° '^ """■ '^ -^--^ "Id, 
 
FRACTIONS. 
 
 65 
 
 Lesson III. 
 
 1. If 2 thirds of a melon cost 4 cents, what will 1 
 
 melon coat ? 
 
 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 I 
 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 V 
 
 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 wiU 1 pound cost ? 
 
 6. If $4i 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 1 20 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, 8 thirds, which ia that 
 number, are 3 times 4, which are 12. Therefore, 8 is 2 thirds 
 of 12. 
 
 Remark. — Representing the conditions and solutions of ques- 
 tions by symbols will aid young pupils in comprehendiug the 
 more difficult parts of arithmetical analysis. The condition and 
 analysis of the preceding question may be represented, thus :— 
 
 If 
 
 = f of some number = 8, 
 
 H< ' 
 
 and 
 
 i of that number = 4, 
 
 =^, which is that number, = 12. 
 
66 
 
 FRACTIONS. 
 
 ^.i 
 
 17. 
 18. 
 19. 
 20. 
 
 23. 
 24. 
 25. 
 26. 
 
 15. 12 is 2 thirds of what number ? 
 
 16. 4 is 2 thirds of what number? 
 10 is 2 sevenths of what number ? 
 
 9 is 3 fourths of what number ? 
 12 is 3 fourths of what number ? 
 12 is 6 elevenths of what number ? 
 5j1. 14 is 7 eighths of what number ? 
 22. 14 is 2 sevenths of what number ? 
 6 is 3 tenths of what number ? 
 9 is 3 sevenths of what number 1 
 15 is 5 sixths of what number ? 
 15 is 3 haifs 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 sevenths of what number ? 
 
 34. 3 fifths of 25 is 5 fourths of what number ? 
 
 35. 2 sevenths of 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 of 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 j what was the cost of the horse ? 
 
 43. In a certain school there are 36 ladies, and 5 
 fourths of the number of ladies equals 3 fifths of the 
 number of gentlemen. How many gentlemen were 
 there in the school ? 
 
 44. 
 
 TIT- 
 
 ,• I I 
 
 rears old, and 4 sevenths of her 
 age is 2 thirds of Hezekiah's age ; what is his age ? 
 
 ivxarjr IB ±^ 
 
FRACTIONS. 
 
 67 
 
 45. A piece of clotli containing 12 yards was sold 
 'for $60, which was 5 fourths of what it cost ; how 
 
 much did it cost, and what was the gain on each yard? 
 
 46. A has 48 geese, and 3 fourths of his numberis 
 equal to 9 sevenths of B's number ; how many geese 
 
 has B ? . , , JO 
 
 47. The head of a fish is 12 inches long, and 6 
 fourths of the length of the head is 3 fifteenths of the 
 length of the body. Required the length of the fish. 
 
 48. A farm was sold for $1200, which was c^ly 6 
 sevenths of what it was worth. How much was lost 
 
 by the bargain ? , ,. i . i. 
 
 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? ■ .^ r 1 4.1, 
 
 50. A man gave 60 dollars for a suit ot clothes, 
 which was 1 fifth of his yearly income ; 1 sixth of the 
 remainder he spent for a watch, and what then re- 
 mained was 4 fifths of his brother's yearly income. 
 What was the yearly income of each ? 
 
 in were 
 
 Lesson IV. 
 
 2 thirds 
 1 half 
 
 1 third 
 1 fourth 
 1 sixth 
 
 1 seventh 
 
 3 fourths 
 7 eighths 
 9 tenths 
 
 5 sevenths 
 
 2 fifths 
 5 thirds 
 
 &c. 
 
 is written thus f. 
 
 (( 
 
 it 
 
 « 
 
 (( 
 t( 
 (t 
 
 (( 
 
 (( 
 
 (( 
 
 (( 
 
 (( 
 
 (( 
 
 (( 
 
 it 
 
 (( 
 
 (( 
 
 (( 
 
 (t 
 
 (( 
 
 (( 
 
 (( 
 
 <( 
 
 (( 
 
 (< 
 
 <« 
 
 (( 
 
 « 
 
 (( 
 
 1 
 
 ¥• 
 
 1 
 7* 
 
 1 
 
 1 
 
 1 
 
 T' 
 
 3 
 ^* 
 
 7 
 "8* 
 
 9 
 TIT* 
 
 5 
 
 f 
 
 2 
 
 &( 
 
 
 
68 
 
 REDUCTION OF FRACTIONS. 
 
 it 
 
 m 
 
 ],. 
 
 Remark.— The above expressions are called fractions. The 
 figure above the short horizontal line is called the numerator, 
 and the figure below the line is called the denominator. For 
 example, m the fraction f, the 3 is the numerator, and the 4 is 
 the denominator. 
 
 ThQ denominator of a fraetTon shows into how many equal 
 parts the thing is divided ; and the numerator shows how many 
 ot these parts are taken. 
 
 . }' ? 7°^ ^^* ^^ orange into 3 equal parts, what 
 IS 1 of these parts called ? 
 
 2. If a lemon be cut into 4 equal pieces, what will 
 1 ot these pieces be called ? 2 ? 3 ? 4 ? 
 
 3. If a bushel of apples be divided into 6 equal 
 parts, what will 1 of these parts be called? 3? 4? 6? 
 
 4. If a basket of peaches be divided into 8 equal 
 parts, what will 3 of 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.— In 1 there are 2 halves, therefore 1 half thenum- 
 oer ot halves equals the number of ones. I half of 4 is 2 • 
 therefore, f equals 2. 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1 1 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1? 
 
 how many times 1? 
 
 how many times 1 ? 
 
 how many times 1 ? 
 
 how many times 1? 
 
 how many times 1 ? 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 19. 
 20. 
 21. 
 22. 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 T6, 
 
 In 
 
 6 
 
 8 
 
 To 
 
 2 
 
 1 2 
 "J 
 
 Xj^ 
 
 2 
 
 6 
 
 3 
 X 2 
 
 TT 
 
 9 
 
 7? 
 1 5 
 
 1 8 
 "2 
 18 
 TT 
 21 
 ¥ 
 
 8 
 
 1 2 
 
 ¥ 
 IG 
 
 T 
 20 
 
 how 
 
 many times 1 ? 
 
REDUCTION OF FRACTIONS. 
 
 69 
 
 ? 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 31. 
 
 32. 
 
 33. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 38. 
 
 39. 
 
 40. 
 
 In 
 
 In 
 
 In 
 
 lu 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 In 
 
 2 4. 
 
 'i. 
 
 4) 
 5 
 5 
 
 10 
 
 5 
 2_5 
 
 5 
 1 5 
 
 5_5 
 
 5 
 GO 
 
 5 
 
 1-3 
 
 
 
 3_6 
 
 y 
 
 48 
 
 « 
 
 _50 
 10 
 
 ±A 
 1 5 
 
 1.2. 
 
 1 8 
 
 10 
 
 2 
 
 ■li' 
 7 
 
 6JJ 
 
 y 
 
 1? 
 1? 
 1? 
 
 1 ? 
 1? 
 
 1? 
 
 1? 
 
 1? 
 
 1? 
 
 1? 
 1? 
 1? 
 1? 
 1? 
 1? 
 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 
 how many times 1 ? 
 how many times 1 ? 
 how many times 
 how many times 
 how many times 
 how many times 
 bow many times 
 ^^. ^.. y how many times 
 
 41. What kind of a fraction is it called, when the 
 mmerator 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 xchole or mixed, 
 numbers. A mixed number is a whole number with a fraction 
 added to it. Thus 3^1- is a mixed number. 
 
 Whenever the numerator is less than the denommator, the 
 value is less than a unit, and the expression is called a proper 
 fraction;— hni when the numerator is equal to or greater thao 
 the denominator, the value is equal to or greater than a unit, 
 and the expression is called an improper fraction. 
 
 46. Reduce {- to a mixed number. 
 
 47. Keduce | to a mixed number. 
 
70 
 
 ADDITION OF FRACTIONS. 
 
 48. 
 
 Eeduce 
 
 15 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 49. 
 
 Eeduce 
 
 1 
 3 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 50. 
 
 Keduce 
 
 2 3 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 51. 
 
 Eeduce 
 
 2 1 
 5 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 52. 
 
 Eeduce 
 
 5 7 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 53. 
 
 Eeduce 
 
 89 
 1 2 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 54. 
 
 Eeduce 
 
 94 
 
 s 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 55, 
 
 Eeduce 
 
 2 5 
 3 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 56. 
 
 Eeduce 
 
 3 7 
 9 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 57. 
 
 Eeduce 
 
 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 58. 
 
 Eeduce 
 
 7 8 
 7 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 59. 
 
 Eeduce 
 
 3 7 
 6 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 60. 
 
 Eeduce 
 
 3 4 
 
 to 
 
 a 
 
 mixed 
 
 number. 
 
 
 
 Lesson V. 
 
 
 I 
 
 1. James had f of an apple, and John gave him i 
 more ; how many had he then ? 
 
 2. Mary had f of an orange, and her father gave 
 her -f- of an orange more ; how many had she then ? 
 
 3. Eobert had | of a melon, and bought f of an- 
 other ; how many had he then ? 
 
 4. Susan had f of a pint of walnuts, and gave f of 
 a pint to her sister ; how much had she left ? 
 
 5. James bought V of a pound of candies, and on 
 his way home ate f of a pound ; how much had he 
 left? 
 
 6. John gave ^ of a pound of raisins to James, 4 
 of a pound to Mary, and kept | of a pound himself; 
 how many had he at first ? 
 
 7. Mortimer gave f of a dollar for a hat, $1| for a 
 vest, and had $3f remaining; how much had he at 
 first ? 
 
 O. Jane nfl,n .^ T^minf^Q nfoinnamrk-n on/l TTn«.«* y%f %..«/} 
 
 ^ ---ti-si-iiiiiiviij itiivi j_taii. lew iiau. 
 
 2^ pounds ; how many more had Jane than Harriet ? 
 
71 
 
 ADDITION, &C., OF FRACTIONS- 
 
 9. Henry gave f of a dollar for his breakfast, f of 
 a dollar for his dinner, and 3^ of a dollar for his sup- 
 per ; how much did his day's board cost him ? 
 
 10. I + "I are how many ? 
 
 11. -J + f are how many ? 
 
 12. f + f are how many ? 
 
 13. iiy+To ^^® ^ow many ? 
 
 14. f + f ^^® ^^"^ many ? 
 
 15. y + t are how many ? 
 • iQ^ 1^ 4. I are how man V ? 
 
 17. 1^4 ^ 1^6 are how 
 
 18. " 
 
 17. 1^ -I- 1^6 are how many ? 
 
 18. |. + 1^3 are how many ? 
 
 19. f -H f + I are liow many ? 
 
 20. f + f + t are how many ? 
 
 21. •rff+ A+ 1^ »r® how many ? 
 
 22. f + I -H f ^re how many ? 
 
 23. f legs ^ are how many ninths ? 
 
 24. y lessV are how many ? 
 
 25. 1^3 — f are how many ? 
 
 26. V — f ^^® ^^^ many ? 
 
 27. V — f are how many ? 
 
 28. V" — § are how many ? 
 
 29. ¥- ^ ' 
 
 30. T9 
 
 are how many ? 
 
 are how many ? 
 
 are how many ? 
 
 are how many ? 
 
 -g. are how many ? 
 
 f I are how many ? 
 
 . i "" f are how many ? 
 
 35. 1. ^ .| _ I are how many ? 
 
 36. * + y — f are how many ? 
 
 37. yl+Tf ""tI ^re how many ? 
 
 38. 2. of 60— J of 24 are how many ? 
 
 39. 7. of 40— f of 10 are how many ? 
 
 31. 
 32. 
 33. 
 34. 
 35. 
 36. 
 
 2 
 
 y — y 
 
 *J^ — \9 
 
 47 6 
 
 IS s 
 
 57 37 
 
 1 + 
 
 7. 
 8 
 4 
 
 ^ 01 uU — f 01 zi-a are now many r 
 7. of 40— f of 10 are how many ? 
 4 of 15 + I of 9-f of 12 are how many ? 
 
72 
 
 MULTIPLICATION OF FRACTIONS. 
 
 Lesson VI. 
 
 1. At I of a cent apiece what 2 apples cost? 
 
 Solution.— If an apple cost f of a cent, 2 apples will cost 
 twice f of a cent, which are f or H cents. 
 
 2. At |- of a cent a piece, what will 5 apples cost ? 
 
 3. At 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 ? 
 
 6. At •§- of a cent a pieeo, what will 25 filberts cost ? 
 
 6. At f of a dime a piece, how many cents will 8 
 chickens cost ? 
 
 7. At f 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 in 52 weeks ? 
 
 10. If a pound of sugar cost 1| dime, what will 
 12 pounds cost ? 
 
 11. At 5f cents a pound, what will 6 lbs. of beef 
 cost ? 
 
 12. At 9 f cents a pound, what will 8 pounds of 
 pork cost 1 
 
 13. At 6|- cents each, what will 12 lemons cost ? 
 
 14. At 7 f cents each what will 20 rabbits cost » 
 
 15. At 12^ cents a dozen, what will 4 doz. eggs 
 cost ? 
 
 16. At llf cents a pound, what will 6 pounds of 
 honey cost ? 
 
 17. At $7-1 a bal. what will 10 bals. tobacco cost ? 
 
 1 8. At $9f a barrel, what will 10 bals. of pork coat ? 
 
 19. "What will 6 boxes of raisins cost, at $3|- n 
 box? 
 
 
MULTIPLICATION OF FRACTIONS. 
 
 78 
 
 20. What will 14i busbela of wheat cost, at $lf a 
 ^21! What will 7 barrels of cider coat, at $3-^- a 
 
 ^^2. If a barrel of flour cost $4, what will 5J barrels 
 
 cost ? „ 1 o 
 
 23. 5 times 4 and f of 4 are how many ^ 
 
 24. 7 times 6 and ^^ of 6 are how many i 
 
 25. 9 times 7 and ^ of 7 are how many r 
 
 26. 12 times 9 and ^ of 9 are how many? 
 
 27. 5 times 10 and f of 10 are how many ? 
 
 28. 13 times 4 and a of 4 are how many :» 
 
 29. 8 times 7 and a of 7 are how many ? 
 
 30. 10 times 13 and H of 13 are how many ? 
 
 31. 7 times 20 and a of 20 are how many ^ 
 
 32. How many are 4 times | ? 
 
 33. How many are 4 times 2% f 
 
 34. How many are 3 times 4^ f 
 
 35. How many are 5 times ^f, + 7 ^ 
 
 36. How many are 7 times .ip^ + 3 r 
 
 37. How many are 8 times 12|, f f 
 
 38. How many are 9 times lO^, —^^s^ 
 
 39. How many are 6 times 12|, + ^y 
 
 40. How many are 12 times Jy, -+- >; r 
 
 Lesson VII, 
 
 1 If yo" give to 6 persons, each f of a dollar, how 
 "TXrwml'thfcTst of 4 yard, of clotb, at | 
 °'3.'l"l7arS'cloth cost Uh what will 10 yards 
 *^°l' '-Er„„ in„i,v nran^es will it require to give to 
 
 ■ab. J.J.WVT riitvi-j C3 - 
 
 each of 9 boys H oranges « 
 
74 
 
 MCLTIPICATION OF PKACTIOJfS. 
 
 „wf ■ r """y^'^wrels of flour dpea that man eive 
 away who g.ves to each of 12 beggars | of a barre" 
 
 6. Anthony gave to each of hit 7 companions «nf 
 a pound of candies, and had i of a nnnn\??ff ? 
 many pounds had he at first j " ^ ^ '"" ' ''"'^ 
 
 ji.'']'°i? *°° S"^^ *o each of 9 beggars -»- of n dniu. 
 and had $7 remaining; how much !fd heat flrs? ' 
 
 ri: ? J ^'"'^ A "^ "-^ "--ange to Jackson !' ' to 
 hrreti^'gt '" ''"'" ' ^"^' P-' "^ - -4e\ad 
 
 gave t^raTwran"! f frdX^rnrt' ' 'T '"«"' 
 of a dollar, and then had onll «! ?"•'='' "f" * 
 
 wuch had he at firsli ^ " remammg ; how 
 
 had she at first ? "' "^"^ "^"^es. ilow many flowers 
 COSH oTtle^t" ' '""''' "' ''"'^'^ -^t' 'f 1 pint 
 2 guartYcosf ! °^"°'''''' ""'^' * "^ " ^'^"t. -hat will 
 peck cisM ^'"'' '"' '"""' '"'^' ^ "'"''' -''«* will 1 
 wilfi p" t'c?:*'" "' ""'=''"'"'''' <=-' »« <^^-ts. .vhat 
 cosMSr'entrf '' ^'^'"^ °' «'>-- -'• if 1 yard 
 
 ly/rdtle'dSesT*'"'"'*-^''"^' °^^"^-'- "• 
 
 cosUoTentsf" * °''' "^^^^ °^'"-'- <=™'' '^ l^a^d 
 COeSfTeitr"' ''P°°'-'"=-'^ -^-fl spool 
 
* MULTIPLICATION OF FRACTIONS. T5 
 
 20. What will 8| yards of silk cord cost, at 6 cents 
 
 ^ ^21, If one yard of wadding cost 5 cents, what will 
 
 9^ yards cost? ^ -c -, j 
 
 22,. What will 6|- yards of muslm cost, if 1 yard 
 
 cost 8 cents ? „ , .. i. t- *. 
 
 23. What will Sf pounds of veal cost, at 5 cents a 
 
 ^°24. How much will 9f barrels of cider cost, at $4. 
 
 a barrel • 
 
 25. What will 12 hats cost, at $3f each 1 
 
 26. What will 6f yards of gingham cost, at 4 dimes 
 
 ^ '"27. What will be the cost of 13 yards of bishop 
 
 lawn, at Ux% » Y^^^ • „ , 1 • i *. 
 
 28. What will be the cost of 8 looking glasses, at 
 
 $15i a piece "? • a 4-^ 
 
 29 What amount of money will be required to 
 
 purchase 30 pounds of rice, at 6f cents a pound J 
 30. What will be the cost of 23 pounds of crackers, 
 
 ^^ ll wVatViuTbarrelsof fish cost, at ei2f a barrel ? 
 32*. If 1 grain of gold cost 9^ dimes, what will 1 
 penny weig ^o^ .^ ^^^^ ^^^ ^^^ ^^^^ ^.^^ ^ ^^^^ 
 
 34.; How many pounds of meat, at 5 cents a pound, 
 
 can you buy for $3f ? ^ r. 4. «4.aa 
 
 35. What will be the cost of 3 quarts of nuts, at 64 
 
 cents a peck ? .mi, 
 
 36 If a coachman charge 5-|- cents a mile, how 
 much must that man pay who rides 12 miles 1 
 
 37 How many dollars, dimes, and cents will 1^ 
 yards of cloth cost, at 62 cents a yard? 
 
 38. How manv dollars, and cents will 4 pecks ot 
 
 grass seed cost, if 1 pint cost 5 cents ? .,..,, 
 
 39. How much will 13 yards of shalloon cost, at Id^ 
 
 cents a yard i 
 
76 Mui.x,Pr..cAT,oN or phact.o^s. 
 
 oes 
 
 liesson VIII. 
 
 1 TT ^ 
 
 1. How 
 
 inany are 5 times -x. ? 
 
 _« *; - 10* 
 
 2. How 
 
 Tjy are |, or Si. 
 
 I'k we have 
 
 o* ^^^ «iany are 3 times ^J ? 
 4 S°^ ^anj are 9 times i P 
 
 ^. How many are 5 times 'i? 
 fi :^ow many are 6 times A%' 
 
 ^ 5°^ ^a^J are 9 times i! ? 
 c • S°^ '"any are 9 times 11 9 
 g f °.^ ^^°J are 7 times il ? 
 9. 8 times if are how many?' 
 il' ^^ *!^es if are how many ? 
 it P *imes iA are how mo„i / 
 
 19 9+' 2 6«ioiiowman^ 
 
 1/t n J.- 2 -iiC UOW 
 
 14. 6 times ^| are how 
 t^' ZJimes 4z are how 
 
 many 
 
 17 TT^^™®^ i-f are how many 
 
 times 
 
 40 
 
 18. How many times 12 are 9 times V, "j 
 
 20 w ""^"^ *™«« 8 are 11 t^es " ? 
 f- How many times 100 are 2^T ^ ' 
 
 21. How imnt f,- nl^ '^ Mmes *pj ? 
 
 22. 5 time7"^i!^!- ^° "'^ ^^ times sJp / 
 ag, , t'-^^^ / >« 4 t,mes Mary's age ; v^gat 
 
 is her 
 
potatoes 
 
 Iciptjiing 
 dividing 
 
 bare 
 
 ber 
 
 MOLTIPLICATION, ETC., OF FRACTIONS. 77 
 
 . 23. 13 times ¥." «q"«l^ ^ "^'^'^r^f °/ ^ftTe 
 a certain wagon cost. Bequired the cost ot the 
 
 ""Tm times W equals, b of ««"°™l''''°f|«"' 
 Gen. Santa Anna had at the battle ot Buena V.sta. 
 
 ° ^ITS^st^t ^if the number of men he had 
 
 -fflJ^i!^ Tthirr^- -a he had 
 
 "ir9tmes^ri^Tith^m-Wofn.enhehad 
 
 killed. How many were killed ? 
 
 ?9. 8 times if is \ of how many times 3 / 
 30. 4 times -tf is- 4 of l>ow many times 5 / 
 31 A laborer worked 12 months at the rate of $104 
 
 a month : how much did his years's wages amount to ( 
 ^2 If 2 quarts of wine cost 48 cents, what will 1 
 
 ^'"3° How much ought I to pay for 3 oranges, at f 
 
 "''aV'IfVc'tain piece of work can be performed 
 in % hours, how ma'ny days will be required to per- 
 
 '^Z ^^t'cL^d^ra ditct^ 15 days, how long 
 
 of 4 persons 16 days, how long would it last a lamiiy 
 
 "'aVTs men can perform a certain piece of work 
 in 56 days, in how many days can 112 men do the 
 
 '"38.' If 3 men can plow 18 acres in 6 days, in how 
 many days' could 9 men do the same C 
 39. 4 men can mow a certain field m 6^ days, m 
 ,„v -i-vs "xn five men perform the same worK . 
 
 XXJ.J "-»"j " """ — — * 
 
 
IS 
 
 MULTIPLICATION, ETC., OF FRACTIONS. 
 
