TO TEACHERS.-It is clear from the foregoing solutions that the usual "three cases "in division of fractions, which from time immemorial have confused the beginner, should be treated as one case. This can be done by writing 1 as the denominator, when the dividend or the divisor is an integer. ART. 160.-Rule for Division of Fractions.-Change all the terms of the dividend and divisor to simple fractions, invert the divisor and proceed as in multiplication of fractions. NOTE. Since the process in division of fractions is, after the inversion of the divisor, the same as in multiplication of fractions, the pupils should use the same methods for shortening their work. 19. Divide of 2 by 4 of 113. 20. Divide of of by of 1⁄2 of 93. 21. At 11 cents a pound, how many pounds of sugar can be bought for 69 cents? 22. I paid $124 for 12 barrels of flour: what was the price per barrel? 23. A dealer paid $173 for 23 yards of broadcloth: what was the price per yard? 24. How many tons of hay at $15 a ton can be bought for $9713 ? 25. If John earns $1 a day, how long will it take him to earn $183 ? 26. A lady bought 13 yards of satin for $51: what was the price per yard? 27. Bought 13 baskets of peaches for $161: what was the price per basket? 28. How many pieces of lace of a yard long can be cut from 6 yards? 29. If a man spends of a dollar a day for tobacco, how long will it take him to spend $15? 30. How many suits containing 83 yards, can be made from 43 yards? 31. If Charles earns of a dollar a day, how long will it take him to earn $14% ? 32. A man chopped 30% cords of wood at the rate of 1 cords a day: how many days were required? 33. A grocer received $29 for coffee sold at of a dollar a pound: how many pounds did he sell? 34. How many tons of hay at $173 a ton can be bought for $2813? 35. If of a farm is worth $11,111, what is the value. of the whole farm? 36. If 264 bushels of potatoes are raised from 3 acres, what is the average yield an acre ? 37. Illustrate by an original problem, division of frac Relation of Numbers. Numbers bear certain relations to each other and may be compared. The unit 1 is the measure of all abstract numbers, and the fractional unit is the measure of all abstract fractions. 1. What part of 4 cents is 1 cent? 2 cents? 3 cents ? 2. What part of 10 apples is 4 apples? 6 apples? apples? 5 apples? 8 apples? of $1? of $1? 3. What part of 4 pounds is 1 pound?of 1 pound? of 1 pound? of 1 pound? of 1 pound? 4. What part of $4 is $2? $3?of $1? 5. What part of $8 is $1? of $1 ? of $1 ? 6. John had $10 and spent of $1: what part of his money did he spend? 7. William had $12 and gave away of $1: what part of his money did he give away? 8. Harry earned $5 and Thomas $3: what part of the whole did cach earn? 9. What part of 5 is 3? Solution.-1 is of 5, and 3 is 3 times or of 5. 23. If 48 horses cost $7,680, how much will 144 horses cost? 24. How much will 250 pounds of sugar, cost, if 25 pounds cost $2? 25. If 42 lemons cost $1.26, how much will 36 lemons cost? 26. What part of 5 is ? Solution.-1 is of 5, and 2 is 2 of of 5 = 2 of 5. cents, how much 39. If of a pound of tea cost 48 will 4 pounds cost? 40. What is the value of 8 hats, if one hat is worth of $1 ? 41. John having $5, spent $4: what part of $5 then remained? 42. Sarah paid 25 cents for 4 pencils: at the same rate, how much will 12 pencils cost? 43. How many times is 6? Solution. 6 is as many times as it contains, which is 9 56. If a yard of cloth cost of a dollar, how many yards can be bought for $15 ? 57. How many times the distance that John can walk in of an hour can he walk in 7 hours? 58. A book cost of a dollar at that rate how much will 30 books cost? 59. If a tract of land containing 15 acres is divided into lots containing of an acre each, how many lots are there in all? 60. How many times is? Solution.- is as many times as it contains, which is 13 times. 73. A man owning of a ship sold what part of the ship did he sell? 72. is ? 12 5 of his share: 74. If 3 yards of silk cost $13, how much will 131 yards cost? 75. Thomas had of a dollar and gave his sister of a dollar what part of his money did he give his sister? : 76. William having of a dollar lost of a dollar: what part of of a dollar remained? 77. Mary had of a dollar and spent of a dollar: dollar was left? what part of of a 78. A man bought an acre: what part of 79. The owner of of an acre of land and sold of of an acre had he left? of a mill sold of his share: what part of the mill did he then own? 80. A house insured for of its value was injured by fire to the extent of of its insurance: what was the loss of the insurance company? |