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8. A man having undertaken to ao a piece of work, did £ of it the first day, £ of it the second day, and ± of it the third day, how much of it did he do in three days?

9. A man having a piece of work to do, hired two men and a boy to do it. The first man could do | of the work in a day, and the other \ of it, and the boy | of it; how much of it would they all do in a day 1

C. It will be seen by looking on plate III, that f is the same as ^, and that £ is the same as \, and that | is the same as ~ ; f, f, can therefore be reduced to ^, and $- to §. This is called reducing fractions to their lowest terms.

1. Reduce f to its lowest terms.* Arts, f.

2. Reduce T5F to its lowest terms.

3. Reduce £ to its lowest terms.

4. Reduce T\ to its lowest terms.

5. Reduce \% to its lowest terms. . 6. Reduce -fa to its lowest terms.

7. Reduce to its lowest terms.

8. Reduce to its lowest terms.

9. Reduce £f to its lowest terms.

10. Reduce T\ to its lowest terms.

11. Reduce to its lowest terms.

12. Reduce to *ts lowest terms.

13. Reduce to its lowest terms.

14. Reduce $f to its lowest terms.

Note. It will be seen by the above section that if both the numerator and denominator be multiplied by the same number, the value of the fraction will not be altered; or if they can both be divided by the same number without a remainder, the fraction will not be altered.

* If this article should be found too difficult for the pupil, he may omit it til! after the next section.

SECTION XIV.

A. 1. A Boy having £ of an orange gave away £ of that, what part of the whole orange did he give away?

2. What is j. of ± 1

3. If you cut an apple into three pieces, and then cut each of those pieces into two pieces, how many pieces will the whole apple be cut into? What part of the whole apple will one of the pieces be?

4. What is \ of £ 1

5. A boy had ^ of a pine apple, and cut that half into three pieces, in order to give away | of it. What part of the whole apple did he give away?

6. What is j. of£?

7. If an orange be cut into 4 parts, and then each of the parts be cut in two, how many pieces will the whole be cut into 1

8. What is | of i?

|j. A man having | a barrel of flour, sold £ of tha|; how much did he sell 1 fO. What is i of

11. If an orange be cut into 4 equal parts, and each of those parts be cut into 3 equal parts, how many parte will the whole orange be cut into?

12. 'What is \ of ±?

13. A boy having £ of a quart of chestnuts, gave away \ of what he had. What part of the whole quart did he give away 1

14. What is \ of£?

15. What is i of }?

16. A man owning \ of a ship, sold % of his share; what part of the ship did he sell, and what part did he then own 1

17. What is i of |?

18. What is £ of

19. What is i of 11

20. What is | of |?

21. What is ^ of 4?

22. What is } of £?

23. What is } of} 1

24. What is | of |?

25. What is £ of }!

26. What is | of |?

27. What is A of |?

28. What is 4 of |?

29. A boy having § of an orange, (that is, 2 pieces,) gave his.sister \ of what he had; how many thirds did he give her?

30. What is \ of f?

31. A boy having f of a pine apple, said he would give one half of what he had to his sister, if she could tell how to divide it. His sister says, you have got £ or three pieces, if you cut them all in two, you can give me £ of them. But | of \ is therefore I shall have, f of the whole pine apple.

32. What is % of |?

33. A man owning f of a share in the Boston bank, sold i of his part. What part of a share did he sell?

34. What is | off?

35. A man owning £ of a ship, sold | of his share; what part of the whole ship did he sell 1 What part had he left?

36. What is £off?

37. Whatis£off?

38. What is £ off?

39. What is | off?

40. What is i of y?

41. What is \ of f?

42. A man owning f of a share in the Boston bank, sold \ of his part; what part of a whole share did he sell?

43. What is i of f?

44. What is -} off?

45. A boy having f of a water melon, wished to divide his part equally between his sister, his brother, and himself, but was at a loss to know how to do it; but his sister advised him to cut each of the fifths into 3 equal parts. How many pieces did each have? and what part of the whole melon wasr each piece?

46. What is i of f?

47. What is} of |?

48. What is |off?

49. What is £ off?

50. WhatisTVof^?

51. What is i of i?

52. What is | of i?

53. What is i of |?

54. What is £ off?

55. What is i of |?

56. What is § of f1

57. What is i off?

58. What is | off?

59. What is f off?

60. What is f off?

61. What is f of f?

62. What is £ of f?

63. What of |?

64. What is T'T off?

65. What is T\ of f 1

66. What is f of r\l

67. What is J off?

68. What is $ of f?

69. If a yard of cloth cost 2| dollars, what will } of a yard cost? /

70. What is \ of 21?

71. A boy had 21 oranges, and wished to give of them to his sister, and i to his brother, but In did not know how to divide them equally. His brother told him to cut the whole into halves, and then cut each of the halves into 3 pieces. What part of a whole orange did each have?

72. What is £ of 2-L?

73. A man bought 4 bushels of corn for 3| dollars; what part of a dollar did 1 bushel cost?

Change the 3| to thirds, and then find \ of y as above.

74. What is | of off

75. If 5 bushels of wheat cost 7£ dollars, what is that a bushel

76. What is i of 7f?

77. A man bought 6 gallons of brandy for 3| dollars; what was that a gallon?

78. What is } of 8f?

79. A man bought 7 gallons of wine for 8^ dollars; how much was that a gallon?

80. What is-i of 84?

81. A man bought 10 pieces of nankin for 6| dollars; how much was it a piece 1

82. What is TV of 6ft

83. If 9 bushels of rye cost 7$ dollars, what is that a bushel 1

84. What is£ of 7f?

85. What ib | of 5|?

86. What is £ of 8£?

87. What is i of 6^? ,

88. What is | of 9|?

89. A man bought 7 yards of cloth for 18f dollars; what was that a yard ? What would 3 yards cost at that rate? *

90. What is | of 18f? What is j of 18£ f

91. A man bought 5 barrels of cider for 27£ dollars; what was it a barrel? What would 7 barrels cost at that rate?

92. What is i of 27f 1 What is } of 27|?

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