 40. A man bought (i barrels of cider at «qi a 
 
 it for'«oo'"'v''r* ''""R'^' « yards of cloth and sold 
 It a5;?d ? '•' "" '' "^ "•"" '* "-'' -hot did" 
 
 82^ w)?°r*''"' ^^ ^'"''^' °*"«'°"'' and sold J of it for 
 no, whici, wasi of what it cost; how much wo .Id T 
 
 would it takp ' / "^"^ ?° *"™ »10' how long 
 woum It take 1 man to earn the same ? ^ 
 
 of Henry '.'i;',"!/""'' ?^"«'' '^^^'^ " i "^ ^e age 
 IVhTi- ; Tu" ii?"""-'' ■* " t""«s as old as Georee 
 
 45 . ft%f^ 1 ^^"'•y ""'i <"■ G^o'ge respectivefy 7 
 4fi I f 00 !' ? *'.""'« ^ °^ ^■'^at number ? ^ ' 
 
 4fi 3 °i^S !^ f °j *«"=e what number f 
 
 cost IhL "i "' "' """"y doHars as Mr. B's horse 
 cost „ hat was the cost of his horse ? 
 
 80 was i l?i°\>''""^ ^'^'^ ^'' "Se. said, that J of 
 
 50 Mn! ten times h,s age. What was his age ? 
 of fL ^?> '.' ^^ Jfa'-a.old, and f of his aee is ♦ 
 oMhe age of h,s brother. What w"as his brltber-; 
 
 S'< 
 
 Lesson IX. 
 
 1. How many thirds are there in 3 ? 
 
 3 thirdZh^h "are t '' "* ' "''"''' ""'' '" ' ""'" ""' '^ '»" 
 Tie following solutiou is preferred to the abore: 
 
 aumbe?i7;i;oreo„e'/7al7H ''""^t """efore, 8 time, the 
 are 9. TheX^S thTreaJ'eT "''''• '"""*'' 
 
 2. How many fourths are there in 3 ? 
 ". xiow many halves are there in 6 ? ' 
 
OIVI8ION or FRACTIONS. 
 
 iro 
 
 4. How many fifths are there in 4 ? m 5 ? 
 6. How many fifths are there in 7 ? m 8 ^ 
 6. How many sixths are there m 4 ? m 3 ? m 5 ? 
 7 How many sevenths are there in 2 ? in 4? in 6? 
 
 8. How many eighths are there ^n J ^ n 4? n 6? 
 
 9. How many fifteenths are there in 2? in 3? m 6? 
 
 10. How many tenths are there in 4 r in6? inT/ 
 
 11. How many fourths are there m 3 and ^ r' 
 
 12. How many tliirds are there in 4 and ^ ^ 
 
 13. How many thirds are there in 3 and i i* 
 14 How many halves are there in 8 and i t 
 15*. deduce 6f to an improper fraction f 
 
 16. Keduce 9^ to an improper iraction f 
 
 17. Eeduce 7?- to an improper fraction ^ 
 
 18. Beduce 5| to an improper fraction ^ 
 
 19. Beduce 41 to an improper fraction ? 
 
 90 Among how many men, can 5^ Dusneis oi 
 whea't be d' s&ibuted, provided each receives | of a 
 
 ^ll'^Amon- how m^ny boys, can 7f oranges be 
 divided; provided each receives -^ of an orange ? 
 
 22 8 and f are how many times -„- f 
 
 Soi!..io..-8 and i equal V; t - contained in V 37 time.- 
 
 23. 9f are how many times f ? 
 
 24. 9f are how many times f f 
 
 26. 7f are how many times ^t 
 26*. 12f are how many times It* 
 
 27. 7t are how many times f r 
 
 28. 7-| are how many times i r 
 
 29. 41 are how many times %r 
 30*. 10| are how many times^f ? 
 31. 8f are how many times -^ r 
 82. 12? are how many times f r 
 
 33. 4 times 3i are how many times ^ / 
 
 34. 9 times H are how many times ^ r 
 oe r. 4-;vv^oc, «2 are how many times ^ r 
 
80 
 
 DIVISION OF FRACTIONS. 
 
 
 I 
 
 ^' 
 
 36. 8 times 8| are how many times | ? 
 
 37. 6 times 2-f- are how many times -^ ? 
 
 38. A boy distributed 9f apples equally among his 
 companions, giving to each | of an apple j how many 
 companions had he ? 
 
 39. Homer distributed $12f equally among some 
 poor women, giving to each $1| ; 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 %\\ a yard, will it take to 
 pay for it ? 
 
 42. Bought 9 yards of cloth, worth $1|- a yard, 
 and paid for it with raisins, at %\% a box ; how many 
 boxes did it take ? 
 
 43. How many bushels of turnips, at $| a bushel, 
 can be bought for 8 bushels of apples, at $f a bushel ? 
 
 44. How many apples, at f of a cent each, can be 
 bought for 6 oranges, at 2\ cents a piece ? 
 
 45. How many yards of cloth, at $f a yard, can be 
 bought for 10 boxes of butter, at %^ a box P 
 
 46. How many geese, at $| each, can be bought 
 for 14 ducks, at $| a piece ? 
 
 47. How many boxes of cheese, worth $2f a box, 
 may be had for 17 boxes of butter, at %\\ a box ? 
 
 48. How many barrels of flour, worth $5| a barrel, 
 may be had for 17 bunches of cotton, at %\\ a bunch 1 
 
 49. How many sheep, at %\\ a head, may be had 
 for 8 calves, at $3| each ? 
 
 ^ 50. How many quarts of alcohol, at f of a cent a 
 pint, may be had for 12 quarts of molasses, at 41 
 cents a quart ? 
 
 51. Mary and Jane together picked 5 times 2^ 
 quarts of strawberries and shared them equally with 
 their companions ; how many companions had each, 
 provided each received \\ quarts ? 
 
DIVISION OS FEACTIONS 
 
 81 
 
 Lesson X- 
 
 „ .«n TENTH COMBINED. 
 
 j«. KMAEKS.-A f''^«7 ""S numerator. 
 
 9 If 3 apples cost ^ o^ *" 
 
 ■wortli ? , . „ 7 are fk ' 
 
 9. How many times 
 
 10. Howmanytmes. 
 
 11. Howmanytime^? ^^,16*; 
 
 12. Sow many t me« ^ 33 ^ , 
 
 13. Howmany me«» 1 , 
 
 14. How many times '4^^^ 
 
 15. HowmanytmeBlL , 
 
 16. How many toeB i 4 ^, 
 
 17. Howmanytime^^ 7^, 
 
 18. How many t^e« « 9^ , 
 
 19. How ma^y t-^*;, 15 are 33^ t 
 
 20. How many times xo 
 
 
 'U?j 
 
82 
 
 DIVISION OF FRACTIONS. 
 
 ■if 
 
 I 
 
 J'i pi'ro"!?''"'^^" ^"^^ «-- ''-- -"-y '=-*^ 
 
 eaS'?^^'"''''" ^ i""'''"^'''' ''"^' '*■ 3 co^t 1% of an 
 
 centLm'tr5nfe:'r^' ''°^' ^2 ''--' i^- --y 
 
 29. If 6 pouuda of cheese cost 31a, cents wl,nf 
 will 1 pound cost ? ■" ' ^"*' 
 
 on eg" ^^ '^^' '°'' °* "™''' "'■'''* ^'" be the cost 
 eosu' ^" ^'*'"''' °'''''°*'' "='"' *-'^' ^'"''t ^i» 1 yard 
 apfe^cef^'" «"t shawls cost $274, how much is that 
 
 8 pat ^'"^ '"''' "'^ '""'*' '°'' *^^*' ''°''' '""'='' ^^ *">' 
 
 Jrtf dteret'friX'X''' '""'"^^' '"'' -''"^ 
 
 dilhe tt I/r^enVr'^ '"- ''* "-'^-=> '-- ""V 
 
 n.anydae|:TfolV^r/°^''^ '='>-*-*^' >>- 
 38. If 3 yards of broadcloth are worth 18^ varda , 
 
DIVISION OF FRACTIONS 
 
 83 
 
 n iq miles v;hUo Josiah ia 
 
 John is walking i mue. ^. ^^ ^nd 20 
 
 chestnuts are w 01 til , on^ 
 
 1 lemon worth 1 ^ ^^.^t ^Ul 1 orange 
 
 41. If 2 oranges cost -3 ot .1 tea , 
 
 coat ? ___^ ^ , ^ ^^,., 1 one orange will 
 
 •at? .nfflcent 1 one orange will 
 
 Tf o oriUigeB cost f <^* ^ *^ ' 
 SoLUTioN.-It - o'^;'"? , . 5 of a cent, 
 cost i of t of a cent, wbicb is ^ ^^^ ^^.^^ ^ 
 
 _» ., ,1^ nf linen cost 
 
 Solution.— XI - : \„wh is I of a cent. 
 
 ;t ^ of t of a cent, ^vbIcb s^ ^.^^ ^ 
 
 42. If three yards of Imen cost $!-„ wU 
 
 -* cost? "^- -■«— TrrVini-, Will 1 
 
 4,2. It three yui^^ 
 
 rard cost 1 . -^^^^ cents, what will 1 
 
 43. If 7 y^^''^^ °* ^ P 
 yard cost ^ . .-i. » 2 riimpa. how many 
 
 3 is con- 
 
 43. if ^ y^^^^'* ""' ^ 
 
 nV If 2 pints of mow. cost H 0--,how ...y 
 
 cents will 1 ga"o" f ."'* ' a «re 6 -, ' 
 
 45. How many times Bare b,^ 
 
 46. How many times 6 are 5 
 47„ How many times 4 are 4i I 
 48. How many imes 2 are 1.5^ 
 48. How many times J «e > 
 
 tailed i. V V. « <''^.'-;;- i„ ti^es 2A « 
 
 52. How many timoB 9 are lU ^^^^ 
 
 53. How many time^J a^^ ^5 times 3^V? 
 
 54. How many t mes 5 a.e 1 ^ , 
 
 55. How many times 7 are ^j ! 
 
 56. How many t.mes 5 are 6 
 % f^r-ySoTXth are worth $2i, what is 1 
 
 ^ta^'imhunches of .rapes are worth 40 cents. 
 ia 1 basket'of peaches worth • 
 
 \" 
 
84 
 
 FRACTIONS. 
 
 Lesson XL 
 
 1. What is i of 2 ? 
 
 2. Whatisiof4? of 8? 
 
 ?• ^hat!siof2? 3? 5? 7? 9? 
 
 4. WhatisiofS? 5? 7? 9? H ? 
 
 5. ;w^hat,3iof2? 3? 4? 71-8? ' 
 f-^^^t|«iof2?3?5? 7? 9? 
 
 7. mat,s|of2? 3? 5? 4? 3' 9? 11 , 
 
 8.mati3iof2?4?3?5»6?7?9V 
 
 10-Ww'*°^IJ^^7?6?3Vl2?l^ 
 10. What 13 tV of 7 ? 2 ? 4 ? 6 ? 9 ? 14 ? 15 a 
 
 cents, which is 4, o, U cenie! ' "'''''* "'^'^'^ * °f 8 
 
 13 ■ Tf f '''''''^' ''°'1 ^ '=^'^*''' ''•>»* T^ill '■ apple cost ' 
 
 14" If I PTl '"f ? '='°'^' '•'"»' ^i" 1 pen cost' ' 
 
 yard cost ? ^ ^' °* ^'P-^ <=°^' ^4 ««°t^. what ^{ 1 
 
 rel'«,st'P '""^'^ '''■''""=• '=°^' «21, what will 1 bar- 
 -ill"- pLl L"u °' ''"'' "''P'^^ -^* 23 dimes, what 
 Jti ^^' ''"''''""' cost 9 dimes, what will 1 chicken 
 
 poundsTosl*27di Jesr"' °' ^'"""-^^ <=-*. ^f « 
 cosM2l^' "'■"' ba-el of flour coat, if 3 barrels 
 
 ^|;Sjot;fcltKS;r"^^ 
 
 ^1. Joshua had 13 rrarbleq nnrl t«„- t. i 
 many + i of - ma.i.]. ^es, and Lewis had 
 y -t ^otu marble ; how manj had he ? 
 
 1 
 
 as 
 
FRACTIONS. 
 
 85 
 
 V -rlprl s barrels of flour equally among 
 22. A man divided 6 ^ff' . ^^^ gacli receive ? 
 11 families ; -^^t T^H of a W did ^ ,. 
 
 did he give to each ^ ^^^ ^^ared them, 
 
 each receive 1 ^s of raspberries, shared 
 
 " r \^^l":UlT;uua of prUBeB cost, if 5 pounds 
 •=^7' wlTwUl 2 boxes of fig. cost, if 7 bo.es cost 
 '''itw -ill 4 1«' *^ °^ strawberries cost, af 9 
 
 quarts cost 7 dimes ? 
 
 ^ oq "What IS i ot ^ i , 3 , „ , 
 io inof2isl,wliatistof2. 
 
 31. What is % of 5 . ^^^ „^ • 
 > nt 5 is *, and i are 2 times ,, 
 
 32. What is f of 3 of 5 T 6 -^ , ^g j 
 
 33. Wb^^^f : fyfrl' 51 7? 9n2? 20? 
 34,. What IS t of V,°*/5> 8 ? 9 ? 15 ? „ , 
 
 35. AVhat IS f of 3 ? ot & . » 3 ? 11 ? 17 ? 
 
 36. What siof4?of6^8^ ,^5P 
 
 37. What s J of 3 ? of ? >^gS 6 1 10 ? 12 ? 
 
 38. What is rr of |? 0.4- | , ,^5, 3^, 
 
 39. What s^^of2? ot4. s ^ ^2^ ^g, 251 
 
 -t2"wh^:t"l°b3 tie Ct of i of a bo. of ra.s.ns. 
 
 '' 1^° Wbft III be the cost of |- of a yard of cloth, 
 at 7 dimes a yard ! 
 
86 
 
 SIMPLE PfiOPORTlON. 
 
 COS?? ^^ ' *'° °^ ^'y ^^«t 'WO, what will 2f tons 
 45. Jeremiah is 91 years olrl «t,^ -» ^i • 
 
 damaged I til f ^oft It/!' ^^ 'f '' b"*. being 
 
 mainder for what it eo^^f tt * " ^^'''^' '"""1 'be re- 
 
 47. Bought l1 yardf ;.• 5.7 f"'']" '^''^ ^ ^°^^ ? 
 
 P.ece eoat. What did it it f JrdV'^" *^"''°'« 
 
 a. t^uetasTer tlft^dTth^t'' ^^ ^* «»- 
 
 '?: Whaf:?^ Sun;.::f otf --l -"> ^ yard, 
 coat $42 ? "^ " °' "I"""" cost, if 5 pounds 
 
 Vo^illojr^' "' ^"""g" ^o^t $32, what will . 
 
 it St.; ^^:^^ K?. which was , of wha. 
 
 travels Jlheret;^^^^^^^^^^^ -- P'-. and 
 10 hours ; the other a^t the rate of ■ ' 'f ^^ """'' '° 
 W; how far apart will th ' fcf i,%T'^^ '" ^ of an 
 55. By a Dine 4° anU^, T ^ "°"^8 ? 
 
 « X minL Xw LucMidl^^^^^ 
 
 It was filled in 9 niZtes ' "'"''"' ^°^^ P™"ded 
 
 inl3,'l;™To:fll7i -t Ta^''': P'- "^ -. 
 same ? ^ ^^"^^^^ '^ *ake 4 men to do the 
 
 57 Tf '' 
 
 week« wiratPpTrt °of aXreTwL'f ??' °^ ^"^ - » 
 5 weeks? "'^''' ^oula they cousuroe in 
 
 «i^wlirt^sSi.^.r^s.:f»%*i.how 
 
SIMPLE PROPORTION. 
 
 87 
 
 69. Anthony Bpent f of all bis ^-oney and the re. 
 mainder he gave tor B ya;ds of cloth, at $2, a yard. 
 
 how much had he at lir«t garments, 
 
 '' m "From a piece of cloth a tailor cui. o gaiua , 
 
 >tl.S^°hrS Cnds*of Le cost, if 7 pound, 
 cost 43 centsj snenduiK i^- of all his 
 
 J!;^uTSto .t^Jngt hoi ™uo. .ad he 
 
 "^ef^ln old lady bought 30 eggs, at the rate of 2 
 nrillw'ret 'm\3 yra. of co^ee cost, if 26 
 P'ef What will 7 gallouB of molasBCS cost, if 6 pints 
 ^tf If'umps cost |T|, what wUl 7 J^^-PB -^ . ^ 
 
 ""eS.' If 15 gold Pen^ <=°«* «20, what will 5 of them 
 '"tl If I of an acre of land be worth $U, what are 
 ^^o"1'2ri'sTof the cost of W. watcU". what was 
 the cost of his watch ? ^^ ^ of his 
 
 ' V2°1f a man in A o« a day walk 8 miles, how far 
 can he walk in 8 days J containing 20 E. Fr., a 
 
 -;.n?Vr crtl U^ wood .5 hour, 
 bow many cords can he cut m 4 days, Dy 
 
 if 
 
 4 
 
88 
 
 SIMPLE PROPORTION. 
 
 75. A man bought 7 sheep, at the rate of 9 for 
 ^5i ; what did they cost him ? 
 
 70. A boy bought 13 oranges,— giving 9 apples for 
 oranges ; how many apples did his oranges cost him ? 
 
 77. It 25 cents buy 7 Jemons, how many cents will 
 9 Jemons cost ? 
 
 78. -I of 45 equals ^1 as many dollars as Andrew 
 has ; how many dollars has he ? 
 
 79. $3G| is i 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 dmies ? ^ 
 
 ^.^;o^^^?^JH^ ^ ^^^^'* of clover.seed cost, if 2 pecks 
 cost $3 and 2 dimes. 
 
 82. 4i times 7 is | of what number ? 
 
 83. f of 30 is -f; of what number ? 
 
 84. I of 36 is V^ times what number ? 
 
 85. f of A's age is 3 times B's age: and Bis 9 
 years old. What is A's age ? 
 
 86 An individual, being asked the number of hours 
 he labored each day, answered, Ix times the number 
 of hours in a day is 3 times as many hours as I labor 
 How many hours did he labor each day ? 
 
 87. I of 15 is ^ of what number i 
 
 88. I of 21 is 1| times what number ? 
 
 89. f of 24 is If times \/hat number ^ 
 
 90. Wrighl; is 10 years old, and If times his age is 
 If times Charle's age. How old is Charles ? 
 
 4^ 
 
 ) 
 
 Lesson XII. 
 
 LESSONS IIGHTH, KIXTH, AND TENTH COMBINED. 
 
 ^ JlEUAJiK.—Frcpils must exercise their oion judqment in 
 employing the shortest of the methods given in lessons eighth and 
 tenth for multiplying and dividing. ^ 
 
 1. If 3 barrels of flour cost $13f, what will 6 cost I 
 Solution.— $1S| equals %'^'. Jf 3 baii-eis of flour coat | V, 
 
of 9 for 
 
 pples for 
 ost him ? 
 ents will 
 
 Andrew 
 
 w much 
 
 ' 3 i^ints 
 
 2 pecks 
 
 SIMPLE PROPORTION. 
 
 89 
 
 Bis 9 
 
 f hours 
 
 lumber 
 
 labor. 
 
 age IS 
 
 nent in 
 th and 
 
 cost! 
 
 3t IV, 
 
 e ,a.eU. wWcb are . time. 8 ba.reU, V.U cost 2 times $V, 
 
 wliich are $¥.<>•■ «"i- . „, what will 20 
 
 2. If 5 pounds of opium cost $27 „ what wui 
 
 Dounds cost ! . I. ^ /.pnta. what will 
 
 3. If 3 pouuds of sugar cost 17 , cenis, « 
 
 24 pounds cost ! „ „ orantres, if 8 
 
 4 How many apples will pay tor J orang 
 
 apples are wortli 12 J orauges ^ 
 
 So»T,o«.-12'. orange, equal V orange, I % -^h is 
 worth 8 apples I o an orange »^^Hh\ ^_^ PF ^^^ ,.^^ 
 
 ^>:s\: ::ro"^^"pp" atidtUes - wor.U9 times I. 
 
 -trtlny chestnuts.. 11 pa^^ 
 
 7 chestnuts are worth 10^ "!„,! 833^ what will 20 
 
 6. If 8 barrels of flour cost ifdd,. ^^"'"' 
 
 ijarrels cost ? , , .• loth to make 3 coats, 
 
 7. If it require 9 » .f "^^ ?'/i° ^^ke 8 coats ? 
 how many yards will it require to ma ^_^^j^ 
 
 8. If 10 meu can perform ^ certain p ^^^^^^ 
 in 9; days, how long will it t..ke S men p 
 
 the same? ,„„t„ffteheeD.if IScostSlOi? 
 
 9. What will be the cost of 6 f ej'" , f ^^^at in 
 ^f\ Tfl nerson corsume lu^o uu&ucio _^ • i-i.^ 
 
 a month, liow much will 13 persons consume lu the 
 
 '"Z ^ifg ' cents will buy 4 peaches, what wUl be the 
 ""V'lt i:fwill pay for 5 weeks' board, howmany 
 
 dotos will p y 1- 8.n.^^;^;e£ in 3* hours, how 
 
 13. If 6 orifices will ^Vj reauired to fill it in^ 
 many of, the same size will be requirea 
 
 of an hour t ,, -u „ i,„nt in 54 days, in how 
 
 14, Tfn men can build a Doatiu u» j 
 
 mmy days could 6 men build It ( 
 
 H 
 
 1!^ 
 
00 
 
 SIMPLE PROPORTION, 
 
 A> 
 
 l'»f 
 
 
 week; r^"' ^"^ ^ y^'''-'^ bo^'d cost, at $;;| fo^ 4 
 
 rels tsYf '""■'■^'^ "^''^^ <'°»' «54i, what wiJI 27 bar- 
 
 if /7'l,"'^°T """"y '^''"'"•s will 1 barrel of fnl„„ 
 
 30 '""''•e's cost 51 J eagles ? tobacco cost, 
 
 20. If J3 pounds of tea cosf ina j- 
 5 pounds cost ? ' ■'"* "injes, what will 
 
 .21. If7| tons of hay tppn « i, 
 winter, how many ton, will t «"?^' *''''°"8'> the 
 time ? ^ '""^ «'" keep 9 horses the same 
 
 tofhe h^ou^Ysfho^'^^'frrVd' °"°^".^-- 3 -ds 
 to overtake thefoxT ■^/fe^'Prfi '^/ '^°"°'' ^"n 
 ., 2S. How many dolla Jil "* "'^ ^°^ ''"" » 
 If he earn $3f inVdaJs' » " """ ""^ '" ^^ days, 
 
 cost a piece, an'd ho^:; much a^S^,''"- '»-'' ^^ it 
 
 win be th: fet thSeTadl^ ''f '"'°", ** ''^'' -h-t 
 feet long, at th! samVtLtofTavl " '°'' "''''"' '» ^^ 
 30. At a certain time of dav 1 1 . , 
 
 01 day, a pole 5 feet long 
 
 i 
 
RUDUCTION OF FRACTIONS. 
 
