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21. Divide 4 by 4; by y;

s by 5. 22. Divide by 5; Å by 8; by . 23. Divide 8 by ; i by 8;

by . To TEACHERS.—It is clear from the foregoing solutions that the usual " three cases " in division of fractions, which from time immemorial hare 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 ihe 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.

WRITTEN EXERCISES.

1. Divide in by 11.

10. Divide 24 by 13. 2. Divide f by 13. 11. Divide by 3. Divide å by 9.

12. Divide by kr. 4. Divide 1% by 12.

13. Divide s by 5. Divide 3: by 16.

14. Divide jo by 10. 6. Divide 8 by it.

15. Divide to by 7's 7. Divide 13 by 3. 16. Divide 8 by 10%. 3. Divide 17 by fi:

17. Divide f by 11}. 3. Divide 16 by 15.

18. Divide of $ by of . 19. Divide ; of 2 by 4 of 113. 20. Divide of 1 of 1 by of 3 of 93.

21. At 11: cents a pound, how many pounds of sugar can be bought for 69 cents ?

22. I paid $1244 for 124 barrels of flour: what was the price per barrel ?

23. A dealer paid $1731'0 for 231 yards of broadcloth : what was the price per yard ?

24. How many tons of hay at $154 a ton can be bought for $9713 ?

25. If John earns $1% a day, how long will it take him to earn $18} ?

26. A lady bought 133 yards of satin for $514 : what was the price per yard ?

27. Bought 13,1 baskets of peaches for $16}: what was the price per basket ?

28. How many pieces of lace is of a yard long can be cut from 63 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 $1410 ?

32. A man chopped 303 cords of wood at the rate of 13 cords a day: how many days were required ?

33. A grocer received $298 for coffee sold at of a dollar a pound : how many pounds did he sell ?

34. How many tons of hay at $17] 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 criginal 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? 7 apples? 5 apples? 8 apples?

3. What part of 4 pounds is 1 pound ? 1 of 1 pound ? 4 of 1 pound ? 3 of 1 pound ? 1 of 1 pound ?

4. What part of $4 is $2 ? $3 ? į of $1 ? of $1 ? 5. What part of $8 is $1 ? of $1 ? } of $1 ? 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 each earn ?

9. What part of 5 is 3 ?

Solution.—1 is t of 5, and 3 is 3 times š or of 5.

What part :
10. Of 12 is 6 ?
11. Of 16 is 8 ?
12. Of 18 is vy?
13. Of 30 is 9 ?

14. Of 20 is 10?
15. Of 36 is 12 ?
16. Of 44 is 11 ?
17. Of 18 is 15 ?

18. Of 32 is 16 ? 19. Of 40 is 18 ? 20. Of 30 is 17 ? 21. Of 45 is 25 ?

22. If five oranges cost 18 cents, how much will 25 oranges cost ?

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 is of of 5 = c of 5.

What part: 27. Of 5 is ? 31. Of q is ? 35. Of 8 is j? 28. Of 7 is? 32. Of 9 is ? 36. Of 11 is 4 ? 29. Of 6 is 8? 33. Of 8 is ? 37. Of 10 is ? 30. Of 8 is? 34. Of 10 is ? 38. Of 12 is 8?

39. If 4 of a pound of tea cost 48 cents, how much 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 jis 6 ?

Solution.— 6 is as many times j as it contains s, which is 9 times.

How many times :
44. is 5 ? 48. } is 9 ? 52.

is 9 ? 45. 4 is 8? 49. $is 5? 53.is 11 ? 46. f is 7? 50.is 7? 54. 4 is 10? 47. & is 6? 51. } is 10 ? 55. io is 12 ?

56. If a yard of cloth cost of a dollar, how many yards can be bought for $15?

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57. How many times the distance that John can walk in f of an hour can he walk in 7 hours ?

58. A book cost to 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 į is $?

Solution.— is as many times i as it contains , which is 13 times.

How many times : 61. is? 65. § is ? 69. f is ? 62.4 is? 66. It is

70. 1 is io? 63. 4 is? 67. $ is ? 71. Ő is ? 64. is? 68. 4 is 3? 72. is?

73. A man owning of a ship sold of his share : what part of the ship did he sell ?

74. If 3} yards of silk cost $13, how much will 13} yards cost ?

75. Thomas had 4 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 4 of a dollar : what part of of a dollar remained ?

77. Mary had io of a dollar and spent of a dollar : what part of 1% of a dollar was left ?

78. A man bought ☆ of an acre of land and sold of an acre: what part of / of an acre had he left ?

79. The owner of 3 of a mill sold of his share : what part of the mill did he then own?

80. A house insured for 7 of its value was injured by fire to the extent of of its insurance : what was the loss of the insurance company ?

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