SUBTRACTION. 152. 1. Mary had $ and spent $. How much had she left? 2. From a lot containing of an acre of an acre was sold. How large a lot was left? -= ? }=}=? 3. A boy paid $7 for his skates, but sold them for $4 less than he paid for them. What did he get for them? 4. If I have $ and spend $ how much will I have left? 5. A girl paid $3 for a grammar and $3 for a geography. How much more did she pay for the geography than for the grammar? 6. A lad hoed of a field of corn. If he hoed & of the field in the forenoon, how much did he do in the afternoon? 7. What must be done to dissimilar fractions before they can be subtracted? WRITTEN EXERCISES. 154. 1. From subtract . EXPLANATION. -Since the fractions are 2-2=44-2=& not similar they must be made similar before subtracting. The least common denominator of the given fractions is 44. = 34 and 3 = 33. 11-11=4• 2. From 4 subtract 2g. EXPLANATION. - Since the numbers are composed of integers and fractions, the integers and the fractions may 29=214 be subtracted separately. The fractions must be first reduced to similar fractions. 117 It is evident that cannot be subtracted from 4, hence 1 or 2 is taken from 4 and united with the, making §. 11⁄2 from leaves, and 2 from 3 (the number left after 1 has been united with the fraction) leaves 1. Hence the remainder is 117. RULE. Reduce the fractions to similar fractions. Find the difference between the numerators and write it over the common denominator. When there are mixed numbers or integers, subtract the fractions and the integers separately. Mixed numbers may be reduced to improper fractions and subtracted according to the first part of the rule. 42. 50. 34 +213 43. 44. 37.75 -21%. 39. 9 -43. 40.81 -57. 41. 9-318. 48. 0 5 +34 +3151⁄2 +61. 51. 5% +64 -325- 38+7,170. 52. 81-3 +2 -21 +5. 53.913-37-18 -23. 54.78 +28-354-43 +34. +-- 55. 5 +65-33 -2} +1}}. 56. 74-35 +812−53 +9. 49. 3+ 5−21+ 3. 57. 62 +45 +83 -45-45. 21 58. A piece of flannel containing 25 yards shrank 15 yards in dyeing. How much did the cloth then measure? 59. From a lot containing 18 of an acre of land, I sold 23 of an acre to one man, and of an acre to another. How much land had I left? 60. If 19 yards are cut from a piece of cloth containing 4217 yards, how many yards will be left? 61. A boy gave 183 cents for a slate, 62 cents for a book, and 37 cents for some paper. How much change should he receive if he gave in payment a two-dollar bill? 62. If 6 is added to each term of 3, is the value of the fraction increased or diminished, and how much ? 5. Since of of an acre is of an acre, what part of an acre is of of an acre? an acre? of of an acre? # of 1⁄2 of 6. How much is of of a foot?of of a foot? 7. Since of of a foot is foot is of of a foot? % of foot?of of a foot? of a foot, what part of a of a foot? of 1⁄2 of a out. of the water was drawn What part of the amount the cistern would hold was drawn out? 13. Mr. Ames, who owned a lot containing of an acre, sold of it. What part of an acre did he sell? 14. If he had sold of it, what part of an acre would he have sold? 3 of 3 1% = ? 15. A man's farm was such that of it only was tilled. He sold of that part. What part of the farm did he sell? 16. A girl who had $ spent part of a dollar did she spend? 17. A yard of crape costs $. cost? of? 4 of 4? of it for candy. What ×? × 1 = ? = What will of = ? of a yard 18. A man who owned & of a mill sold of his share. What part of the mill did he sell? of = ? 19. A fruit seller had & of a dozen cocoanuts and sold of them? What part of a dozen did he sell? 20. A train ran & of the distance between two places in an hour. What part of the distance did it run in & of an hour? 21. Two boys counting their money found that one had $ and the other had as much. What part of a dollar had each? 156. 1. Find 4 43 WRITTEN EXERCISES. of, or multiply by EXPLANATION. - To multiply by is to 3 of 3-10 find 1 of 4, or 3 times 3 of 4. 4 of 4 = 4%, and of = 13, or 1. RULE. - Reduce all integers and mixed numbers to improper fractions. Find the product of the numerators for the numerator of the product, and of the denominators, for its denominator. 1. When possible use cancellation. 2. The word of, between fractions, is equivalent to the sign of multiplication. Such expressions are sometimes called compound fractions. Thus, of is equal to × 7. 3. Integers may be expressed, in the form of fractions, by writing 1 as a denominator. Thus, 4 may be written as 1. |