 91 
 
 <3a8t8 a shadow 74 feet ; what is the length ot that pole 
 which at t .e same time, casts a shadow 4. leet ? 
 
 31. If it require $211 worth of provisions to serve 
 8 men 2 days, how many dollar's worth will serve 5 
 
 "32' mat is the length of a pole the shadow of 
 which is 12 feet long, at the same time, a pole 2 steel 
 in length casts a shadow 4 feet long 1 
 
 Lesson JIIII* 
 
 T> „.„«. Bv inane* Wm Le^^ons 8th and 10th, we obserTe, 
 same number, does not ultor tbe v» ue ot tbe f. AcUon^ .^ . 
 to convert a traction *»»" f5»\t,h „' mSX°d d^ 
 
 quired denominator. 
 
 1. I is how many eighths ? . , r • ^ 
 SoJxio..>-There are f in one, and in i there .s i of |. or 
 
 3. and in I there are 3 tiraes f or -j. 
 ^ BEMraL^MuUiply -h teru. of the giv^^^^^^^^^^^ 
 number that will causo the deuommator to become vu 4 
 denominator. Solution 2d.-i» equal ^. 
 
 2. i is how many eighths ? 
 
 3. i is how many tenths r 
 4*. I is is how many sixths ? 
 
 5. i is how many sixths ? 
 
 6. \ and i are how many sixths i 
 
 7. f are how many sixths 1 
 
 8. ^ are how many twelfths 1 
 9*. I are how many twelfths % 
 
 10. I are how many eighteenths ■ 
 
 11. f are how many tenths ? 
 
 12. f are how meny tenths ? 
 
 13. f are how many twentieths 1 
 
 14. I is how many tenths 1 ^ ^ 
 
 15. Harris gave f of an orange to his sister , how 
 many fifteenths did he give her \ 
 
 .BJ'-f 
 

 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 
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 1-4 ill 1.6 
 
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 7^/ 
 
 -% 
 
 v 
 
 w 
 
 v/ 
 
 % 
 
 Photographic 
 
 Sciences 
 Gcrporation 
 
 \ 
 
 
 23 WEST MAIN STRfceT 
 
 WEBSTER, N.Y. i4580 
 
 (716) 872-4503 
 
 iN 
 
 ^\. 
 
 C% 
 
 \ 
 
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 6^ 
 
 r# 
 
 >-:^' 
 
K?, 
 
 V C^ 
 
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 m, ^ 
 
 Ua 
 
 4S 
 
92 
 
 ADDITION AND SUBTRACTION. 
 
 f^ 
 
 )i5l 
 
 It' 
 
 16. How many sixteenths in 
 
 17. How many sixteenths in | ? 
 
 18. How many sixteenths in {- ? 
 
 19. How many fourteenths in -f ? 
 
 20. How many fourteenths in a ? 
 
 21. How many fourteenths in f ? 
 
 22. How many ninths in f ? 
 
 23. How many twentieths in |- ? 
 
 24. How many fortieths in | ? 
 
 25. Hew many forty-ninths in f ? 
 
 26. How many fifteenths in -f ? 
 
 27. A man gave i of a bushel of potatoes to one 
 poor woman, and VV of a bushel to another; what 
 part of a bushel did he give to both ? 
 
 28. How could you dinde an apple so as to give |- 
 of it to 1 boy, and i of it to another ? 
 
 29. f +1 are how many fifteenths? 
 
 Solution.— I equals j%, and § equals J-§, /^ and 4§ are if, 
 or 1 j\. 
 
 30. f + f are how many twelfths ? 
 
 31. f + ^ are how many eighteenths ? 
 
 32. 1+ 1 are how many twenty-fourths ? 
 
 33. -f- are how many times -^\ ? 
 
 34. What is the sum of f and f ? 
 
 35. What is the sum of -f- and -f ? 
 
 36. What is the sum of i and f ? 
 
 37. What is the sum of f and f ? 
 
 38. What is the sum of f and | ? 
 89. What is the sum of ^ and | ? 
 
 40. What is the sum off and f ? 
 
 41. What is the sum of -} and i ? 
 
 42. What is the sum of f and f ? 
 
 43. What is the sum of -f , -i and | ? 
 
 44. What is the sum of f , |- and | ? 
 
 45. Prom | subtract |-. 
 
 46. From |- subtract ff . 
 
 47. From f subtract f . 
 
 4 
 4 
 t 
 
OF FRACTIONS. 
 
 48. Prom 2 ^ subtract f . . 
 4,9 T'rom 4 subtr^ict a- 
 50 :From 3 subtract i- 
 5l! Tj'rom 9 subtract t- 
 52 Prom 5 subtract |.^ 
 53; rrom 3 subtract U- 
 54. :From 8 Bubtr.. 2-3. 
 ^^5 ;From 6 subtract 64^. 
 56 U-3^.arehowTnauyT 
 ^7 7-2f are bow many? 
 ^^- 9^3| are how many? 
 59 10-3I- are bow many? 
 rft 12-3^ are bow many? 
 A? 13 Ja^ are bow many? 
 fi 9i-4 are bow many? 
 fio 7^— 5f arebowmany? 
 ^1* Qi-li are bow many? 
 65-4-liarobowmany1 
 fifi 5^-2! are bow many? 
 
 fi7 9I-7I are bow many ^ 
 fift 23+3|-|arebowmany? 
 
 ^^- .1 T ? t ^ !^ are bow many ? 
 
 70-||^3|^3arebowmany? 
 
 .l^J-l are bow many? 
 itl+i-l are bow many? 
 
 ... 1+ ^ ^lUw manv times -^ ? 
 TA 2i are now m^^v ^^ 4, ? 
 74). -6^ »*^ TYianv times -fo • 
 
 75. 3'r are bow mauv . • ._ ^ 7 
 7VS «!- are bow many tunes , e ; 
 T^* -i? ?. i,nw many times 
 
 93 
 
 71- 
 
 72. 
 73. 
 
 74). 
 
 are bow mau y y^-- - , 
 are bow many tmes . 
 
 are bow many times j^ 
 are bow many toes . ^ 
 are bow many tunes , . 
 are bow many tme«.e. 
 
 J..2 81 eve bow many times ^ ^r 
 
 00 i6>- are bow many times TO • 
 
 ^r ;-' ^--^ v^^w many times 1* • 
 
 b4. I'^a "^" "^ 
 
 77. 
 
 78. 
 
 79. 
 
 80. 
 
 81. 
 
 82. 
 
 2 
 4 
 
 T 
 1^ 
 
 9 
 5 _ 
 
 \ 3 
 
94 
 
 REDUCTION OF FRACTIONS. 
 
 J, V.I 
 
 »»: 
 
 l.i 
 
 
 fift' ftltl -^ , *"^ '""'''' '"^^ *■=«" a whole one ? 
 
 S7 1 1 °/* " ^T "'"''' '■'^^ *•""» a whole one ? 
 
 ,nfa' ^-h^^ S^y^ * "*■ ''" ''«■' >"»"ey for a dress 
 
 wh'a^ pL^'omTj^Trptd r'' ^ *"'^^° P"~ ^ 
 
 50oHn!r f™^ was killed, | taken prisoners, and 
 500 escaped = how many were there in the army ? 
 
 90. t af the length of a pole is in "the ground, x of 
 
 lengtl':fThrprr' ''-' '" "'^ "'-' -^^' « *e 
 
 91. A market woman sold -J of all her oranees to 
 one man and i of them to another, and then had on^ 
 9 remaining ; how many had she at first, and how 
 many did she sell to each ? 
 
 t}lhi^ ^r'/*'J^''u'P.'?''',"^ ^ °f ^'^ fo'-t^ne. found 
 hifortunir * ' ^'^^'^ remaining; what was 
 
 .»f^iA''r'r.f'"'Sht * of Euphemia' chickens a 
 cat killed i of them, i of them died, and she had l^ 
 remaining ; how many had she at first, and how many 
 
 'S trrL\ y: ''•"'^ "''' '"' ^espeeHvIlyT"^ 
 y^ baid A to B it to my age you add its and i ifa 2 
 
 the sum will be 38 ; how old was he ? ' *' ^' 
 
 92. A IS 40 years old, and f of his age is a of twice 
 
 as much as his wife's age ; how old wa^s his Vife? 
 
 Lesson IV. 
 
 1 !Redllf»P ± i-.n if a l«or, — i J. 
 
REDUCTION OF rRACTlONS. 
 
 95 
 
 a 
 
 -R prince ^ to its lowest terms. 
 I* deduce i to Its lowest terms. 
 i'Re^luee^ to its lowest terms. 
 
 t' leduee X to its lowest terms. 
 
 r deduce li to its lowest terms. 
 
 7* See P to its lowest terms. 
 
 R lleduce U to its lowest terms. 
 
 q deduce li to its lowest terms. 
 in deduce ii to its lowest terms. 
 1 1" See i| to its lowest terms. 
 1 V leduee 'A to its lowest terms. 
 
 1 q deduce 4 to its lowest terms. 
 I!' Eeduce i|- to its lowest terms. 
 
 15". Beduce if to its I^^^^.^^Xction remaiu the 
 1 A -Wbv does the value ot the tracwon . 
 
 saS wheJyou divide both numerator ..Xdenonn.a 
 
 for by tbe same number . „„niprator and de- 
 
 XaTorh/The"'^Ca^wh^oes it not 
 
 =?nh^tmfs^-Sowest terms. 
 
 20. Eeduce 8 times ^ ^^^ ^^^^^^ . 
 
 21. Beduce 6 times , to ^^^^ ^^^^^_ 
 
 22. Beduce * tvmes i^^° ^^^ ^^^^^^ 
 
 23. Beduce 12 times to ^^^^^_ 
 
 24. Beduce ^2 .^'^f_^Cit, lowest terms. 
 
 *5- 5i"^! 7 t mes " to its lowest terms. 
 26. Ked»f/ *^^';, 11 to its lowest terms. 
 
 27- 5'f ! 4 t mes " to its lowest terms. 
 28. Eeduce 4 1 mes 3^ w .^^^ t^^ms. 
 
 fo:Sre 9^11 to its lowest terms. 
 
^0 
 
 COMPOUJVD FRACTIONS. 
 
 DPI 
 
 Lesson XV. 
 
 wilV/Vfi!" ''''^.'''' ""PP^^^ ^"^° ^^^'o ^qual pieces, what 
 will 1 ot these pieces be called ? 
 
 2 If you cut } of an apple into two equal nieeps 
 ralfedT ''' "'^^^ ''^^^'^^ ^^'^" ^ of thesrpie^ces be 
 
 3. If Alice has i of a lemon, and »ives half of it- f« 
 Am, what part of a lemon will Ana receive ? 
 
 of a 
 
 ie»'oTs-ii irftiL:"^"-^^"- ^"^ -^-'-^ i "f 
 
 4. George, having half of a melon, gave i of it to 
 Marcns; what part of a melon did JlLusreceve? 
 
 5 Crary had -J- of a dollar, and gave ^ of it to 
 
 TnV\'t P/^' f'' '^'•"''' '"d J°'hra ;ece ve , 
 
 6 Kobert had J of a dollar, and gave * of it for a 
 cake ; how many cents did the cake cost him ? 
 
 I,n,l . . '■^'"■t' ¥ * °f " P<""^d of candies, and Mary 
 had 1 as much ; how much had Mary ? ^ 
 
 8. Jane had a of a poand of sugar, and Ann -'- a, 
 much; how much had Ann ? ' 
 
 gave '\f tL!!??^^^- "^- f ^ 9»art of chestnuts, and 
 
 fhlreceive ? " ' '* P"'' °'' " '""^^ '^''^ 
 
 > ond'"*"uT°^'^*5^'''^''«'" a bank, and sold 
 . of that ; what part of a share had he remaining ? 
 
 wW f"^?^^ *; "^^ "'''P' and sold i of his share • 
 what part of a whole ship did he sell? ' 
 
 J-^. What is ' " - - 
 
 Solution.--* of ^ is ^\^, 
 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 
 What 
 What 
 What 
 What 
 What 
 What 
 
 IS 
 
 is 
 is 
 is 
 is 
 is 
 
 X 
 
 5 
 
 l_ 
 
 3 
 
 1 
 
 i 
 
 1 
 
 8 
 
 I 
 
 T 
 1 
 
 of 
 
 of 
 of 
 of 
 of 
 of 
 
 -. p 
 OI 
 
 1? 
 
 5 
 
 1? 
 
 2 • 
 X7 
 
 7 • 
 
 i 9 
 
 6 • 
 
 i.? 
 
 9 ■ 
 
 i? 
 
 8 • 
 
 •1? 
 
COMPOUPm FRACTIONS. 
 
 97 
 
 of i? 
 
 19. What is . ^ 
 
 20. What 18 T^ °: j' ^felUoftheway 
 
 to the ground It ^^/^^^^^^^^^ distance was it 
 the ground ; what part of tue wnoi« 
 
 above the ground ? ^ ^ Nelson is 
 
 ^tr;?r.! owning ^^^^^j^^i:i^:^^az 
 
 modated his neighbor with | ot it , now 
 
 remaining ? , . „ i ^f „« eagle, gave i of it to 
 24. A man, having ^ ^t ^\^?^._'(f. ^hat part of 
 
 cents had each ? i? „ r>;p and save i of it to 
 
 25 Elizabeth had | of a pie, ana gav« 3 
 
 Or, Solution. — ^ of | is f , 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 81. 
 
 82. 
 
 83. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 38. 
 39. 
 40. 
 
 What 
 
 What 
 
 What 
 
 What 
 
 "What 
 
 What 
 
 "What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 is 
 
 2 
 1 
 4 
 1. 
 5 
 
 5 
 
 JL 
 
 7 
 
 1. 
 
 8 
 
 1. 
 
 9 
 
 1 
 
 9 
 
 X, 
 
 8 
 
 5 
 1 
 
 4 
 1. 
 9 
 1 
 
 7 
 1 
 7 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 3 ? 
 
 1^ 
 
 3 • 
 2.? 
 
 3 • 
 3.? 
 
 4 • 
 
 3.? 
 4 • 
 
 a.? 
 
 3 • 
 
 4 ? 
 
 5 • 
 3 7 
 
 3.? 
 8 • 
 
 6 ? 
 
98 
 
 COMPOUND FRACTIONS 
 
 • (I 
 
 
 fttitfl 
 
 I ■ ■■; 
 ' ■ i 
 
 
 41. 
 42c 
 43. 
 
 44. 
 45. 
 46. 
 47. 
 48. 
 49. 
 50. 
 
 51. 
 
 52, 
 
 63. 
 
 54. 
 
 55. 
 
 5Q, 
 
 57. 
 
 68. 
 
 69. 
 
 60. 
 
 61. 
 
 62. 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 s 
 
 IS 
 
 .1 
 
 J. 
 4 
 3 
 5 
 
 a 
 
 3 
 
 T 
 
 3 
 
 X 
 8 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 of 
 of 
 of 
 of 
 of 
 of 
 of 
 of 
 part of 1 IS 
 ..^^„ part of 2 is * 
 Solution.— f of + is 2 2 :g ^ ^f , „„ . .'^ 
 
 h which is ^ of 2. ^- ^ '' ^ of 1' «nd 18, 
 
 Solution 2c1. — 1- of i I'q 2 i :„ i « „ 
 of h or A of 2, auc?|*a;:|- time': ^t'o^-^ Jf^ ',■'» * "^ 2. i ie* 
 
 64. What part of 2 is ' 
 
 part of 2 is 
 
 part of 3 is 
 
 part of 4 is 
 
 part of 5 is 
 
 part of 9 is 
 
 part of 2 is 
 
 part of 2 is 
 
 part of 4 is 
 
 part of 6 is 
 
 part of 3 is 
 
 :s 
 
 13 
 
 's 
 s 
 
 is 
 
 L3 
 
 's 
 
 y 
 
 4. 
 5" 
 3 
 
 f 
 
 5 
 
 '£ 
 3. 
 4 
 ^ 
 8 
 Jt 
 5 
 
 *. 
 7 
 J5 
 7 
 8 
 IS" 
 
 i? 
 
 7 • 
 5 * 
 
 A? 
 
 y • 
 
 -i ? 
 
 4 * 
 
 i ? 
 
 8 • 
 
 I? 
 1? 
 
 f? 
 
 2.? 
 
 7 • 
 
 «.? 
 
 8 • 
 
 7 * 
 
 6.? 
 
 7 * 
 
 8 ? 
 
 9 • 
 
 3.9 
 
 7 * 
 
 2-? 
 3 • 
 
 1 
 
 he 
 ta 
 
 •w 
 
 a 
 r 
 
 of 
 of 
 
 therefore, | of 
 
 6 • 
 3 • 
 
 64. 
 
 Q5. 
 
 QQ, 
 
 67. 
 
 68. 
 
 69. 
 
 70. 
 
 71. 
 
 72. 
 
 73. 
 
 74. 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 What 
 
 J. 
 
 4 
 3. 
 4 
 
 X 
 
 « 
 
 JL 
 3 
 
 1 
 
 5" 
 3. 
 7 
 2_ 
 
 6 
 
 1 
 
 3. 
 
 5 
 J. 
 
 7 
 i 
 
 of 
 of 
 of 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 of 
 
 1 * ? 
 
 -I? 
 
 i? 
 
 If? 
 
 f.p 
 
 H? 
 
 i? 
 
 JL ? 
 lO f 
 
 I? 
 
 4f? 
 
iof 
 
 COMPOUND FRACTIONS. 
 
 99 
 
 I of 
 
 3 
 
 1 ') R ? 
 
 76. What part of 4 i= „ ^-^ ^,.,|^ 
 
 76. -What l«r of 7 ^ . ^^ ^.^^^^^^ . 
 
 77. Anthony had » o' * °\" ^ 
 
 what part of ^"'""yr.f a quart of Btrawberries ; 
 
 78. Albert had V 9^1^^' ,'^e provided 1 quart con- 
 bow many strawherriea had he, pr 
 
 tained 42 Btravvbernes . ^ ^^^^ ^^ y, ^^otUer ; 
 
 wJ^tptli^o^^C^Shere.^^^^^^^ ^^. 
 
 and on nis way borne spilled 3 
 
 a Dail-fuU had be remainiDg . ^ ^^^^d of molas- 
 
 Ifant ro"»K N''^' P^'^ °^ "^ '°^*"' 
 
 Ld be remaining ? ^ £ candies, and gave 
 
 .^f^£tASslaf:hT;artofapouudd.dshe 
 
 what part of a do"" ^ad he rema ^^ ^ le-augar, 
 f g^ 'XtWaSer • ?bat part of a pound d.d 
 
 to the one that could te 1 how mu ^^^ ^ 
 
 what part of a P«e-appl« ^d J^c^ob ^^^ ^ ^^^ . ^^, 
 
 87, Jamea gave | ot s oi » 
 
 «an; cer^ts did the op cost hm ^^ ^ . ^„^ ^^ny 
 
 88. Eobert gave v °' .'^^"i"" 
 
 cents did the cap cost hun^ ^.^^^^ for a comb; bow 
 
100 
 
 SIMPLE PROPORTION. 
 
 I 
 
 4 I 
 
 
 ».-. 
 h 
 
 jll:. 
 
 91. A man. having 4| barrels of flour, sold J of it ; 
 how much remained unsold ? 
 
 92. A man gave J of $3i for a silver pencil ; what 
 was the cost of the pencil ? 
 
 93. Jane worked 8.^ hours in a day, and Delilah 
 worked only * as many ; how many hours did Deli- 
 lah work in a day ? 
 
 94. B. gave $32J for a cow, which was .J as much 
 as A gave for his ; how much more did A's cow cost 
 than B's ? 
 
 ^ 95. Darius is 18| years old, which was | of Dan- 
 iel s age ; how old is he ? 
 
 96. If 1 yard of cloth cost $5f , what will -?. of a 
 yard cost ? 
 
 97. If 4 yards of cloth cost $9^ what will 4 of a 
 yard cost ? - o 
 
 98. If 6 barrels of beef cost $18i what will i of a 
 barrel cost ? 
 
 99. If I of an apple cost | of a cent, what will 1 
 apple cost ? 
 
 100. If I of an orange cost 1} cents, what will -^ 
 ot an orange cost ? 
 
 101. If 4 pounds of butter cost 6i dimes, how 
 many cents will If pounds cost ? 
 
 Lesson XVI. 
 
 1. If 4 bis. of flour cost $14f, what will 4 of a bl. 
 cost f " 
 
 coai?^^ ^ ^"^^' °^ ^^^^^ ^^^^ ^^^' ^^^* ^^^^ ■^^^ ^"®^* 
 
 3. If 2i bushels of apples cost 6i dimes, how 
 many cents will | of a bushel cost ? 
 
 4. If f of an apple cost | of a cent, what will 1 
 apple cost ? 
 
 6. If I of an orange cost f of a cent, what will -' 
 01 an orange cost ? 
 
 I 
 
DIVISION OF FRACTIONS. 
 
 101 
 
 im^ 
 
 6. If2f yds.of silk cost $3^ what will 51 yds-cost? 
 
 7. If 5 1 yds.of satin cost $5 ,^, what will 2 yds. costf 
 
 8. If in 3t hours A can do a piece of work, how 
 long will it take him to do a piece 1 1 times as large ? 
 
 9 f of A's age is f of B's age ; and 1 of B s age is 
 f of C's age. How old are A. and B respectively, 
 provided C is 8L years o\d1 
 
 10. Bought 31 boxes of goods, at $6y\ a box, and 
 paid for it with sheep at $2 a head ; how many sheep 
 
 did it take ? 
 
