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8. A man having undertaken to do a piece of work, did } of it the first day, I of it the second day, and 1 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 į of the work in a day, and the other į of it, and the boy } of it ; how much of it would they all do in a day?

C. It will be seen by looking on plate III, that is the same as ļ, and that i is the same as j, and that is the same as ģ ; , , can therefore be reduced to }, and 4 to 3. This is called reducing fractions to their lowest terms.

1. Reduce ž to its lowest terms.* Ans. 2. Reduce to its lowest terms. 3. Reduce to its lowest terms. 4. Reduce is to its lowest terms. 5. Reduce il to its lowest terms, 6. Reduces to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce ji to its lowest terms. 9. Reduce }} to its lowest terms. 10. Reduce to its lowest terms. 11. Reduce to its lowest terms. 12. Reduce to its lowest terms. 13. Reduce a to its lowest terms. 14. Reduce 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 till after the next section.

SECTION XIV.

A. 1. A boy having į of an orange gave aways of that, what part of the whole orange did he give

away ?

2. What is į of į?

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;?

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 į of į?

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 ?

8. What is of?

9. A man having i a barrel of flour, sold of that; how much did he sell ?

10. What is į of ?

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

12. What is of?

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

14. What is į of } ? 15. What is į of į?

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?

17. What is į of}? 18. What is į of ?

19. What is į of }?
20. What is į of j ?
21. What is of 1?
22. What is
23. What is
24. What is į

?
25. What is a
26. What is

? 27. What is į of i? 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 į of ?

31. A boy having 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 nie į of them. But į ofis therefore I shall have of the whole pine apple.

32. What is į of ?

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

34. What is į of ?

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

36. What is į off ? 37. What is į of f? 38. What is '} of $ ? 39. What is į of $ ? 40. What is į of 4 ? 41. What is į of } ?

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

43. What is of?? 44. What is of ?

45. A boy having 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 was each piece ?

46. What is off ?
47. What is } of į?
48. What is į of
49. What is į of ?
50. What is jó of
51. What is 1 of ?
52. What is of
53. What is off ?
54. What is it
55. What is į of
56. What is
57. What is
58. What is
59. What is
60. What is
61. What is j off ?
62. What is 1 of 3 ?
63. What is of ?
64. What is to of
65. What is jó of
66. What is of ?
67. What is 1 of ?
68. What is ã of ? ?

69. If a yard of cloth cost 21 dollars, wha: will 1 of a yard cost ?

70. What is 1 of 2; ?

71. A boy had 2 oranges, and wished to give } of them to his sister, and į to his brother, but he

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 ļof 2 ?

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

Change the 3j to thirds, and then find of as above.

74. What is of 57 ?

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

76. What is į of 7?

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

78. What is 1 of 83 !

79. A man bought 7 gallons of wine for 84 Nole lars; how much was that a gallon ?

80. What is 4 of 84 ?

81. A man bought' 10 pieces of nankin for 67 dollars; how much was it a piece ?

82. What is to of Oz?

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

84. What is of 7* ? 85. What is į of 5 ? 86. What is į of 31 ? 87. What is of 65? 88. What is į of 94?

89. A man bought 7 yards of cloth for 181 dollars ; what was that a yard ? What would 3 yards cost at that rate ?

90. What is of 18?? What is of 187?

91. A man bought 5 barrels of cider for 271 dollars; what was it a barrel ?. What would 7 barrels ccst at thai rate ? 92. What is 4 of 274 ? What is of 271?

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