 11. How many times -| is -^ ? 
 
 Solution Isx.-f equals ^j,, and f equals i^. ^^ is contaia- 
 ed in ^^, V or 1| times. 
 
 Solution 2nd.-^ is contained in 1, ^ times, and in f, 1 
 times f times which are V. or 1| times. 
 
 Solution 3ed.-1 is contained in h f times. If 1 is contain- 
 ed in I, f times, i is contained in ^ 5 times f times, ^tidi are 
 Vtimf; and | is contained in it, i of V ti«nes, which is V. or 
 1-J times. 
 
 12. 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 2^. 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 How 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 manv 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 many 
 
 times i 
 times ^ 
 times 
 times 
 times 
 times f 
 times f 
 times ^ 
 times T 
 
 times -f- 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times 
 
 times li 
 
 6 
 
 3. 
 
 8 
 
 2 
 
 3 
 
 I? 
 
 8. 7 
 
 7 - 
 
 ■3 
 14 • 
 8 • 
 
 5. 
 
 9 
 
 2. 
 
 S 
 
 4 
 
 7 
 
 ^ 
 
 6 
 
 8 
 
 IS 
 
 is 
 is 
 
 is fV^ 
 is li? 
 is 
 is 
 
 is 3^? 
 is 21? 
 is 2i? 
 is 5f ? 
 ia -^'^ 
 
 la T¥ • 
 is 3i? 
 is 4i? 
 is 2i? 
 
102 
 
 DIVISION OF FRACTIONS, 
 
 'ffi 
 
 *i 
 
 'I 
 
 Ml' 
 
 m 
 
 ,11 
 
 28. How many times 2^ is 1|? 
 
 29. How many times S\ is 5|? 
 80. How many times 4^ is 6g? 
 
 31. A farmer sold a quantity of rye for $96, which 
 was only * of what it was worth ; how much did he 
 loose by the bargiu ? 
 
 32. A man sold a cow for 1} times what she cost 
 him, and by so doing gained $(5 ; how much did the 
 cow cost him ? 
 
 33. A merchant sold a quantity of goods for \-} of 
 what they cost, and by doing so he lost $lo ; how 
 much did the gooda cost him ? 
 
 34). A farmer, having lost 12 sheep, found, that only 
 l 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 the flock 24 geese were 
 added, the sum would equal 1|- times his original 
 flock ; how many geese had he ? 
 
 36. If I of a yard of cloth cost $|, what will % of a 
 yard cost ? 
 
 37. A boy, being asked his age, said, that 8| years 
 •was f of twice as much as his age : how old was 
 he? 
 
 38. If gof the candies I have cost;7 J cents, what 
 will i of them cost ? 
 
 39. What will | of a barrel of flour cost, if 5 of a 
 barrel cost $2| ? 
 
 40. What will f of an orange cost, if 4 of an orange 
 cost 2i cents? & t s 
 
 41. How many yards of cloth will be required to 
 make a coat, if 1| will make f of a coat ? 
 
 42. f of 2 are how many times f ? 
 tV of 8 are how many times -| ? 
 I of 7 are how many times 3 ? 
 
 of 8 are how many times |- ? 
 
 of 12 are how many times | of 6 ? 
 
 43. 
 44. 
 45. 
 46. 
 
 3 
 ■4 
 3. 
 4 
 
 )\ 
 
FRACTIONS. 
 
 103 
 
 47. I of 7 are how many times j? of 2 ? 
 
 48. If f of 3 yarda of cloth cost Uh what will -J 
 of 7 yards cost ? 
 
 49. If I of G yards of cloth cost $2 J. how much 
 will J of 7 yards cost ? 
 
 60. If 1 of ] of a barrel of flour cost $11, what will 
 } of i of ^' of a barrel cost ? 
 
 1. 12 
 
 Lesson XVII. 
 
 of what number ? 
 
 Solution.— If f of some number is 12, ^ of that number is j^ 
 of 12, or 4 ; and ^ which is that number, are 4 times 4 which 
 are 16. Therefore 12 is | of 16. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7, 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 18. 
 14. 
 16. 
 36. 
 17. 
 18, 
 19. 
 20. 
 
 16 
 18 
 20 
 26 
 25 
 30 
 32 
 39 
 36 
 36 
 24 
 9 
 12 
 38 
 16 
 16 
 16 
 40 
 40 
 
 8 f 
 
 8 ^ 
 
 S ■5. 
 
 S -r' 
 
 5 
 
 7 
 5. 
 » 
 8 
 
 » 
 
 7 
 Jl 
 1 1 
 
 
 
 (! 
 7 
 3. 
 7 
 
 1l 
 "5 
 2. 
 
 4 
 
 "5 
 
 7 
 2 
 "5 
 
 S 
 ji 
 5) 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of w^hat 
 
 of what 
 
 of what 
 
 of w^hat 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 of what 
 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number ? 
 number *? 
 number ? 
 number ? 
 
 -40 is I of 45. 
 
 Solution. ^ 
 
 Remark.— When pupils are familiar with the analysis of these 
 questions, the intermediate steps may be omitted, as m the 
 above solution. 
 

 I. -- <. 
 
 104 
 
 21. 
 22. 
 23. 
 24. 
 25. 
 26. 
 27. 
 28. 
 29. 
 30. 
 31, 
 32. 
 33. 
 3d.. 
 35. 
 36. 
 37. 
 38. 
 39. 
 40. 
 
 72 is 
 72 is 
 12 is 
 16 is 
 18 is 
 32 is 
 46 is 
 48 is 
 48 is 
 36 IB 
 30 is 
 30 is 
 10 is 
 16 is 
 
 24 is 
 
 25 is 
 35 is 
 40 is 
 48 is 
 96 is 
 
 8 
 9 
 
 10^ 
 2. 
 3 
 4 
 
 2 
 5 
 
 jL 
 
 7 
 
 "3" 
 
 *. 
 5 
 
 Jk. 
 
 G 
 
 "7 
 _5_ 
 'J 
 8. 
 7 
 
 A 
 9 
 
 _*_ 
 1 5 
 
 3. 
 
 3 
 Jl 
 
 9 
 _5_ 
 1 2 
 
 8 
 . 6 
 10 
 
 2. 
 
 3 
 
 BRACTIOJSS. 
 
 of what number? 
 of what number ? 
 of how raauj times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 cf how many times 
 of how many time.i 
 of how many tfmes 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 of how many times 
 
 2? 
 
 3? 
 
 9? 
 
 4? 
 
 23? 
 
 5? 
 
 4? 
 
 2? 
 
 iofl2? 
 
 iof]0? 
 
 f of9? 
 
 i of 16? 
 
 f ofl2? 
 
 iof9? 
 
 f of9? 
 
 f oflO? 
 
 f of25? 
 
 f ofl6? 
 
 1 ^ 
 
 2. 
 
 2 
 
 ■"5 
 
 3. 
 
 3 
 4 
 
 4. 
 
 o 
 
 T 
 
 5. 
 
 *. 
 
 
 3 
 
 6. 
 
 3 
 10 
 
 7. 
 
 3 
 9 
 
 8. 
 
 6 
 
 ^9. 
 
 5 
 
 
 10. 
 
 6 
 
 7 
 
 11. 
 
 f 
 
 12. 
 
 f 
 
 13. 
 
 * 
 S 
 
 Lesson XVIII. 
 
 of 6 is I- of what number ? 
 o( 10 is I of what number ? 
 of 8 is f of what number ? 
 of 21 is I of what number ? 
 of 15 is f'o of what number ? 
 of 40 is I of what number ? 
 of 27 is -I of what number ? 
 of 27 is 1^ of what number ? 
 of 81 is Y%^ of what number ? 
 of 49 is -^ of what number ? 
 of i 2 is 1^ of how many times 2 ? 
 of 16 is f c f how many times 2 ? 
 of 10 is f of how many times 4 ? 
 
FRACTIONS. 
 
 105 
 
 14. i of 16 is T^ of bow many times 6 ? 
 
 15. ^ of 15 is f of how many times 6 ? 
 
 16. f cf 20 is f of how many times 3 ? 
 
 17. -I of 12 is f of hcv many times 5 ? 
 
 18. f of '20 is f of how many times 3 ? 
 
 19. ^ of 36 is 4^ of how many times 4 ? 
 
 20. I of 72 is -| of how many times 12 1 
 Solution.— f of 12 is 64. 64 is ^ of 96. 96 is 8 times 12. 
 
 21. I of 96 is I of how many tiroes 90 ? 
 
 22. 1^ of 117 is J of how many times 4 ? 
 23o -f of 56 is f of how many times 8 ? 
 
 24. -I of 60 is f of how many times 5 ? 
 
 25. f of 36 is f of how many times 12 ? 
 
 26. f of 72 is f of how many times 5 ? 
 
 27. I of 40 is yV of how many times 21 ? 
 
 28. f of 32 is I of how many times 9 ? 
 
 29. f of 15 is -f- of how many times 2 ? 
 
 30. •§- of 15 is i of how many times 9 ? 
 
 31. I of 24 is f of how many times 3 ? • 
 
 32. i of 45 is f of how many times 3 1 
 
 33. -f of 14 is f of how many times 5 ? 
 
 34. I- of 18 is f of how many times 7 ? 
 
 35. _5_ of 40 is f of how many times 6 ? 
 
 36. ^ of 45 is -5^ of how many times 3 ? 
 
 37. f of 35 is f of bow many times 2 ? 
 
 38. f of 81 is f of how many times 9 1 
 
 39. f of 5 is -f of how many times 7 ? 
 
 40. f of 7 is ^ of how many times 3 ? 
 
 41. B's horse cost $60, and | of the cost of the 
 horse, is i of two times the value of his wagon ; what 
 is the value of his wagon ? 
 
 42. A coat cost $20, and 4 of the cost of the coat 
 is I- of 8 times the price of a hat ; the price of the hat 
 is required 1 
 
 43. If a cow coat $30. and f of this, is f of 10 
 times the price of a sheep ; what is the price of a 
 sheep ? 
 
106 
 
 FRACTIONS. 
 
 
 1*^ 
 
 > 
 
 4i. A's farm is worth $1200, and |- of its value, is 
 I of 10 times the value of its yearly productions ; 
 what is the value of the yearly productioDS ? 
 
 45. The articles contained in a certain store cost 
 $500, and tV of their cost is g 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 | of the 
 cost of his clothes, is |^ 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 
 I of that is ^V of 2 times the value of the cargo ; 
 what is the value of the cargo 1 
 
 48. A's house cost S1400, and J of its cost, is 3^ 
 times i of the cost of the furniture contained in it ; 
 what was the cost of the furniture ? 
 
 49. Provided a house was Mwth $1200. andf of its 
 value was f of i times the value of the farm on which 
 it stood ; what was the value of the farm 1 
 
 50. If a sleigh cost $100, what would be the cost of 
 a wagon, if f of the cost of the sleigh was xt of twice 
 the cost of a wagon ! 
 
 51. Lambert is worth $2500, and |- of his fortune is 
 31 times | 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 J of this distance, is f of i times the 
 distance from Albany to Eome ; what is the distance 
 to Kome ? 
 
 53. Fort-Plain is 56 miles from Albany, and ^ of 
 this distance is 15- times ^V of the distance from Al- 
 bany to Eochester ; what is the distance to Eochester 1 
 
 54. Waterloo is 192 miles from Albany, and J^ of 
 this distance is 
 
 1 o 
 
 
FRACTIONS. 
 
 107 
 
 to Utica, and 3 miles more ; v/hat is the distance to 
 XJtica ? 
 
 55. Buffalo is 825 miles from Albany, and f of this 
 distance is 7^ times Jj of the distance to Batavia, 
 and 5 miles more ; what is the di&tance from Albany 
 to Bavatia ? 
 
 Distance on the Railroad between Albany and Boston. 
 
 56. Boston is 200 miles from Albany, and f of this 
 distance is 1?- times ^ 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 
 Ij times this distance, is 4| times }j of the distance 
 to Wilbraham ; what is the distance to Wilbraham ? 
 
 58. Kinderhook is 16 miles from Albany, and f of 
 this distance, is f times -| of the distance to Dalton ; 
 what is the distance to Dalton ? 
 
 59. Brighton is 195 miles from Albany, and f of 
 this distance is i of 2 times the distance to Worces- 
 ter ; what is the distance to Worcester 1 
 
 60. Grafton is 162 miles from Albany, and f of this 
 distance is \ of 3 times the didtance to Westfield, less 
 2 miles ; how far is it to Westfield ? 
 
 Lesson XIX. 
 
 1. J of 9 is f of how many times -|- of 25 ? 
 
 2. f of 16 is ^ of how many times -f of 21 ? 
 
 3. f of 40 is ^ of how many times ^ of 16 ? 
 
 4. I of 80 is f of how many times |^ of 21 ? 
 
 5. f of 36 is \ of how many times f of 1 2 1 
 
 6. f of 45 is f of how many times f of 14 ? 
 
 7. |- of 30 is f of ^ow many times ^ of 10 ? 
 
 8. \^ of 48 is \ of how many times f of 7 ? 
 
 9. 4 of 45 is I- of how many times f of 8 ? 
 
 Solution.— 4 of 45 is 36. 
 is 27 times 6. 
 
 86 is # of 162. i of 8i3 6, 162 
 
108' 
 
 10. 
 
 5 
 
 T 
 
 11. 
 
 7 
 
 
 12. 
 
 3 
 5 
 
 13. 
 
 4 
 T 
 
 14. 
 
 4 
 9 
 
 15. 
 
 5 
 6 
 
 16. 
 
 4 
 9 
 
 17. 
 
 i 
 
 18. 
 
 8 
 9 
 
 19. 
 
 4 
 
 20. 
 
 4 
 5 
 
 FRACTIONS. 
 
 of 35 is -I of how many times -f- 
 of 54 is ^ of how many times f 
 of 25 is f of how many times f 
 of 28 is I of how many times |- 
 of 18 is f of how many times |- 
 of 36 is f ot how many times |- 
 of 54 is f of how many times ^ 
 of 32 is I of how many times -| 
 of 108 is f of how many times 
 of 40 is -j^ of how many times 
 of 20 is f of how many times I 
 
 of 111 ? 
 
 of lOi? 
 
 of 10? 
 
 of 25? 
 
 of 12? 
 
 of 12? 
 
 of 16? 
 
 ofO? 
 
 f of 1 of 15? 
 
 i of i of 20? 
 
 of f of 12 ? 
 
 
 Lesson XX. 
 
 1. If 1 horse eat i of a bushel of oats in 1 day, 
 how many horses will eat a bushel in the same 
 
 2. If the wages of 8 weeks amount to $48, what 
 will' the wages of 2f weeks amount to ? _ 
 
 3. A ship's crew of 12 men have provision for 5 
 months ; how many 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, i of its length is under water, 
 and 9 feet out ; how long is the pole ? , ,^^ ^ , 
 
 6. A pole is standing in the water, so that 15 teet 
 is above the water, which is f of the whole length of 
 the pole ; how long is the pole ? 
 
 7. If t 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 heroes 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 buBhels of corn, 
 how many bushels will 4 horses eat in 3 days ? 
 
 , 
 
COMPOUND PROPORTION. 
 
 109 
 
 
 11. If 4 horses eat 16 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 |^ of a 
 ton ? 
 
 13. How many hundred weight of hay can 3 horses 
 consume in 25 days, if 2 horses in i of a day consume 
 -=^1— of a hundred weight ? 
 
 400 
 
 14. In how many days can 4 men cut 16 cords of 
 wood, if 1 man in 1 day cut i 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 ? 
 
 16. If it require 6 days for 2 men to lay 36 rods 
 of wall, how many men can in \ of the time build 72 
 rods of similar wall ? 
 
 17. If 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. If 1 horse eat 1 bushel of oats in 4 days, in 
 how many days would 6 horses eat 48 bushels ? 
 
 20. If f of 6 be 3, what will \ of 40 be ? 
 
 21. If 3bef of6,whatwill^of40be?^ 
 
 22. If 2 men in i of a day earn ^^ of a dollar, in 
 how many days can 3 men earn f of a dollar ? 
 
 2S. If it require i 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 ? 
 
 Jj;^" Suggestion. — li£view unless the pupils thoroughly un- 
 derstand the preceding Chapters, ^gj 
 
 The study of Chapter VII- may be omitted until the class 
 has learned Chapter VIII., ^Ci ceptiog the miflcellaneous quesj 
 tioDS.) , , 
 
110 
 
 QUESTIONS 
 
 CHAPTER VII. 
 
 Iiesson I. 
 
 1. $24 is f of twice aa 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, equalled i as many dollars as they all 
 cost ; what did 1 barrel cost ? 
 
 3. 35 is f of how many times f 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 -5^ of 3 times its value ; what is the value of 
 his horse 1 
 
 6. 72 is f of how many times f of 12 ? 
 
 7. 36 is f of how many times f of 12 ? 
 
 8. 48 is f of how many times i of 18 ? 
 
 9. ^6 is f of how many times i of 8 ? 
 
 10. 60 is f of how many times | of 16 ? 
 
 11. 84 is V^ of how many times i of 25 ? 
 
 12. A spent $60, which was f of 4 times aa much 
 as he was worth ; how much was he worth ? 
 
 13. B sold 9 sheep, which was -^^ times ^ of his 
 whole flock ; how many sheep had he remaining ? 
 
 14. D, at a game of cards, lost $20, which was f 
 times I of all the money he had ; how much had 
 he? 
 
 15. C found $45, which was 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 f of twice as 
 many as he had at first ; how many had he left ? 
 
 17. A boy gave away 8 apples, which was f of 
 
 t 
 
 ] 
 
 t 
 
 I 
 t 
 
QUESTIONS. 
 
 Ill 
 
 twice as many as he had left ; how manv had he at 
 first ? 
 
 18. 12 is f times } of what number? 
 
 19. 86 is y\ times § of how many times f of 13^-? 
 
 20. Jeremiah is 18 years old, and his age is f times 
 I of his father's age ; how old is his father ? 
 
 21. Mary ^ve 6 cents for a comb, which was f 
 times i 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 re- 
 maining, at 2 cents apiece ? 
 
 23. Henry had 20 marbles, which was f of twice 
 as many as Harry had ; how many had Harry ? 
 
 24. Margaret is 16 years old, and her age is f of 3 
 times Martha's age ; how old is Martha ? 
 
 25. f is f of twice as much as what number ? 
 
 26. A man bought a horse foi $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 
 f of what he was worth ; what was the value of the 
 horse ? 
 
 28. A man when he was married, was 20 years of 
 age, which was | times f of the age of his wife ; how 
 old was she ? 
 
 29. Shepherd was worth $160, which was f times 
 ■^ of his father's fortune ; what was the father's 
 fortune ? 
 
 30. A and B were playing cards, B lost $14 which 
 was -j^o times f as much as A then had ; and when 
 they commenced f of A's money equalled f of B's. 
 How much had each when they began to play ? 
 
 31. A and B were playing cards, A lost $20 which 
 was ^ of the number of dollars B then had more 
 
 1 1 i- 
 
 iii was J-'- Limes as mucn as 
 
 than A ; provided this su ^ ^ 
 
 A had at first ; how much had each when thev beffan 
 to play? " ^ 
 
112 
 
 <iU£STIONS. 
 
 Xiesson II. 
 
 rt„\" 1^ ''°^: "'*" "P™^*"? i of all his money, found 
 
 af =ir,^|<,| z^ Zrs^^'tA, tit. Tn- 
 
 This by the condition of the question is 16 cents JflnfJ' 
 money he had at first is 16 ce^nts. i of i\ il Vof 6 cent! wh ch 
 
 Solution 2d -He spent f of his money ; therefore he had 
 
 IfiTnT^.^ '^'*; which equals 16 cents. ^If ^ of Ws money's 
 16 cents, he must have had 40 cents. ^ 
 
 2. Euth, after losing f of all her roses, had only 8 
 remaining ; how many had she at first ? ^ 
 
 3. Jane gave f of all her flowers to Ann, and had 
 4 remaining ; how many did she give to Ann ? 
 
 4. George, after eating ^^3. of all his oranges, had 
 only 8 oranges remaining ; how many had he at first ? 
 
 if 'n , i'^ expended ^ of his money for a pie, ^ fop 
 a ball, i for a to^, and had 6 cents remaining • how 
 many cents had he at first ? ^ ' 
 
 6. In a certain school i of the scholars study gram- 
 mar, 3 study antiemetic, and the remainder, which is 
 lU study geography ; how many scholars in all, and 
 how many attending to each study ? 
 
 7. A third part of an army was killed, i part taken 
 
 thTarr^"^ ^^^ '''"^'^' ^'^ ^""^^«« ^^^^^ 
 
 8. If from my age you subtract i and | of my age 
 the remainder is 2 years ; how old am I ? ^ ^ 
 
 .Ja f?' ? v°5 ^^H^ }'''^ ^^°y Paeons he caught, 
 said, that If to f of the number, 36 were added, the 
 
 hHalch ? ^"^ ^""'"^ *^^ '''''''^'''- ^°^ "^^^^ ^^^ 
 
QUESTIONS. 
 
 113 
 
 10. If to f of the cost of B's horse you add $100. 
 the sum will be twice the cost of the horse ; what was 
 the cost of the horse ? 
 
 11. A gentleman, after spending ^ of his fortune 
 and 2, of the remainder, had $2400 remainin*^: what 
 was his fortune ? ° 
 
 12. A gambler lost ? of all his money, and the 
 next night he won f 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 f of it ; 
 the remainder, which was $iO 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 caughb until he had 
 spent i of it, the remainder ($100)" was given back: 
 how much had he at first ? 
 
 J;^- I^ *o i of the cost of A's watch you add 
 ^10, the sum will be $21 ; what was the cost of his 
 watch ? 
 
 IQ. If to f of B's age you add 15 years, the sum 
 would be 39 years ; how old is B ? 
 
 y?'.J^ ^''°^^^ ^^^°^ ^®^®^ ^^°^ "^^^y s^^^P ^6 liad, 
 said, if to i of my flock you add the number 9^ the 
 sum will be 99.^ ; how many sheep had he ? 
 
 -lol?* ^ ^^ *^^® length of a pole is in the water, and 
 12 feet in the air ; how long is the pole ? 
 
 19. If to I of A's age you add 16 years, the sum 
 will be 1 L times his age ; how old is he ? 
 
 20. A man, being asked how manv pigeons he 
 caught, replied, if to f of the number I caught you 
 add 20, the sum would lack 4 of being equal to IJ 
 times the number ; how many did he catch I 
 
114 
 
 PARTNERSHIP. 
 
 M I 
 
 Lesson III. 
 
 1. Divide the number 36 into two parts, wliich 
 shall be to each other as 7 to 2. 
 
 SoLLriON.-Sinre the two parts are to be to ench other as 7 
 IhZfT'^ '^r^^ ^' '"^^ ^ -^ 2, which are 9 equal par s 
 
 fir«f n mhoA . ^' """^ ^ ^^''^ ^ '''^^'^ *, which are 28 fthe 
 hrst number,) and .;. are 2 times 4, which are 8 (the other num 
 
 Mf:l ?'' 'V'^" '""^' P^''* «f the solution, say : ^of 86 is ps' 
 the hrst number; and | 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 ? 
 
 d. AandB hired a pasture for $14; A nut in 4 
 cows and B put in 3 cows ; what ought eath^top^y ? 
 
 4. A aiid B bought a lottery ticket for $5 ; A paid 
 S3, and B paid $2. They drew a prize of $60 ; wh^t 
 was each one's share ? ' 
 
 5. Two men bought 40 mules : the first paid $5 as 
 tf r'ece" e'' '''^^ ^'' ^^^^ "^^ ^^^^ 4ht tch 
 
 6. Mary and Elizabeth went to school SO davs 
 and as often as Mary went 3 days, Elizabeth weufs 
 days ; how many days did each go ? 
 
 r^.-A Ti?i!'^'' ^^^ ^ ^'^^^^^ ^"d ^^ake 4 cents; they 
 e^afh ?o :e'::i:r^ '^''' ^PP^- ^ ^- --/oughl 
 
 firs^t D^idT2T ^'''^^* ?i°*^'y *^^^^* ^^^ $^2 ; the 
 first pnid $2, the second $7, and the third $3. They 
 
 drew a prize of $240 ; what was each man's share ? ^ 
 in 2 hnria T"" ^''^^/ P^'*"'® ^°^ ^24 5 the first put 
 
 Dut inThn ""' 'f """^ P^f ^^ ^ ^°^«^«' ^^^ tbe third 
 put in 4 horses ; how much ought each to pay ? 
 
 on}v'^tfT''At}'''i ^" ^^^^^«««' ^^« able to pay 
 only I of his debts ; how much will that man receive 
 to whom he owes $90 ? receive 
 
 11. A man, meeting an equal number of poor wo- 
 
PARTNJIRSHIP. 
 
 Ud 
 
 men and boys, gave to each woman 7 dimes, and to 
 each boy 2 -dimes ; and to them all he gave $9: how 
 many women and boys were there respectively ? 
 
 12. Two men bought a barrel of fish for l$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 | of a bushel ; how many bushels did 
 each receive ? 
 
 14. Three men hired a pasture for $36 ; the first 
 put in 3 horses, the second 2 horses, and the third 4 
 horses ; how much ought each to pay ? 
 
 15. Two men hired a pasture for $60 ; the first 
 put in 4 horses, for 2 weeks, and the socond put in 3 
 horses for 4 weeks. How much ought each to pay ? 
 
 16. Three men hired a pasture for $15 ; the first 
 put in 4 sheep for 5 weeks, the second put in 8 sheep 
 for 5 weeks, and the third put in 10 sheep for 9 weeks. 
 How much ought each to pay ? 
 
 17. Two men entered into partnership ; the first 
 put in $40 for 10 months, and the second put in $80 
 for 5 months ; they gained $95 : what was each man's 
 share of the gain ? 
 
 18. A and B agreed to cut a field of wheat for $20 ; 
 A sent 6 men for 4 days, and B sent 3 men for 10 
 days ; 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 ; w^hat ought each to pay provided 2 sheep in 
 1 week eat as much as a horse in the same time? 
 
 21., Simpson, Bomer, and Eyer, enter into a joint 
 speculation by which they clear $460. Simpson 
 claims to have furnished f ; Domer, J ; and Eyer, ^ 
 of the entire capital. Bow much according to these 
 calculations ought each to receive ? 
 
116 
 
 ALGEBRAIC QUJ33TIONS. 
 
 er 
 
 u 
 
 Lesson IV. 
 
 l.«h? \^ ^ *PP^®^, ^^""^ *^«» ^' and they togeth 
 had 14 ; how mauy had each ? ^ ^ 
 
 hlvlofiJL A . ^ "P^^"' ' ^" ^^^<^^» «^^ A'8 Dumber, and we 
 
 uer equals 14 — 4, Oi' 10; and once ha numbei' eauals A nf in 
 or 5 apples. And B's number is 5 + 4 = 9 apples * ' 
 
 Knfi; ?^"'S^ ^"l" ^ ^°°^'' '"^^^ *b»^ Handford, and 
 both have 26 ; how many has each ? 
 
 Knfi; r ot^""? ^ '"^'■^^^' "^^^« t^a^ Richard, and 
 A ^r® ^ ' ^^"^ "'^^y ^^»« each ? 
 
 hnv^ 2l^'{ ^""^ ^ '""'f '^^'^ *^^^ ^a^t^a, and both 
 have 24i ; how many has each ? 
 
 5. Alice has 7 pins more than Abner, and both have 
 2i) ; how many has each ? 
 
 ^' I 0^ I is A of what number f 
 .nl; .^^^^'^^^ of two numbers is 36, and their differ- 
 ence is 16 ; what are the two numbers ? 
 
 ^ V • ^?y,^o"g^<= f of a melon for 8^ cents : how 
 much IS that apiece ? ' 
 
 hpfn?"""®!^"^ ■^^''?^^ '"''^^ ^°^g^t an equal num. 
 mnrfj^'^'^'V °\*^"^^ ^^^^ hoSe Hannah had 4 
 ITv&^htV^^ '^^^ ^^^-^^-^^^24; how 
 
 onpt Jr ^/' ^^'^ ?^^ ^"^ ^^^^^ "^«^^e^ of block.; 
 n A ^ ' ^""^ ^any had each at first ? 
 
 much i.-r^? ""f '°M ^^^ ^1^^^ ^^icJ^ ^as f as 
 ^9 as it cost ; what did it cost ? 
 
 ffene' un^T^^^f ^'^l'^ • \^^^^ strawberries a,. Eu- 
 gene, and both Um. 18 pints ; how many had each ? 
 
 Tro Au^''' ''''- ""^^0 than twice as many as 
 Ira,^and both had 36 ; how many had each ? ^ 
 -^* ^.usaahuu^ as many cents as Sarah; Sarah 
 
ALOEBRAIC QUESTIONS. 
 
 117 
 
 as 
 
 lost 10 of hers ; then together they bad 60 ; 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 liad 50 eggs remain- 
 ing. How many had each at first ? 
 
 16. A of a number + 14 = 44,; what is that 
 number ? 
 
 17. A boy being asked his age, replied, :{ 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 ; 
 now much money had A ? 
 
 19. Two boys had 49 marbles, but the first has 7 
 the most ; how many has each ? 
 
 «^n^* i^ *"^^ bought a sheep, a cow, and a horse for 
 WiO; 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 f as much as his dinner cost ; what was the 
 cost of his dinner? 
 
 4.U ^\'^ gentleman bought a watch and chain for $80 ; 
 the Cham 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 
 tor 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 orauges re- 
 maining. How many of each kind did he buy ? 
 
 25. 5 times a certain number— 12 is 48 ; what is 
 that number ? 
 
 26. f of a certain number— 5 is 40 : what is that 
 number ? 
 
Ill 
 
 118 
 
 ALGEBRVIC (QUESTIONS. 
 
 27. A boj, being asked hia age, replied, U years 
 j^. •^Y^^^'i'^^^gasked how many sheep his father 
 
 29 A boy bought IS lemons ;— for ^ of thpm l.n 
 paid Scents for 2, and for th. rematder he pa^d 3 
 cents a piece; for what must he sell them a piece to 
 gam 10 cents on the whole ? ^ ^ 
 
 30. James, John, and Joseph together have qfl 
 peaches 5 James has 2 more than John, and Jo ephh.s 
 as^many as both James and John / how many hL 
 
 pafd2fe?t7f.!!.T^^^.^T.°^''^ ^°^* °^*^«^ ^^ 
 2 and sold^ of th' "I t' ^^"^^'^^er, 3 cents for 
 I'/fiT ^ f ^''"'' ''^ *^^ ^^<^^ of 2 cents for 3 
 and the remnuuier, at 3 cents for 2. How much did 
 he gain by so doing ? ^" "^^ 
 
 Ijesson 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 ^ 
 
 wi ; 'i^'i'? '^^'^ '^"' "^^ '"^ ^^^^^1 «f beer in 20 weeL s 
 what part of it can he drink in I week ? ' 
 
 oft ol^il''^''''f I" • ^'^ t° '"'P'^ '^ ^^««^^ ^^J^at part 
 or It can be emptied m 1 hour ? 7 t-oiu 
 
 4. If a family consume a barrel of pork in 30 dava 
 what part of a barrel do they daily consume ? •' ' 
 
 nev wL Z'^T't ^^ ^T '" P"""'"™ " certain jour- 
 ney, wha. part of it can be performed in 1 day? 
 
 indR L if? t " *'"'''''" P'^'=« °*' ^■o'-'^ w 8 days, 
 ^an el'So'inVdXr^ '^ '^ '^"--^ -^^' P-' o/S 
 
 couM^d?*'""'^ "°- "r'f '° '^?'''*'" ^ '5''^^' ""^dD 
 <-i.ma ao ..,= ,.,uiu lu G days; what part of it could 
 
ALGEERAIC QUESTIONS. 
 
 119 
 
 each do in a day, and how much could they together 
 do in a day ? 
 
 8. If 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 Eud 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 loug 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. f of a barrel of flour cost $4|, what will |. of a 
 barrel cost 1 
 
 15. A and B can build a boat in 20 days, and with 
 the assistance of C, th<^y can build it in 8 days. How 
 long would it take C to do it alone 1 
 
 36. A farmer and his sou 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 1 
 
 19. A box of tea, usually, lasted a man and his 
 wife 9 months ; when the man was absent it would 
 
 1 
 
 fU, 
 
 oaf; . ..„ 
 
 
 10 
 
 
 lasted the man alone ? 
 
 XT 
 
 xxuw 
 
 iOilg 
 
 u ould it have 
 
120 
 
 ALGEBRAIC QUESTIONS. 
 
 li'l 
 
 <3a, '; anHla I'd" ' 'T"^ " ,'"^^' °' ^^^^ - 24 
 
 I of thiTtt^-Te^rea* ''^r/' ^^ ^^^^ 
 each arid thereby gaLd"o;t''.„f '"" "J ^ "^"t^ 
 bought How ^„»oh"d1^ 4 ^or pirf "'""^^ 
 
 4J; f :rehr'h:a:tTr;.^ °^-°* ■•-^ °^ 
 
 c^a h^tLTeaThe%%rA:j'r"^^''-^°^a 
 ^b. Isaac can make a pair of boots in 2 ^c . 
 
 themtoeut a cord thjll ''°/ '"""''^ '' t«ke 
 
 28 if •■' nP„! ' 1 ° *°®y worked together? 
 
 of an appfel:t"/"P'^ '=°^' * "^ ^ -"^. -ha' will | 
 
 can A and B ^ow in a^dal "haf6 ^ ''°" ""•=" '"'"■« 
 
 « bear oa^ it t1° iliVuZ'JV "'^ '"'"^''"^ 
 take them together to rnr«,l,?' "^ 1"°^''''"''' '* 
 ^fter the wol? harbe^t^rn'ri TanTotI ' ''''' 
 
ALCEBRAIC QUESTIONS. 
 
 121 
 
 Lesson VI. 
 
 1 'Lewis, meeting some beggars, gave each of them 
 2 cents, and had 12 cents remaining ; if he had given 
 them 4 cents each, it would have taken all the money 
 he had. How many beggars were there. 
 
 Solution.— By the last condition of the question, he gave 
 each beggar 2 cents more than by the first, and to them all 12 
 cents mure than by the first condition. Therefore there must 
 have 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 of 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. i of $100 is ^^ of I times the salary of the 
 President of the United States. What is his salary ? 
 
 6. $40 is f of Jq of the salary of the Vice Presi- 
 dent of the United States. What is his salary ? 
 
 7. 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 | of 
 twice as much as it cost ; how much did it cost ? 
 
 9. By selling a quantity of cotton for $560, I gain- 
 ed f of what it cost ; how much did it cost f 
 
 10. A and B are 187 miles apart, and are traveling 
 towards each other ; one at the rate of 8 miles an 
 hour, and the other, 9 miles an hour; how many 
 hours before they will meet ? 
 
122 
 
 ALGEBRAIC QUESTIONS. 
 
 her 20 dimea^more hoT' /"'"'^ "7°"^^ '"'^'^ cost 
 contain ? ' ^""^ """"y y^fds did the piece 
 
 oranU T/het„7ht th"ose ' a^ 2''eenr^- r"'"- "^ 
 hare had no money left -Ld h t ' ?"=''' "^^ ^™uld 
 cents each he would havrwant^^ \T^^ *'"°^«' ^' 3 
 iave paid for them wlt ^" "^^o*^ «ore to 
 
 quired to buy ? ^°* "^^^ °'''"'?« was he re- 
 
 ofmu3lt;iCtre%1nr^'"-«^^^ 
 yard, and some at 12 cenf« « i""?r "* ^ «ents a 
 that at 12 cents a yard ?t wo^f ^""^ '^' ^^^en 
 more than the other kind W ^"^ '"'"' ^6 cents 
 wish to buy? "^'^ '""''• HowmanyyardsdiJshe 
 
 niw ofTou'&:;:Lt%rnri/°h \"^ \-^'- 
 
 atScentsanounW l,o^ ij? ' " "o bought beef 
 
 but if he bZht Jork Ifs . T ^^ ''^"*^ remaining; 
 
 have only 6 f^ts rematbri'" T"^' ^' ^""'d 
 was he sent ? '«'"aming. Por how much meat 
 
 time's- tl^slTnu^X^'Xt Th 't^ '' T- ^''^ ' 
 
 16. A boy being askedftg tid T I?"'' ' 
 
 IS 24 years more than 2 timea m v ^! , 'T^ ""^ age 
 
 17. A boy, beine askerf 1,.^^ ="' '"''^ "'^ was he? 
 
 he had saidf 4 timfs tt ie7>7l\'7'^ "^P^P^" 
 tunes the number • hnwll^ i .'^ ^^ '^ss than 7 
 
 ., 18. AperZ ;ishi^"t?{!^''*«°fP«Porhadhe? 
 
 f he bought that which fa, 10^.'''"' ''""'='•• ^"nd, 
 
 have 20c?ents reml-nLg but if h': t ^TS^^ '^°"W 
 
 was 12 cents a pound he wo, W 1 ^"i'f *" "'"* which 
 
 "-'> "^ vvuuid have $20 
 
ALGEBRAIC QUESTIONS. 
 
 123 
 
 remaining; but if he gave .1^5 a head he would lack 
 ^^0 of having money enough to pav for them. How 
 many sheep did be wish to buy ? * 
 
 ,20. A, B, and C, talking of their ages; says A to B, 
 I am 4 times as old as you ; savs B to C I am ^ as 
 old as you, but says A to C, I am 40 years older than 
 yoa. liequired the ages of each ? 
 
 Lesson VII. 
 
 1. A laborer agreed to work 40 days upon this con- 
 aition ; that for every day be 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 ? 
 
 ^ • ""T^n r^^ H ^'^"^ ^^^°^^^ ^'^« ^'^ole 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 ever^ 
 day he was idle he lost $2 (his daily wages) + $1 (the cost of 
 his board) which are |3 If in 1 day he^se $3 ; he will lose 
 $1 in j of a day, and $30 in 30 times I of a day, or 10 days. 
 Therefore he was idle 10 days, and worked 40 — 10 days or 
 60 days. "^ ' 
 
 2. A man agreed to work 60 days on this condi- 
 tion ; that for every day he worked he should receive 
 ^1^, and for every day he was idle he should pay Si 
 for his board. At the expiration of the time he re- 
 ceived $68. How many days did be work ? 
 
 3. A man w^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 
 140. How many days did he work ? 
 
 4. How many times | of 12 is | of 40 ? 
 
 _ ?; ;^ and B bought a quantity of flour for $50 ; A 
 paiu ^i as oiten as B f 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 $1/^0 more than A, and C paid as mucli 
 as A and B both ; how much did each pay ? 
 
 7. A merchant sold a quantity of cloth for $84, and 
 thereby lost % of what it cost ; what did it cost ? 
 
 8. T-^is 2i times % of how many times IJ? 
 
 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 j 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 oell 
 
 in all ? 
 
 12. A farmer sold an equal number of ducks and 
 turkeys ; the ducks at 4 dimes each, 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, contammg 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 has 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 condition, 
 that foe every day he labored, he should receive 
 3 dimes, and for every day he was idle, should 
 pay 2 dimes for his board. At ths expiratioa 
 
ALGEBRAIC QUESTIONS. 
 
 125 
 
 of the time he received only $1. How many days 
 
 was he idle ? , . i j 
 
 18. A boy bought a whistle, a whip, and a drum 
 for 70 cents. For the whip h 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 3 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 ot their 
 ages is 25 ; 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, 
 wasbroken into two pieces. The shorter piece was f 
 of the length of the longer. "What was the length ot 
 each piece ? 
 
 Solution.— I of the length of the longer piece, which is the 
 length of the shorter,+t (the length of the longer)- I of the 
 length of the longer, which is *he length of both, or 14 feet. 
 If I of the longer is 14 feet, i is ^ of 14 feet, which is 2 feet, 
 and 4 (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, the length of which is 20 feet, is in the 
 air and water, f of the length in the air equals the 
 length in the water ; what is the length in the air and 
 water respectively ? i j ^ ^ 
 
 3. If in 2 days a man traveled 160 miles, and ^ ot 
 the distance he traveled the first day, equals the dis- 
 +o««n V.O frnvplpd thft second day : how far did he 
 travel each day ? 
 
126 
 
 ALGEBRAIC QUESTIONS. 
 
 4. B and C togetlier have 40 marbles ; how many 
 has each, provided % of B's minibor is equal to C's ? 
 
 5. From New York City to Eedhook is 100 miles, 
 and I of the distance from New York to Ehinebeck, 
 equals the distance from Ehinebeck to Eedhook. How 
 far from Ehinebeck to New York, and how far from 
 Ehinebeck to Eedhook ? 
 
 6. If a horse and a colt were worth $90, and the 
 horse was worth 1 3- 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 ; f 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 ^ of the first + 8 shall equal the second. 
 
 11. Divide the number 97 into two such parts, that 
 -f- 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 f 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 -^- of the weight of the head 4- 8 pounds 
 equals the weight of the body ; what is the weight of 
 each? 
 
 14. A ship-mast 51 feet in length, was broken ofl" 
 in a storm, and f of the length broken off, equaled f 
 of the length remaining ; how much was broken off, 
 
 *luu uuW mucn remuiiieu : 
 
 15. A boy being asked how many apples and 
 
ALGEBRAIC QUESTIONS. 
 
 127 
 
 oranges he had, answered, in all I have 36, and, f of 
 the number of apples, equals I of the number of 
 oranges ; how many of each kind had he ? 
 
 16. I of one number equals -} of another, and their 
 sum is 57 ; what are the two numbers ? 
 
 17. A farmer has 290 sheep in two difiVrent fields ; 
 and f 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 ; i of the number of the 
 first kind, was to equal f of the number of 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 i of the time past midnight ; what 
 was the hour ? 
 
 Remark. — Since the time past noon is | of the time past 
 midnight, the time from midnight to noon, which is 12 hours, 
 must be f of the time past midnight. 
 
 . 20. A person, being asked the hour of the day,^ said, 
 the time past noon, is l of the time past midnight ; 
 whiit was the hour ? 
 
 "■' . A person, being aaked the hour of the day, said, 
 T .1 past noon, is ^ of the time from now to mid- 
 
 ni-: "hat was the hour? 
 
 SoLurroN — From now to midnight is f, and i added (the time 
 past noon) is f. Consequently from noon to midnight (which is 
 12 hours) is f of the time it lacked of being midnight; and ^ of 
 the time, is i of 12, which is 3 hours, the time past noon. 
 
 22. What is the time of day, provided f of the time 
 from now to midnight equals the time past noon ? ^ 
 
 23. A man, being asked the hour of the day, said, 
 f of the time past noon, equals | of the time from now 
 to midnight ; what was the time ? 
 
 24. A pole, the length of which was 68 feet was in 
 the air anu water ; ^ oi tuu it;ugtu m mc au, equaicu 
 
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 numhers is 176, and f of the 
 first + 4i equals J of the second ; required the num- 
 bers ? 
 
 20. A person, being asked the time of day, said f 
 of the time past midnight equals -j'^o 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 c 'clock is it? 
 
 28. Says A to B, | of my age + 4 years equals f 
 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, f of the time past noon, equals | of the time 
 from now to midnight +| 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 1|^ 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 an long as its head and tail j 
 whai 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 = f, or the lengtli of the body. There- 
 fore, f— J, or i 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 82 inches. 
 
 2. Th 
 
 
 
 long as its head 4- i of its body, and the body is as 
 
ALGEBRAIC QUESTIONS. 
 
 129 
 
 long as the head and tail together ; what ia the length 
 of the fish ? 
 
 3. The head of a fish ia 12 inchea long, the tail ia 
 na long aa the head + i of the body, and the body ia 
 as long aa the head and tail ; what ia the length of 
 the fish ? 
 
 4. The head of a fish weighs 10 pounds, the tail 
 weighs aa much aa the head -f I as much aa the 
 body ; and the body weigha as much aa the head and 
 tail ; what ia the weight of the tail ? 
 
 5. -5- of a certain number equals f- of the same num- 
 ber + 10 ; what ia that number? 
 
 6. A boy, being asked his age, replied, f of my 
 age exceeded ^ of my age by 4 years ; how old was 
 he? 
 
 7. Jamea, being asked how many arithmetical ques- 
 tions he had answered correctly during the week, re- 
 plied, I 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 |- of all his money, 
 and I of what then remained, had only $12| remain- 
 ing ; how much had he at first ? 
 
 10. If f of a ship be worth | 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 -J exceeded its i by $2 ; how much had he ? 
 
 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 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 boii'^ht a hat, a coatj and a vvateh : the 
 bat cost $6, the watch cost as much as the hat + f of 
 
130 
 
 ALGEBRAIC (iUESTIONS. 
 
 tho cost of the coat, and the coat coat as much as the 
 
 nM "■'' """^ ^- "'■ " '^"'-^ °'' 1« i^ -^ of what 
 
 17. If from a certain number you take its i and its 
 ^-. the remamder w,ll be ]3|. wh'at is that nuXr ' 
 
 18. After spending -| of ,ny money, I earned »„<■ 
 muen as I spent, and then had onf; «20 Jess Aan 
 what I had at first ; how much had I'at first/ 
 
 tt let^tt^^ the^fifh? - "'« '-" -^ *ail? What' 
 
 20. The head of a fish is 12 inches lone- its tail i, 
 
 10 inches longer than its head increS'bv 1 the 
 
 ength of the body ; and its body is 20 inches longer 
 
 of theth?' '"^' ''^" '°="''"'-- ''^^' - t^e l-fth 
 
 Lesson X. 
 
 1. James is 20 years old, and John is 4 years old 
 
 dd a?jr Vr^l 1" .J--%-^- - -w I tt^aes as 
 oia as John, be only twice as old ? 
 
 2. Sarah is 10 years old, and Sallv is 4 • in >,««. 
 many years will Sally be J 'as old asljnhV " ''"^ 
 
 d. Jacob IS 40 years old, and Alfred is 2 • in how 
 many years will Alfred be i as old as Jacob? ^""^ 
 
 6 K ;^ ^^*i'? *'l":d °f e- «hat win the i of 20 be ? 
 o- li i or lii oe lu, what will f of 10 be ? 
 
ALGEBRAIC QUESTIONS. 
 
 131 
 
 7. Divide the number 85 into two parts, that shall 
 be to each other as -^ to |. 
 
 ^ 8. When A was married, he was 3 times aa 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 ? 
 
 Remaek.— The conditioue of tho above question elvo tlie 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 f of the 
 same number + 30 ; what is that number, and what 
 is 3- 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 | 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 ; what 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, 
 J of his age equalled 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 manv 
 leaps must the hound take to gain 1 on the fox ? ' 
 
 15. If tho hound takes li 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 
 hound take to catch the hare ? 
 
 17. A fox is 60 leaps before a hound, and takes 5 
 leaps to ^he^:.ound 2; and 4 of the hound's leaps 
 equala 12 of the fox's. How many leaps must the 
 hound take to catch the fox ? 
 
132 
 
 ALGEBRAIC QUESTIONS. 
 
 18. Alfred is GO steps before Silas, and takes 9 
 steps to Silas 6; and 3 of Silas's steps equals 7 of 
 
 t\ u '!• ?u "^ "^^^^ '*^P'' ^* *^is ra^e> will each 
 take betore they will be together ? 
 
 12/ iTma^'b^.^ *"'' '''^^^'''' ''''''^'''''' ^^ square feet, or as near- 
 
 19. How many panes of glass in a box, provided 
 they are 6, by 8 inches ? 
 
 Remaek.— Flud the area of a pane of glass by reducino- fhp 
 inches to parts of a foot, and then multiply these PtsSer 
 The urea of a pane 6 by 8 inches is i of a equare foot. 5w 
 mamder may be solved as follows : i"ere- 
 
 SoLUTioN.-If to make | of a square foot it require 1 pane 
 to make f or 1 square foot, it will require 3 times Cs 
 panes ; and to make 50 square feet, (1 box,) it will require 50 
 times 3 panes, which are 150 panes. ^ ^ 
 
 20. How many panes of glass in a box, provided 
 they are 8, by 10 inches ? proviaea 
 
 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 ? F'oviaea 
 
 i\.?' ^?o u ^ vl P^^'f ' °^ S^^'^^ ^" a bo^' provided 
 they are 12, by 15 inches ? 
 
 Lesson XI. 
 
 1. What number is that, to which if its h be added, 
 the sum will be 15 ? ' 
 
 2. What number is that, to which if its i be added, 
 the sum will be 24 / * 
 
 3. What number is that, to which if its i be added, 
 the sum will be 40 ? «ucu, 
 
 4. What number is that, to which if its i be added, 
 the sum will be 30 ? «uucu, 
 
 o. „ j^ j^uj^j^^ ^Q ^^^^^^ ^|. added, 
 
 the sum will be 88 ? ^ auucu, 
 
ALGEBRAIC QUESTIONS. 
 
 133 
 
 6. How old is that man, to whose age if you add 
 its i and its f , the sum will be 104 years ^ 
 
 7. What number is that, which being increased hv 
 itsi, its 'h and 18 more, will be doubled ? 
 
 8. A. man, being asked his age, said, my a^^e in- 
 creased by Its I and 20 more, is double mj age. 
 W hat was his age ? "^ ° 
 
 9. Suppose I buy a certain number of boxes of but- 
 ter, at $2 a box, and as many more at U a box ; and 
 
 much ?"" ^ ' '^'' ^ ^''''' °' ^°'"' ^^^ ^°^ 
 
 ^,9- f .l'^.^' ^eing asked how many oranges he had. 
 replied, if my number were increased by its ^ its ^ 
 and 42 more, the sum would equal 3 times my num*- 
 ber. How many had he ? j ^ 
 
 J 1. Suppose 1 buy a certain number of melons • 
 sonie at 10 cents each, and as many more at 40 cents 
 each ; and sell them all, at 30 cents apiece ; how 
 much do I gain on each melon ? 
 
 12. If by selling 1 apple I lose ^ of a cent, how 
 many apples, at this rate, must I sell to lose 6 cents ^ 
 
 1^. A boy bought a certain number of lemons, at 
 ^f^*^/ piece, 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 of apples 
 at the rate ot 2 for a cent, as many more at the rate 
 ot 3 tor a cent ; and sold them all at the rate of 5 for 
 
 Tf"' and b^^^o doing lost 4 cents. How many of 
 each kind did she buy ? ^ 
 
 15. A woman bought a certain number of effffs, at 
 the rate of 3 for a cent, and as many more, at 4 for a 
 cent ; and sold them out, at the rate of 8 for 3 cents 
 
 she bu ^? ^^'""^^ ^ '^^''*'* -^"""^ ""^""^ ®^S^ ^'^ 
 
 .. « , "~ •• "&^^^'^ «■'-' f^^aro ^uxu lu tne propor- 
 tion ot 2, f , and i ; how much must each receive ? 
 
134 
 
 AEGEBRAIC QUESTIONS. 
 
 18. The difference of 2 numbers is 15, which is 
 
 more, at the rate of 5 for $1 and !nl/?h "' T°^ 
 geraee of 10 yards Zfs] ^nd ttoeW Lf$f 
 How many yards did he buy ? ^ * ' 
 
 theratfof rfor°sf t V*"° """''^^ of melons, at 
 in / ., n"^ *^' *°'^ ^ Many more at the rate of 
 10 for $1; and sold them all at the rate of 8 for $2 
 and thereby gamed $6. How many melons dM t' 
 
 Lesson XII. 
 4 t^XlariTbTw^a^^t^fhT''' «-^ 
 
 tJc'eSlTtheVf '° ' ^"""^ P*''^ ^^''^ "- ^hall be 
 
 3. Divide 21 oranges between two bova so iUf nr.o 
 may have twice as many as the othLr ^ '* "''" 
 
 4. ±raukhn and Francis together have 15 nn«rfo 
 
 to|tht'|:y;rar|;Lr^^^^^^^^^^^^^^ - 
 
 7. Harriet 13 twice as old as Ellen, and the sum of 
 
 TT7JbJ''^^'- T'"''^ ""eageofeachT"^ 
 
 o. A ana ±J are 36 rods aT^n^^f «v,Jj ^ i x , 
 
 i.^- •-* «iiu i/iuvei cowards 
 
ALGEBRAIC QUESTIONS. 
 
 135 
 
 apples 
 h and 
 
 1 
 
 all he 
 
 1 
 
 it one 
 
 ^^B 
 
 uarts 
 
 V 
 
 ncis. 
 
 1 
 
 aud 
 
 1 
 
 shall 
 
 1 
 
 mof 
 
 1 
 
 ards 
 
 1 
 
 each other ; how far will each travel before they meet 
 provided A travel twice as fast as B ? "«/^eet 
 
 9. What number must be added to twice if^plf 
 that the sum will be 57? ®^^' 
 
 10. A, after spending i of all his money and -I of 
 
 tVhTaTh:UTrsn' '^' ^^^^ ''' ^^-^--^^ ^ ^- 
 
 one Vha^t1'o\%ro'tL'^ ^^*° *^° ^"^^ P^^*«' *^^* 
 12. In a certain school, there are 8 times as many 
 boys as girls and in all there are 52 pupils ; how 
 many boys and how many girls in the school ? 
 13 James and Jackson together have 45 marbles, 
 
 has eachT °^ ^ ""' "^^""^ ^' ^^''^'°'' ' ^"""^ °*^^^ 
 
 14. A man and his son together earned $280 in a 
 year ; how much does each earn, provided the boy 
 earns only i as much as his father ? ^ 
 
 15. A boy bought a melon and a citron for $1; 
 how much did each cost, provided the melon cost only 
 i as much as the citron ? ^ 
 
 +1, ^^' j^,"^^" bought a horse and a saddle for |;120: 
 the saddle cost only x as much as the horse ; what 
 was the cost of each ? 
 
 17. A man, being asked the cost of his oxen, said 
 my oxen and waggon together cost $240, and the oxen 
 
 of each r ^' "''' ""' *^^ '^^^^'''' ' ^^^^ ^^^ *^® ^^«* 
 
 18 A man bought a sheep,a hog, and a cow for $42, 
 tor the hog he gave twice as much as for the sheep, 
 and for the cow, 3 times as mucb as for the sheep. 
 How much did he give for each ? 
 
 19. A farmer and his two sons earned $560 in 1 
 year ; the father earned twice as much as his elder son, 
 and the elder son earned twice as much as the younffer 
 son. How mufth diH t^nnh oo«« o ^ & 
 
 v^i« v,t.ll.ii 
 
 20. A, B, aud C together, in 1 day, can dig 105 
 
136 
 
 ALGEBRAIC QUESTIONS. 
 
 day" "' ^- ^°^ '"^"y bu^l'els can each dig in a 
 
 fj,f fl" "^ """ ''°"Sht three pieces of cloth for «lf!0. 
 the first p:ece oulv cost ^ •!« mn^l, „» I '? '^ ' 
 
 the second, only /as much ^thAv f^ 'lr'°'"^' "'^'^ 
 did each piece cost" ^"'''- "°*' "«'='>• 
 
 asii^trwrdTdtTri^rd'rd'rt'"^' 
 
 iyely -^ ' ^"""'^ed, and unhurt respect- 
 
 = ^e'-D' °^ ^'^' ■*: * °'' S's money equals S5500 • nr„l 
 i of B'a money is 4 times i of A '= w ' , 
 money has each ? ' '^^ ^- ^o'' "^'-ich 
 
 and B.^f"'*" ""^^ ^y™° *°ge*«'' have 60 blocks • 
 hafete °™«*'«»-yas Herman; how mty' 
 
 bet e^ro&"t"r -*° 2 parts, that shall 
 
 theUorlionTf'*^"^!^;:*" ^'"" ". "PP'^ ^ 
 receive ? " * »» 3 5 bow many o^g^t ^^^[^ .^^ 
 
 yefr^'. w'Z °^ ^r^ and Hezebiah's age is 25 
 Is old as Mary r ' ^'■°"'''' ''^^^''''"' '^ ""'^ * 
 oatfi'nf^''^ ?** his father can thrash 35 bushels of 
 
 th Lhes oSv ^T ""7 '^V ''"^ thrash, i? Henry 
 OQ A 7 "■ "^ """"h as his father ? •'^ 
 
 •^». A pole, whose length is 70 fpof ;= ;„ n 
 and water; how much ;<. i n tu • j ' '° *''^ air 
 ivelv if' ^ptu 1 il ^".^^airandwaterreapeet- 
 tKteH " ''"^* '" "^^ «'^ ^^-^^'^ "'« 'e"gthTn 
 
 beTo-eStV^ra"sTt'oT '°'° ''^'^ "^^'^- "^^ ^'-" 
 be to eSh otfcu^' '' '"^° ' '''''' ">^' ^''^U 
 
ALGEBRAIC QUESTMNS. 
 
 137 
 
 *S4if!?™"wriS'.ij7"»'' 
 
 QQ A 1.' , "iuiJii oejonors to each ^ 
 
 twf • i^ ""'^ ^^'?S'^^ ^^^** ^^200'to be divided be 
 tween his son and daughter, in the propo t on of 1 
 
 Jl How much ought each to receive } 
 
 twt J^s^^^^^cr;^^^^ ^^r% 
 
 each kind was there ? ^ ^"^ ' ^°^ ^'^^^ ^^ 
 
 35. A man bought a cow and a hor-^P fn». ^qr 4.i 
 
 each? quarts, ho^ nianj belongs to 
 
 BbairbfSci':trarx^^"'° ^'^^ p^^*^- *»-' 
 
 equalled the distance he wa^lealThen^W Sei' 
 How far did the fox run, and how far In advene! of 
 the hound was be when the chase commenced? 
 is to he I'T t'^o numbers is 140, and the larger 
 beJs? ' as 1 to f, what are the two num' 
 
 40. A and B together owe $69, but B owes onlv 
 
 ^41 Thtr ^ ''. Tr r'='^ '"'^ -•'h owe/' °°'^ 
 
 41. Ihomas and Thornton found $240 but ronM 
 not agree about the division of it thp^' tl f 
 threw it on the floor and each got ;hat h'e could fi 
 
 TWrrV'"' ^'r.^^ sol only Vas much a 
 inornton. How much did each get? 
 
 th^Z: ^% J?"''"'" """"""l consisting of 48 puoils 
 
 boys and htw "'' "' "r? ^°y' "^ gS-ls : how^many 
 ooys, and how many girls m the school ? ^ 
 
 «160-, if i::''.^„.:f !Lr*iy- "ought for 
 gold one ; how much was tUc-o^oFe^crr" " '''' 
 
138 
 
 ALGEBRAIC QUESTIONS. 
 
 44. Divide the number 17 into two parts, that shall 
 be to each other as f to f . ■ ^ ' **" ''"^^ 
 
 45. A farmer had 180 sheep in two fields, and i of 
 the number in the first field equalled i of ihe num- 
 ber in the second ; how many in each field ^ 
 
 othtr afi'^t^^^^ '''^'' *''''' ^""'^^ ^^""^ '^^^^ ^" *° ^^^^ 
 47. I of the distance a hare ran after a ■ 1 start 
 edm pursuit equalled the distance she ... ,8 before 
 the hound when they started ; how far did the hare 
 
 snin/ r ^''^.^^^''"ght, provided the hound ran 
 SO rods to overtake her ? 
 
 in tt ^ *"i^ started from the same point, and ran 
 in the same direction ; B ran 60 rods ; tnen X of the 
 
 T'T^^ ^i^ ™" e<J>'«"ed the distance A was 
 60 rods ? "'"''' ^''^ ^ S"'" °'' ^ '° ^"•^"'"g 
 
 . 49. A fishing-rod the length of which is 24 feet, is 
 in two parts ; f of the longer part equals the lenetli 
 °f*^e 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 ahfad of the 
 
 Howl r f 7.1^^1^^' ^'^°'' it ^"^ overtaken! 
 Sretmtencel?"^ ''"^' ^^^ *'^« ^-- ^^^^ *•>« 
 
 emtVJm^? """'"''■ °/''''"P + f of B's number, 
 equals 900 ; how many sheep has each, provided | of 
 B s number is twice f of A's number ? 
 
 Lesson XIII. 
 
 1. A person had two silver cups, and onlv one 
 cover for both. The first cup weighed 6 oz If the 
 
 theVeco^n^/ ^r/fi " ^'"' 7«gh twice as much as 
 
 tue second, but if tliA 5Jpf»r»r.ri «,,^ u^ i •. 
 
 , - - — — ^ t^t^vvixva vup uQ uuvered It will 
 
ALGEBRAIC QUESTIONS. 
 
 13a 
 
 Zl'^}, ^/J,™'' ""^ T""^' «' *^® fi^«t- What is the 
 weight of the second cup and cover ? 
 
 Solution— By the last condition of tlie Question S t.'m^a « 
 oz the weight of the first cup, or 18 ounces^ equal \heweS.? 
 
 cove;weir.h isT?"' ''''''' , PT'^^^^-^'y '^« two cupsT d 
 covei weigh 18+6 ounces, which are 24 ounces And hv fho 
 
 first condition, the first cup and cover weigh twi'ce as mu^h n! 
 the second cup. Therefore' the 21 ouncerS.u X diXt to 
 two par s which are to each other as 2 to 1. One of th" e 
 parts will be the weight of the second cup, and 2 the weLht of 
 the first cup and cover, &q. ^ weignt ot 
 
 fJl t}^'^l}''l^'''^ ^^^^^'' ^"P"' ^'^^ only one cover 
 Jorboth. Tde Srst 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 ? «^^tfiiu 
 
 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 P 
 
 4. A boy bought a squirrel, a rabbit, and a bird, 
 ihe squirrel cost 15 cents. The squirrel and rabbit 
 cost twice as much as the bird ; and the rabbit and 
 Dircl 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 r 
 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 cow. 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 -} as much 
 as both horses ; ana ihe younger horse cost i as much 
 as the other horse and saddle together. What did 
 tbe saddle and older horse cost respectivelv ? 
 
 7. A man traveled three successive days. The 
 tirst day he traveled 30 miles, which was 4- of fh^ ,!,•«, 
 tance he traveled the other two days ; and 4 times 
 
140 
 
 ALGEBRAIC QUESTIONS. 
 
 t^ie distance he trnv^laA *i, 
 
 di.ta„co he travS e tltZ7\J"{ T'''^^ the 
 
 fer did he travel each day ? "'' *"''^ <Jaj8. How 
 
 8- A la worth $1000 iin<l B j ^ 
 "-orth 9 times as much a" A » . n ^°^'*^'' »re 
 
 .^3^^?^4T^ ^- «- -hlfB^^^dTtjrtt 
 
 °f tw vest equalled the cos? oV h ..^ '"""' "'^ «°«t 
 
 What was the cost of hfs v«f ° ]^^"l ""''" ^^^ hat- 
 
 10. B's harness cost SI2n 1?^''^' respectively? 
 
 of his horse audseth* and th.h '''''* °^ '''« <'°«* 
 together cost twice as ^^1? *''\hameas and horse 
 •""cl, did the horse and sS ^n f*""* '^''^^- Ho^ 
 
 11- A tree in falling k^i ?'™«P««t'''ely? 
 pieces. The top piece L^«/ Z"?*" *'^'^« "^^^^al 
 of the length of the othe?tw« • ^°°^' '''''''h '^as • 
 length of the bottom dL*" ^'Tll ""'' ^ times thi 
 other two pieces. How lo^X %*.'" J'"Sth of the 
 long was each pieee^ ^ "^"^ *® tree, and how 
 
 A ?«^20^fels'oldTndtlf ;fj."'^ ^- "^^ ^"owing that 
 iB 4 timers A's age Id tW «.'"■" °^ ^ """d C's age 
 of A and B's agl ' ^ **"** ^^ ''ge is i of the sum 
 
 13. Find the fortunes of j\ Ti n rw t, 
 know.ns that A is worth «9n' L^^' ^' "^d P, by 
 B andC are wort" aTd thaf r ^^'"^ f * «^ »"eh al 
 A and B , and, also That if 10 /' '^°' "^ * "^ •»"«*' as 
 
 f d C's fortun'e were d t ded int: *' ^"™-°^^' ^^ 
 h and i it would i-oo^o I- , . t"® proport on of -a 
 
 and^i ^f P>s fortun7 '*"''^^ ^^' * "^ »•«, ^ of E's 
 
 gcd;ed w'shilt|s'rro°d'':n1 B*f f^^'r «"^- ^ 
 -ttow many rods diW ooli;^- "'^ ^ shiJlmffs a rod 
 
 «S0? Ins'f duf oP-?^'d«d each^ei^d 
 
 NoTp P J , g ^'^^ rods, and B 62i 
 
 ^o..-Co„s.der ,ie above a Pe„, „, ^. ;„„,,,„„ ''^- 
 
REDUCTION. 
 
 141 
 
 CHAPTER VIII. 
 Lesson I. 
 
 this, matbematSlyVeakinl win „„,'" "l" ''""■• Although, 
 a /ear^'^"*" ^ ^"^' """^ ^ ""''">'« *" ^^e fraction of 
 
 monlUave4S;l wWchL ;„Vl t"^" n"' "»'' * 
 how many thirds! lu one t ere I'r! a* n^f'- i".^*y«-"-s 
 
 remainder. (>^n equentlv Te '^^^^^^ <jf«o«.»a<or, without, 
 oontinne to divide gSthe^ea J m.^h^^'^'/'""' """^ ^"' *>«. to 
 numerator and denominator withon ' „ "' " '?"t''''"'' ■■" '"'"» 
 fraction i, reduced to il^s lowe.rterms. "" ' """' '"" 
 
 yef;. ^'^""' ^ ^""" "'"' ^ ""°"*''= *» the fraction of a 
 a year^"''"''' ^ ^""■' """^ ^ '"°'^'''« *° *''« f™«on of 
 a ytar^"^""' *^*''" ""'' ^" ™°"*^ *" t^e fraction of 
 a /ear^"^""^ '' ^""'' """^ " "°"*'=« *" 'l-e fraction of 
 a ylr^"''"'" ^ ^'''"■' ^""^ ^ '"°"*''« '" the fraction of 
 
 of a yS"-^ ^^ ^'"' ""■* ^ """"'hs to the fraction 
 
 8- Eeduce 11 years and 11 mnnffcp *„ *i.. f„_.- _ 
 of a year. ' » -"^ •"= iiatiion 
 
142 
 
 REDUCTION. 
 
 a yt^'""' ' y^-- -d 6 months eo the fraction of 
 oUyef:''"'' "^ y''"' ""-^ 8 months to the fraction 
 fracL"":' r;eaV"" ' "'""''^ -d ^5 days to the 
 
 1 v!»r n •■;' '■''■•" ?•■"•' of a year *T , """"■• ** ""o-'l'^, 
 I ^f ^r- ""fpforo 1 month is 1 If, ''"^ "^ ' 2 months in 
 * of t\, wh cb is J, „f „ '' 7^ "' " y"'"'. and J of a month S 
 ye«.', 9 halves are^^l t"ml^ 4,f "t ''*»'" ■"""»>' " X „V a 
 yoars, eqnal V» years ' ^^' '''"'•'' "^ A or S of a ye". 2* 
 
 fri^'S^a/"" ' ■"-*''^ -d 6 days to the 
 fraction'':f'r:e'ar^^ ' ■"-">« -d 18 days to the 
 fr.ltio^otV.r'' ' --*''« -d 18 da,s to the 
 fracL^1r;ea/-" ' "'-^'^^ -d 6 da,s to the 
 ha,^"--0--"i". t.. intermediate steps in the analysis we 
 
 years equal M 
 
 fraction olry'ef/'""'' ' ''''»'*''^ ""^d C days to the 
 fraction of a'yearf ^"' * ""'"*''■ '^d 24 days to the 
 fra|;S"a year--^ ' "'-*''^ -d 18 days to the 
 fraction of ryear*""" ^^ "'"""^^ «°d 6 days to the 
 ^^^tftioZu%iT' '<> ""'"*''« ''°d"l2 days to 
 
PERCENTAGE AND INTEREST. 143 
 
 Lesson II. 
 
 which is regulated by law ''''' P®'' *'«"^- P^r anuum, 
 
 * or ,y of the p,.l„oi,,al eqS ,he ""iere™"- " " •'"""'- 
 When „o time is specified lyeaMsu.d.«t„„d. 
 
 the intretr' "'"'- '''"'* P"' "' t^« Pri"cipal equals 
 
 per cent, ^ of the prinSpt^^^s :L\Z'; J''"'""- "• * 
 the "inferestT ''''"•' ^'^''* ?"* "^ *''« P^eipal equals 
 the infere' ?r ''"*" """^ P*"* °^ *»>« P^^P"' equals 
 fue ■interlPr"''"" ^"""'P"' "^ ^l^^ P^^^Pal equals 
 the iutestT ''*'*•' ^'"'* P*'* "f "■« Pri'-^^-p"! equals 
 gain/' ^^^ P'' '''°*- ^''''* P«' °f *e "ost equals the 
 the\wT ''"*•' ''''''* P'"'^* of the principal equals 
 gait ?^^ ^^ P"" ""''*•' '=«* P-'rt of *e cost equals the 
 gain ?^' ^^ P'' '^°*-' '''"'* P"'* of the cost equals the 
 per cenM"' " '^' ^'^^'* of «80 for 1 year, at 15- 
 
 the IXI^Z ot^0Um'!t],Zit:,l *' P"""'?"' »<!"«'' 
 per LI?"' ^ '^' ''''''''' °f *i2af<,r 1 year, at 25 
 
144 
 
 PER CENT. 
 
 12. What is tho iuterest 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 waggon and sold it, at a 
 gain of 30 per cent.; ho v much was his gain ? 
 
 Solution.— If he gained 8i per cent, he gained ^^^, or -^ of 
 the cost. -^ 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 
 60 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. — The principal or cost is always 100 per cent. 
 
 1. If ^\ of the principal equals the interest, what 
 is the rate per cent. 
 
 Solution 1st. — If -^xs of the principal equals the interest, the 
 rate per cent, is -^ of 100 per cent, which is 6 per ceut. 
 
 Solution 2d. — If the interest of 1 cent is 3% of a cent, the in- 
 terest of 100 cents is 100 times 3^^, or ^%o, or 6 cents. There- 
 fore, it is 6 per cent. 
 
 2. If gV of *^® principal equals the interest, what 
 is the rate per cent. % 
 
 3. If A- of the principal equals the interest, what 
 is the ra^ per cent. ? 
 
PER CENT. 
 
 145 
 
 4. It' -80- oF tho cost equals the gain, what is the 
 rate per cent ? 
 
 5. If a^y of tho coat equals the gain, what is the 
 rate per cent? 
 
 (>. If aV of the principal equals the interest, what 
 Is the rate per cent ? 
 
 7. If ^- of the cost equals the gain, what is the 
 rate per cent ? 
 
 8. If the interest of 844 for 1 year is $4, what is 
 tho rate per cent. ? 
 
 SoLtjTiox.— If the interest of i?44 is $4, ,\, or ^\ of the 
 principal equals the interest. Therefore, the rate per cent. 
 13 ^^ of 100 per cent, which is 9^j per cent. 
 
 9. If the interest of $72 for 1 year is $6, what is 
 the rate per cent. ? 
 
 10. If the interest of 396 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 '^vl cents ; 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 gain 
 per cent. ? 
 
 14. If by laying out $37, I gain a sum equal to | 
 of it, what do I gain per cent. ? 
 
 15. Harvey bought a hogshead of molasses for $25 
 and sold it for $3H > how much did he gain per cent. ? 
 
 16. Bought a knife for 37 cents and sold it for 57J 
 cents J what was the gain per cent. ? 
 
 17. A stationer sold a quantity of paper for |- of 
 what it cost him ; how much did he gain per cent. ? 
 
 18. James received for his horse ^ of what it cost 
 him ; how much did he gain per cent. ? 
 
I 
 I 
 
 t 
 
 145 FIR CENT. 
 
 19. A man sold a barrel of pork for f J^ 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. ? 
 
 SonffioN.— If the interest of $500 for 4 years is $240, for 1 
 year it is i of $240, or $60. Therefore, 3^, or ^ of the pnn- 
 ?ipal equals the interest. L the interest of $1 for 1 year is 
 IX the interest of $100 is 100 times $^S. or %%o^ or $12. 
 TErefore, it is 12 per cent. 
 
 21. A man, being asked, at what per cent, his money 
 was on interest, replied, I receive $120 interest m 10 
 years for $24K) ; what was his rate per cent . ? 
 
 22. A bought a horse for $150 and sold it for $100 ; 
 what was his gain per cent. ? 
 
 23. Elisha bought 10 horses for $800, and sold 8 
 of them for what they all cost ; what v\ras his gain per 
 
 24. VV of t^e money C paid for books, is ^ of what 
 he gained by selling them. How much did he gain 
 
 per cent. 1 . . , > a i.- 
 
 25. -i-K of the money I have on interest, is 4 times 
 the yearly interest received. What is the rate per 
 
 26 ' i| of the cost of A's merchandise, is ^ of what 
 he gained when he sold it. What was his gain per 
 
 27.*!;^ of the cost of B's wagon, is f of what he 
 gained by selling it. What did he gain per cent. ? 
 
 28. A book was sold for | of f of what it cost. 
 What was the loss per cent. ? 
 
 29. i of i of the cost of a sleigh, was what it was 
 80ld for. What was the gain per cent. ? 
 
 30. A merchant bought a quantity of goods for 
 I860 and sold them for $1075 ; how much did he gam 
 
 Por PAirfc. f 
 
PERCENTAGE. 
 
 147 
 
 Lesson IV- 
 
 1. At 5 per cent, for 4 years, what part of the prin- 
 cipal equals the interest ? 
 
 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%%, or i 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 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 'I 
 
 9. At 4 per cent, for 6 years, what part of the prin- 
 cipal equals the interest? 
 
 10. At 6 per cent, for 5 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 6 per cent, for 4 years and 8 months, what 
 part of the principal equals the interest ? 
 
 Remark.— It 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 paits of the question. 
 
 SoLUTioN.~8 months is ^\, or § of a year. 4? years equal 
 y years. If the interest of $1 for 1 year js 6 cents, for^^r* 
 years it Is V* i-"^'-''* ^ cents, or 28 cents. Therefore, j^iOr 
 ^'. of the principal equals the interest. 
 
148 
 
 INTEREST. 
 
 11 I I 
 
 13. At 4i 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 10| per cent, for 1 year and 6 months, what 
 part of the principal equals the interest ? 
 
 16. At 4!j- per cent, for 9 years, what part of the 
 principal equals the interest? 
 
 17. At 3 J percent, for 2 years and 2 months, what 
 part of the principal equals the interest ? 
 
 18. At 61- per cent, for 4 months and 24 days, what 
 part of the principal equals the interest ? 
 
 19. At 7 l per cent, for 10 months, what part of 
 the principal equals the interest ? 
 
 20. At 3^% 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 6 p.c. 
 
 Solution lsT.~Tbe interest of $1 for 4 years, at 6 per cent. 
 is 24 cents ; and for $50 it is 50 times 24 cents, or $12. 
 Solution 2nd.— The interest of $1 for 4 years, at G per cent. 
 
 ia 24 cents. Therefore, -rVu. or u% of the principal equals the 
 interest, ^"g of |50 is $12, the interest. 
 
 2. What is the interest of $10 for 2 years, at 5 p.c. ? 
 
 3. What is the interest of $48 for 6 years, at 5 p.c. t 
 
 4. What is the interest of $70 for 7 years, at 5 p.c. ? 
 
 5. What is the interest of $68 for 5 years, at 6 p.c. ? 
 
 6. What is the interest of S70 for 2 years, at 5 p.c. ? 
 
 7. What is the interest of $75 for 5 years, at 3 p.c. ? 
 
INTEREST. 
 
 149 
 
 8. What is the interest of $120 for S 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. What is the interest of $145 for 6 years, at 5 
 per cent. ? 
 
 13. What is the interest of $200 for 10 years, at S 
 per cent. ? 
 
 14. What is the interest of $250 for 3 years, at 8 
 per cent. ? 
 
 15. What is the interest of $220 for 11 years, at 
 10 per cent. ? 
 
 16. What 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. 1 
 
 18. What 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. What is the interest of $405 for 10 years, at 8 
 per cent. ? 
 
 21. What is the interest of $50 for 2 years and 2 
 months, at 6 per cent. ? 
 
 Solution.— 2 menths is ^ of a year. 2^ years equals ^ 
 years, If the interest of $1 for 1 year is 6 cents, for V ye*" 
 it is l^ times 6 cents, or 13 cents. Therefore, ^ of the prin- 
 cipal equals the interest Von «f $60 is iJ, or |6.50, the in- 
 terest, 
 
 22. What 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 6 per cent. ; 
 
Ijl 
 
 ti'. 
 
 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. 1 
 
 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. 1 
 
 Solution.— 15 days is i of a month. 4^ months equab f 
 months. | months equals ^^, or § of a year. 2^ years equal 
 V years. If the interest of |1 for 1 year is 4 cents, for V 
 year it is V ti^^a 4 cents, or ^ cents. Therefore, ^^^ of the 
 principal equals the interest. ^^% of $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 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 percent. ? 
 
 38. What is the interest of $75 for 2 years 11 
 months and 6 days, at 15 per cent. ? 
 
 QQ TxrViof ia fhA infpr*i9f. of iftl.^Ofor 2 vears 10 
 
 months and 12 day s, at 15 per cent. ? 
 
 n 
 
INTBRKST- 
 
 151 
 
 40 What is the interest of 8300 for 2 years 9 
 „,ontbs and 18 days, at 1| per cent. ? 
 
 Lesson VI. 
 
 1. What is the amount of $75 for 2 years, at 6 per 
 
 cent. ? 1 „f «i fnr 1 year is 6 cents, for 2 
 
 SoLtT.os.-If the interest of *1 for 1^ ^ ^ f 
 
 vears it is 2 times 6 cents, or 12 ««™- ,i»5 jj |9, the int«eet; 
 C principal ^f ''''/^^J^'an^d^we have $84, the amount, 
 to which add $76, the principal, anu ^ 
 
 2. What is the amount of $90 wr d yea . 
 
 ■^ t What is the amount of $100 for 4 years, at 5 per ' 
 't'Whatisthe amount of $160 for 10 years, at 5 
 P's" WhL is the amount of $160 for 8 years, at 5 
 P%: Wklt is the amount of $200 for 12 years, at 5 
 ^'r Wiat is the amount of $210 for 2 years and 6 
 •" t Whttls'Ae'mUnt of $250 for 4 years and 3 
 "t Whttl'the 'amVuut of $240 for 4 years and 2 
 ■To' mat Tthf amount of $500 for 3 years 3 
 
 nt\tt%11Cnnf-|200for5 years 4 
 „,onthsand24days,at5percent.? 
 
 Lesson VII. 
 
 1 What principal wiU in 4 years, at 6 per c»nt.. 
 give $12 »teref ^^ ^^^ ^ ^^^^ ,, , .^nts. for * 
 
152 
 
 INTEREST. 
 
 years it ifl 4 times 6 eents, or 24 cents. Therefore, ^Ver or VV o^ 
 the principal equals the intereet which is $12. If ^ of the 
 principal is $12, ^ of the principal is | of $12, or $2 ; and 1+; 
 or the principal, is 26 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 1 
 
 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. Wb ..; 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. H^w 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 be $270. 
 What was the cost of each, provided the store cost i 
 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 J as much as the cow, and the cow, I m 
 much as the horse ? 
 
INTEREST. 
 
 15S 
 
 Lesson VIII- 
 
 1 . What pvineipal will itt 4 years, at 5 per cent., 
 amount to 8360 1 
 
 SoLCTioN—If the intevest of $1 for 1 jear is 6 «"">'* 
 ;t 1. i HmM 5 cents, or 20 cents. Therefore, -ff^, or J ol 
 rorta pa ™q«al°re interest; to which add J, the principal 
 the principal mi „_i.„:t,al eaual to the amount, $360. IC 
 
 r„'f te prin\ pal s*8™ 4 of thi principal is i.of«»60 which 
 |-s $«0, anA>e principal), i. 6 times PO, ^hich are $800. 
 
 2. What principal will in 3 years, at 6 per cent., 
 
 "TwKrtocipal will in 6 years, at 10 per cent., 
 
 'TwKrinlipal wUl in 4 years, at 5 per cent., 
 
 "Tt is°worth 4 as much as B ; and the interest on 
 their united fortunes for 2 years, at 5 per cent., is 
 $880. AVhat is each of their fortunes • 
 
 7. A merchant sold a q"''"''*? ?/ "^^Vt-hP IriJ 
 =md thereby gained 7 per cent. What did the cloth 
 
 "°t. What principal will in 2 years, at 7 per cent., 
 
 ''TwKrtacipal will in 10 years and 8 months, 
 at 9 per cent., amount to $490 ? , . , , , , ^_ „,, 
 
 lof The amount due on a note, ^l"«li '^''"f =°;" 
 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 * of A's fortune for 4 years and months 
 at 6 per cint., amounts to §127 ; what is bis whole 
 
 fortune? ^ _ , . „„i. ,,„ 4„fo%.ttaf. fnr 
 13. If ii of B'8 tortune, being pui- on xuu....« 
 
154 
 
 INTEREST. 
 
 3 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 prin- 
 cipal and rate per cent, are such that in 5 years hhe 
 amount would be $750, and in 7 years, $8iO ; 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 ? 
 
 IG. The amount of Eobert*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. 
 
 I 
 
 Lesson IX. 
 
 1. In what time will $40, at 6 per cent., give $12 
 interest ? 
 
 Solution.— If the interest of $40 is $12, ^, or ^^ of the 
 principal equals the i-iterest. If the interest of $1 for 1 year 
 is 3% of a dolhir, of $100, it is 100 times $j% or |30. If it re- 
 quire 1 year for $100 to give $6 interest, to give $30 interest it 
 \vill require as many years as $6 is contained times in $80, 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 
 
 7. In what time will »40, at 7 per cent., give *8.40 
 
 'T'ln Ihat time, at 8 per cent., will $80 give $9.00 
 
 '"Klhat time, at 6 per cent., will $10 give $2.40 
 
 '''tain what time, at 4 per cent., will $20 give 
 $5.60 interest ? 
 
 Lesson X. 
 
 1. At what percent., will $50, in 1 year and fi 
 months, or (li years), give $6 interest ? 
 
 SoLOTios.-If the interest of |60 for U, or f years is $6, for 
 X of a ve™ it is i of t6, or $2 ; <mi for ?, or 1 year, .t is 2 times 
 
 I2! 0? IT Therefore: A. «' A of ""« ^^TIT ot^iwO 
 nual interest. If tlie interest of *1 for 1 year is 85V ot il'J". 
 hTs iSo times $^^. or $8. Therefore, it is 8 per cent. 
 2. At what per cent., will $40 annually give $2 
 
 '" t'tft what per cent., will $80 annually give $3.20 
 
 '"tlVwhat per cent., will $120 annually give $12 
 
 '"I'lVwhat per cent., will $120 in 4 years, give 
 
 *^6.' tntat per cent., will $100 in 3 years, give 
 
 ^'?.^U whal per cent., will $5 iu 14 years, give $7 
 
 '"T iVwhat per cent., will $25 in 1 year and 9 
 
 T^^VX-l^r^'n *S0 in 5 years and 8 
 
 •"TrAtThf Jirt^t! will $500 in 7 years and C 
 months, give $15 interest ? 
 
15G 
 
 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 substract the principal, and the 
 remainder will be the interest. Then proceed as in the pre- 
 ceding lesson. 
 
 2. At what per cent., will $12 in 3 years, amount 
 to 313.44 ? 
 
 3. At what per cent., will $20 in 6 years, amount 
 to $26 ? 
 
 4. -At what per cent., will $24 in 10 years, amount 
 to $36 ? 
 
 5. At what per cent., will $30 in 7 years, amount 
 to $30.30 ? 
 
 i\ At what per cent., will §50 in 10 years, amount 
 to $75 ? 
 
 7. At what per cent., will $36 in 5 years, amount 
 to $39.80 ? 
 
 8. At what per cent., will a given principal double 
 itself, in 20 vears ? 
 
 Sou .xON. — A i^iven principal will double ifself in 1 year, at 
 100 per cent.; and in 20 years, at ^o of 100 per cent, or 5 
 per cent. 
 
 9. At what per cent., will a given principal double 
 itself, in 4 years ? 
 
 10. At what per cent., will a given principal double 
 itself, in S years ? 
 
 11. At what per cent., will a given principal double 
 itself, in 5 years ? 
 
 12. At what per cent., will $80 in 7 years give $80 
 interest ? 
 
PER O^NT. 
 
 15' 
 
 
 13. At what per cent., will «640 in 6 years give 
 
 ^^^4. 'm whit per cent,, will 25 cents in 8 years give 
 
 '>fi ofints interest ? . ..^^ 
 
 15 At\.hat per cent., will S97 in 9 years give S97 
 
 '" iTlt what per cent., will S372 in 23 years give 
 
 *1?/ At Thai per cent., will $1 in 30 years give SI 
 
 '° irlt what per nant., will «15 in 12i years givo 
 
 *^19°Tt'wh;t per cent., will 842 in 141- years give 
 
 **20° Tt'what per cent., will 5 cents in 16J year, 
 aive 5 cents interest ? 
 
 Lesson XII. 
 
 1. In wbalJ time will a given principal double itsell, 
 
 fit 5 ner cent, ? 
 
 ., ,L„^ _A Biven principal will double iUelf m 100 yea™. 
 .tTperC^irt I per -.t, in -| of 100 years, wl„ol> >s 
 
 '" 2!Tn what time will a given principal double itself, 
 '''3.^1" :ttLe will $25, at 3 per cent., give S25 
 ^°*nn what time will $27.5, at 6 per cent., give §275 
 '"*!.' U what time will a given principal double itself, 
 "■^ I ^11 :tt time will 54, .t 7 per cent , give S4 in- 
 
 'TVn -..hat time will S94, at 9 per cent., give 894 
 interest ? 
 
158 
 
 PER CENT. 
 
 8. In what time will 6 cents, at 8 percent., give 6 
 cents interest ? 
 
 9. In what time will 33 J at 10 per cent., give 33i 
 interest ? o » 
 
 give 
 
 10. In what time will 1 dime, at 12i per cent., 
 ^e 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 $1, the 
 gain must have been $7— $5, which is $2. Therefore, * of the 
 cost equals the gain. If on $1 I gain |J. on $100 I will gain 
 100 times ^, or $40. Therefore, the gain is 40 per cent 
 
 2. A book was bought for $2, and sold for $3 ; what 
 was the gain per cent. ? 
 
 3. A shawl cost $5, and was sold for $8 ; what was 
 the gain per cent. ? 
 
 4. A cow was bought for $20, and sold for $25 ; 
 what was the gain per cent. ? 
 
 5. A merchant bought a hogshead of molasses for 
 $80, and sold it for $95 ; what did he gain per cent. ? 
 
 6. A barrel of pork cost $12, and was sold for $11 ; 
 what was the loss per cent. ? 
 
 7. A horse was bought for $140, and sold for $60 ; 
 what was the loss per cent. ? 
 
 8. Bought au orange for 4 cents, and sold it for 6 
 cents ; what was the gain per cent. ? 
 
 9. Bought a melon for 15 cents, and sold it for 20 
 cents ; what was the gain per cent. ? 
 
 10. Bought a book for 5 dimes, and sold it for 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 cents 
 
PERCENTAGE. 
 
 159 
 
 
 apiece, \ of which equaled his gain ; how much would 
 he have gained per cent., if he had sold them, at 12 
 
 cents apiece ? ^ , i j 
 
 13. A merchant sold sugar, for $80 a hogshead, 
 and thereby cleared ^ of his money ; if he had sold 
 it, at $92 a hogshead, what would he have gained per 
 
 cent. ? 1 p di or» 1 
 
 14. A quantity of cloth was bought for $3G, 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. ? wi i. 
 
 16. A man sold a horse for $120, and thereby 
 cleared V of its cost ; how much would he have lost 
 
 .' .,.1 1 _j __i.i u:w> *• — (ttQA 9 
 
 Of ^ 18 
 
 per cent., if he had sold him for $80 ? 
 
 17. What per cent, of 
 
 "3 ^^ C 
 
 Of 4 is 
 
 1 ? 
 
 ^V?*0ffis|1 Offisf? Of2^is|? Of3^is2^V'? 
 
 18. i of $6 is what per cent, of J of $100 ? 
 
 19. 4 of $28 is % of what per cent, of -} of $300 ? 
 
 20. Walter sold a horse for 120, and thereby 
 cleared ^ of its cost ; what would he have lost per 
 cent., by selling it ^r $80 ? 
 
 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.— If he gains 6 per cent, he gains ^go.* ^^ 20 °^ ^^^^ 
 cost. ^V of $20 is $1, the gain. Therefore, to gam o per cent. 
 he must sell the cow for $20+$l, 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 f 
 
 3. A man bought a barrel of rum for $10 ; tor what 
 must he sell it, to gain 10 per cent, on the cost ? 
 
 4. A gallon of wine was bought for 20 dimes ; how 
 
 mi 
 
 cost? 
 
 "f ;f L anl/l fl nint. to srain 20 per cent, on the 
 
lao 
 
 DISCOUNT. 
 
 5. A hogshead of molases 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 ? 
 
 7. A wagon cost $140, and was sold for 5 per cent, 
 less than it cost ; for w^hat was it sold ? 
 
 8. A merchant, by selling 40 yards of cloth for 
 1164, 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 ffailon ? 
 
 Lesson XV. 
 
 1. What principal will, in 4 years, at 5 per cent., 
 
 amount to $60 ? 
 
 t 
 
 Solution.— If the interest of $1 for 1 year is 5 cents, for 4 
 yearc it is 4 times 5 cents, or 20 cents. Therefore, -j%% or -V 
 of the principal equals the interest ; to which add -|, the prin- 
 cipal, and we have & of the principal equal to the amount, or 
 |60. If I of the principal is $60, | of the principal is -^ of S60. 
 ■which is S;10; and |,(the principal), is 6 times $10, which arc 
 $50. 
 
 2. What principal will, in 3 years, at 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 ? 
 
 b. What principal will, in 9 years, at 8 per cent., 
 amount to $86 ? 
 
 6. What principal will, in 8| years, at 8 per cent., 
 amount to $260 ? " 
 
DISCOUNT. 
 
 161 
 
 r what 
 tent, on 
 
 it, lost 
 t? 
 ?r cent. 
 
 oth for 
 t did it 
 
 must it 
 
 ►f ram. 
 ?ailon ? 
 
 cent., 
 
 t8, for 4 
 
 he prin- 
 ount, or 
 
 i^ofseo, 
 
 liich are 
 
 ' cent., 
 
 ' cent., 
 
 ' cent., 
 
 cent., 
 
 cent.» 
 
 
 7. What principal will, in 4| years, at G per cent., 
 amount to $640 ? 
 
 8. What principal will, in 5-f- years, at 7 per cent., 
 
 amount to $42 ? 
 
 9. What principal will, in 6f years, at / per cent., 
 
 amount to $b7 ? 
 
 10. What principal will, in 8f years, at 6 per cent., 
 
 amount to $76 .'' 
 
 Remark.— The present worth of a debt payable at some fu- 
 ture 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 it 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 
 mte per cent. 
 
 See the above solution. 
 
 11. What is the present worth of $26, due 5 years 
 hence, at 6 per cent. ? ^^«- j?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 piesent worth of $86, due 8 years 
 bende, at 9 per cent. ? ^.,^^« i « 
 
 15. What is the present worth of !ibl02, due 9 years 
 
 hence, at 4 per cent. ? , .^^ , a 
 
 16. What is the present worth of S72, due 4 years 
 
 hence, at 5 per cent. ? , « i 
 
 17. What is the discount on $46, due 3 years hence, 
 
 at 5 per cent. ? 
 Remark.— 2Vie discount equals the amount minus the presetU 
 
 worth, 
 
 18. What is the discount on $54, due 5 years hence, 
 
 at 7 per cent. ? , . i. ^« 
 
 19: What is the discount on $65, due 5 years hence, 
 
 "" 20rWhat is the discount on $93, due 3 years hence, 
 at 8 per cent. ? 
 e 
 
162 
 
 PERCENTAGE. 
 
 21. What is the present worth of $186, due 44 
 years hence, at 5 per cent. ? 
 
 22. What is the present worth of $66, due 5| years 
 hence, at 6 per oent. ? 
 
 23. What is the present worth of $128, due 4t 
 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 ? 
 
 Shlution.— If I gain 25 per cent. I gain J of the cost ; to 
 which add f, the cost, and I have f of the cost equal to $2.50 
 If f of what I gave for it, is |2.50, i of the cost is 4 of $2 50 
 of 50 cents ; and ^ (the cost) is 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 tent., 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 to loose 25 per 
 cent. ? ^ 
 
 5. If by selling a piece ot cloth for $46, I gain 15 
 per cent., how ought 1 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. Afarm 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.inore than its 
 value ? 
 
 8. A mechanic lost 20 per cent, on the cost of a 
 
 Wfio-ornn h 
 
 1- 
 
 1 I 
 
 "CT QAlllVirv ■• 1- ■»j-\'M Hf /I f ft _ A-^^ . 1_ _ j_ 1 i ■* . 
 
 J --.^liiu^ XV iu'i >ff-x\j i luv vvijiic ougnt ic CO 
 
 nave been sold, to have gained 30 per cent. ? 
 
PERCENTAGE. 
 
 163 
 
 h due4| 
 ) 5| years 
 
 i, due 4| 
 
 reby gaia 
 
 be cost ; to 
 tl to $2.50. 
 f of $2.50, 
 which are 
 
 at a loss 
 
 ^eby gain 
 se 20 per 
 
 eby gain 
 se 25 per 
 
 gain 15 
 e lost 30 
 
 9. A horse was sold for $90, which was 10 per 
 <;ent. 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 cant. ; 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 ? 
 
 gained 5 
 I'ave sold 
 
 per cent. 
 ; to have 
 than its 
 
 3st of a 
 fnt it to 
 
 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 ia to receive 5 per cent, or j^ or ^V:, of all 
 he collects, fg, all he collects, minus A-. his fee, equals ii of 
 ail he collects, or $190, the amount he fs^to pay his "employer. 
 If 4§ of what he collects equals $190, ^V is -^^ of $190, which 
 
164 
 
 MISCELLANEOUS QUESTIONS. 
 
 i8$10; and f§ (what he collects) k 20 times flO nr t>mn 
 Therefore he must receive $200 - $190 J= $lo. 
 
 .J'J^'''' ""r^ ""^^^^ ^ *^ ^^^^^^^^ ^'or collecting $90 
 and his own fee, of 10 per cent, on all he collect^s ? 
 
 a debt n • trT!l^^ "''^n ^-^ ^'^^ ^' ^"^^^^^"t ^« Pa- 
 a debt ol $38 and the collector's fee, which is 5 ner 
 
 cent, on all the money collected ? ^ 
 
 4. How much cider must that man make to brine 
 away 15 barrels after the owner of the mill rece ves 
 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 
 miller has taken 10 per cent, of all he took there ' 
 
 Miscellaneous Questions. 
 
 1. At 5 per cent, for 4 years, what oart of th** 
 principal equals the interest ? ^ ^ 
 
 T..;^' •^''i*''''^' '"''''^ ^^^""^^ "* ^ per cent., will a given 
 
 n pL c'ent""' '' *'' ''"^' '' '' "^^^ '^ ' /««'«^ 
 
 8. At what per cent, will a given principal in 14 
 
 '^^ntvahi"^^ ?™' ^°' ^ y^"^' ""•"""ted to 
 J^i^l M , ^''"* P*"" <=«'^*- did he annually re- 
 ceive on the value of his farm* <^M,y le 
 
 pefcltf " **" ^^""^ °^ ^''^^ ^°' 5J years, at 6 
 
 give SntSf' "'" '° '^ y^"^' "* « P- -*•' 
 mo'nu'I to" »S55 r^ "'"■ •" *^ y^«-- «* 3 V» cent.. 
 
MISCELLANEOUS QUESTIONS. 
 
 165 
 
 or $200. 
 
 tin^ $90 
 lects ? 
 it to pa^ 
 is 5 per 
 
 to brincr 
 receives 
 
 lill, that 
 fter the 
 lere? 
 
 of the 
 
 a given 
 ! years, 
 
 1, in 14 
 2 years 
 
 :, what 
 
 ited to 
 Uy re- 
 
 9, at 6 
 
 cent., 
 
 cent.,. 
 
 .. ^-4* Y^^^ P^'" ^^"^•» "^'^^ ^ Siven principal double 
 itself, m 12 i years ? 
 
 10. The interest of A.'s and B's fortune, for 8 years 
 at 5 per cent., is IJ420. What is the fortune of each' 
 provided A'a fortune is twice B's ? ' 
 
 11. The interest of j of A's aud ^i of B's fortune. 
 
 for 7 years at 5 per cent., is $2100. AVhat is each 
 
 of their i-ortunes, provided f of A's fortune equals i 
 of B s ? ^ * 
 
 12. B sold his horse, for ^ of U 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 
 »nd 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 h I and i ? 
 
 17. What principal will, in 8 years and 8 months, 
 at 7f 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 ? f », b 
 
 20. -If the interest of $200, for 1 year and 6 months, 
 13 $18, what is the rate per cent ? 
 
 2J. At what per cent., will $500, in 4 years and 9 
 months, give $190 interest r 
 
 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 what per cent, will 
 
 ipal double 
 
 ., ,^ . ^ X -- - given pri 
 
 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 • 
 oJ^tIK^^^^' ^^ '?^^ ^P^e^^e to gain 30 per cent. ? ' 
 
 ,nnlf -f i Tr* °n «,^^°^Pag^e cost 40 cents, how 
 must it be sold a gill to gam 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 heiice, at 6 per cent. ? 
 
 31. What is the present worth of $87, due 3^ years 
 hence, at 5 per cent. ? ^ y ^'■^ 
 
 .Jh'ln^ hogshead ot; molasses containing 84 gallons 
 cost $30; how must it be sold a gallon, to gain 40 
 per cent, r 
 
 33. The money I have on interest, in 9 years, at 
 
 ci alT amounts to $190; what is the prin- 
 
 ^dm* ^I'r ?°"®; "^^'^ "^^^^^^ ^ P^^ ^e^*^ ' I 'nought 
 $400 worth of goods ? 6 months afterwards I sold 
 
 them, and gamed 10 per cent, on the cost. How 
 much did I gain .^ j,^^^ ^23^ 
 
 ^&. A speculator bought a horse for $36, and sold 
 It tor 25 per cent, more than he gave for it ; which 
 however was 10 per cent, less than what he asked 
 
 Qu x^ ^"^^ ^^^ ^® ^^^^ ^0^ *be horse ? 
 
 ^6. A gentleman being asked how much money he 
 had on interest, replied, that if instead of 6 per cent, 
 he should receive 10 per cent , he would receive $268 
 mterest more than he did then. How much money 
 had he on interest ? "^ 
 
 37. A meTchant bought broadcloth for $1.20 a vard 
 and sold It for 331 per cent, more than he g^vrs for 
 It ; which, however, was 33i per cent, less than bis 
 marxied ^jvice lor it. How much was his marked 
 price per yard ? 
 
sipal double 
 
 )ldfor $90; 
 
 Jost $1.20 ; 
 )er cent. ? 
 cents, how 
 
 ? 
 
 !8, due 10 
 
 3 10 years 
 
 le 3^ years 
 
 84 gallons 
 to gain 40 
 
 ' years, at 
 i the priu- 
 
 , I bought 
 ds I sold 
 sfc. How 
 s. $28. 
 , and sold 
 t; which, 
 he asked 
 
 3? 
 
 money he 
 
 per cent. 
 
 eive $268 
 
 jh money 
 
 20 a yard 
 
 giiTQ for 
 
 than bis 
 
 I marked 
 
 MISCELLANEOUS QUESTIONS. 
 
 167 
 
 38. A merchant sold a quantity of cloth for $120 
 and by so domg gained 50 per cent. He then sold 
 another quaiitity, for $120, and thereby lost 50 per 
 
 much ? ^''" "' ^''' ^^ '^' ^"''S"^^» ^^^ ^^^ 
 
 39. B sold a horse for $60, and gained 20 per cent. 
 He then sold another horse for $60, and lost 60 per 
 
 ^ A rS . ® ^^'"^ °'' ^°«®' »»^ ^«w much ? 
 
 40. Ihe interest on 1^ times A's, and 4 of B's for- 
 tune, lor 8 years, at 5 per cent., is $520. What is 
 
 firi\* ^ f ^,'' J^'*"°^ ^^^«d *o f of E's, which is 3 
 times ^ of D s bemg put on interest for 8 years, at 5 
 
 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 
 
 h Pmr"^^? *^®^ ^""^ *^ ^^«^^ «*^e^ as i, i, and i ? 
 
 43. The interest of A's, B's, and C's fortune, for 
 53 years at 6 per cent, is $800. What 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 Z to S, being put on interest for 6 years, at 4 per 
 
 eaeh ? ^"'''''"^' ^"^ ^^^^' "^^^^ ^^ ^^e fortune of 
 
 45. D's money added to 4 times E's, which is equal 
 to 1) 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 + ^ of B's money, being 
 
 Sinn 'p ^^'1 ^ TT^,^^ ^ P^^ ^^"^' a^o«^t« to 
 piOO. Provided i of B's money is twice i of A's ; 
 
 now much money has each ? 
 
 47. I of tt^g ^og^ Qf ^,g j^^^g^^ increased by -^ of the 
 
 coat "r Ina fayryi V.^,'^._^1 J . • . ,«•'-? 
 
 _^ ,_ ..,^ ,«xm, vciijg piuufu on interest lor 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 1 of -| 
 of the codt of the farm ? 
 
 48. If f of A's fortune in 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 
 S mouths, at 6 per cent., amounts to $256. What 
 was each of their fortunes, provided \ of A's fortune 
 equals B'a ? 
 
 60. The interest for 6 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. How 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 J as long, at ^ as great a per 
 cent., amount to $104 ; how much did he pay for each, 
 provided the shoep cost -J- 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 Domer's fortune for3 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 foj'tune ot each, provided \\ times Domer's part 
 of the principal equals f of Eyer's, ai ! -^ of Eyer's 
 part of the principal equals \ of Simpson's ? 
 
 53. The interest of the sum of \ of A's, and | of 
 B'a fortune, for a certain time, at 2 per cent., was to 
 thi% 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 ? 
 
 Remahk. — Since the interest was to the principal as 9 to 250. 
 ^fp of the principal equals the interest. Hence, 1 year 9 months 
 and 18 days is the time required, tfcc. 
 
nly -1 of I 
 
 months, at 
 hia whole 
 
 ! years and 
 
 I. What 
 .'s fortune 
 
 t., on I of 
 Qterest for 
 ;he money 
 after pay- 
 
 i cow, and 
 give such 
 reat a per 
 Y for each, 
 I cow, and 
 
 3on's, ^ of 
 1 7 months 
 L the same 
 
 II. What 
 Iter's part 
 of Eyer*s 
 
 and I of 
 t., was to 
 is interest 
 per cent., 
 provided, 
 long was 
 
 IS 9 to 250. 
 vr 9 months 
 
 QUESTIONS, QUERIES AND PUZZLES, 
 
 FOR 
 
 PUPILS AT HOME. 
 
 w.l: ;^r,i'°'}^^ '!^ ^° J^"^^^^^ ^^ ^ ^^^ that is lO rods ahead of 
 him, and t^/»/g the hound runs 10 rods the fox runs 1 rod 
 
 ^; ti.'^nf .V .' ?°;''^^ T' ,'^^,f ^''^^ ^^^i^n^^. the fox runs one- 
 venth of that distance.) Will the hound overtake the fox ? 
 The conditions remaining the same, what is the greatest dig- 
 •Kance they can run ? & wiw 
 
 ^^ t Jji°''? V '^}^ P/''^'^ °^ ^ ^''^ ^^*^^ '^ t^" rods ahead of 
 kim and while the fox runs 1 rod the hound runs 10 rods. 
 , far will the hound run before he overtakes the fox ? 
 
 3. Place four 5 s in such a position that they shall equal 6^ 
 
 4. A boy was sent to a spring with a 5, and a 3 quart 
 measure to procure exactly 4 quarts of water. How did he 
 measure it? ' 
 
 5. What is the difference between twice 25, and twice 6 
 and 20 ? J w 
 
 6. A man had 9 pigs and put them in four pens, with an 
 «ld number of pigs m each pen. How did he divide them ? 
 
 7. Two men have an 8 gallon cask full of wijie, which they 
 tlesire to divide equally between them. How can they effect 
 this division, provided the only measures they have arc a 5 
 gallon cask and a 3 gallon cask? 
 
 e uaM?° ^^^^ ^'^ ^^ ^^^^ ^ manner that they shall exactly 
 
 9. Place 9 apples in 10 rows so that each row shall contain 
 .1 apples. 
 
 10, A squirrel finding 9 ears of corn in a box, took from it 
 ciflijy 8 ears; how many days was he in removing the com 
 rrom the box ? 
 
 »# y^: ^y^^^J^^ y^u take iX, and from IX you take ten : and 
 vT fifty from forty be taken, there will then just half a dozen 
 
1,1! 
 
 no 
 
 qUESTIONS AND PUZZLES. 
 
 60 apples an/Lld 'hem'^ff ^ ' f. If ^ Vh''' ' ^^^^ ^^^ 
 120 apples and sold thorn, at th^ raL^ ..f «' f o'"" '''°^^°' ^^'^^ 
 
 iather's aon." What relation wn^.L .?' ' '' "'■ 's mv 
 14. A man havtng ^C^™^,^'™'>'■'•'"•°''''=l'^™""'•'■ 
 clC8irou8 Otero Jns\ river' He^foihn.f '"f '^ <•■»■•''' ^«'' 
 » time, and if he lelt tl,7fn; „11. '' '"'" »"'>' <"'^ ■'•"oss at 
 
 ««,,tLe foxwitldln °.l^-i:S3'°Z'iS M f,^'r" '"^ '<'™ 
 oorn, the goose would oaf t°tmT„' '"'' °''''''^' •'"=S»3cancl 
 
 .II skfely ScrossThe river ' '"• "°" ''"•''" ''«?<'' ^^<"" 
 
 tJ..' day H cnS 5 fcen:!' •:,]:"",-» [-,? '» '-S'u : during 
 Ho» .nany days .oulTll uI'ef'L"^!^,,- Z "'"■' "'^hS 
 
 cbin-t ^To'hiff^S'-prfo?.^'" ^Xei^' T^ r^^ ^''^ -- 
 mak. thechan.'e, ?ent timl, ni */ ? "<'"'"'i" hoing unable to 
 
 then gave the ^aChot^'iM^^.e fe^°V * I""]"'"' J"" 
 the purchaser of the hat tiad^o),. t„ , ^,''* '"'°1'«''' »««" 
 
 oonnterfeit, and therefor ret?Suto7hf ""*', "'° ^'"'^'^^ 
 cemd $60 good money. Ilow .™oh , W foT'"""' '"'^ «" 
 tkeopwation? '"""""^"'"tt "lomcrchant iosebr 
 
 leaVfeJ'npo'ntrjhM'V f"' .*''^''' "■■"'■^ °"» over t„o 
 ten peLies SmtJyVn'ylrp'', "ef ;r f"'"?" ""^ """' ^^ 
 
 »»«. How man^ po'n'drdTdtot'jf iJ^t*^, °"'"' " '"'■'^'■="' -" 
 
 feet everfjL" ' Howmtv"- ^ ™" '' ''"' *^1'' "^eonds a 
 20. A drove?'beint »?^-^7>,''™'" """"' '^^ ""« '» get »ut V 
 
 " ify horses to^?Le? have twlf ''"? '""'f"' '"= ''^'°' ■■"PlM : 
 horses had he ? '"^^"'^ ^'""^ '"=gs." How many 
 
 t. be 1^"" ^^ '" '""' " """ner, that you can show i(s half 
 
 32. " I am constrained to plant a grove 
 To please the lady that I lov! 
 Th,s ample grove is to compose 
 
 K?rtres*r„i\i".-'-:?'!' -- ; 
 
 JJive trees in each row i m.f-t 
 Or I shall nover see her face."' 
 
 iCC. 
 
QUESTIONS AND PUZZLE.s. 
 
 171 
 
 2S.. Do the wabrs of the Mississippi river tlow up hill v 
 
 same in each column, whether added 
 pcrpendicularlj, horizontally, diagon- 
 ally, or taking any fourof the numbers 
 m the form of a square. 
 
 1 
 
 II 
 
 14 
 
 ir. 
 
 r, 
 O 
 
 16 
 
 la 
 
 
 
 Magio Squams-An East India Poms^ 
 
 the figures" from ! o 05 ^"I'" ''-"' !•"""» '^ 25,_^rite 
 
 horizontallT or diaironnllv .h? "'"'.added perpendicularly, 
 
 one-mh ofVe\'u3ti^ler e\"?ntt™n'?/'ir"*X' 
 of the numbers 7, 9, 11 etc ""^"Ders, i to 2o,— andso 
 
 position of th^e "^'aa e ust ZZ ^T'^'l' "^^^^^"^ ^« '^^ 
 upward to the nX nVj?l ' ^'''' \ ^'■°^*^^*^ diag-onally 
 
 011 the 1 iL fde^of ;^/^" '?" °^^ ^^ this go to the^quari 
 the ri^ht or Lt ifnfnhi^ '^"'3°^^^^ "^ ^^^^ "«^t line at 
 
 the sqCelm^di^tely bew'^" '' "'" ^'" "°* ^^ ""^> ^^^^ 
 
 These figures can be varied in 
 at least four different ways. If 
 the number 1 bo taken, they can 
 hQ varied .u; different ways ; if 
 Jff .•^"' ^^''^ ^^'' ^^° ^-a^ied 
 
 jJiorc, 
 
 • perhaDs 
 
 17 
 
 23 
 
 4 
 
 10 
 
 11 
 
 24 
 
 1 
 
 7 
 18 
 
 8 
 
 14 
 
 20 
 
 21 
 o 
 
 15 
 16 
 22 
 3 
 
 5 
 
 G 
 
 X^ 
 
 10 
 25 
 
 18 
 
 » 
 
 Tomovro : ^m^rm by ro^riL a^d on^, to'^^e street 
 
u 
 
 l )* 
 
 El t 
 
 I 
 
 Canadian Editions. 
 
 PBIOB BACH 
 
 Bullion's Aualytical and Practical Eng- 
 lish Grammar 50 Cts. 
 
 Introduction to ditto 25 " 
 
 Stoddard's Juvenile Mental Arithmetic, 13 " 
 
 Intellectual do. 20 " 
 
 Carpenter's Spelling Book 10 
 
 Mayor's do. . . » 10 
 
 Walker's Dictionary 30 " 
 
 Catechism of the History of England. . 10 " 
 -_— Bible and Gospel History 10 " 
 
 LOVELL'S SERIES OF 
 
 Stationery of every description. 
 
 ^The Trade Supplied at very Low Prices, 
 
 ADAM MILLER, 
 
 62 King Street Eastj Toronto. 
 
 L 
 
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