8. A man having undertaken to do 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?

C. It will be seen by looking on plate III, that is the same as, and that is the same as 1⁄2, and that is the same as ; 4, 3, can therefore be reduced to, and to. This is called reducing fractions to their lowest terms.

3

11. Reduce to its lowest terms. 12. Reduce to its lowest terms. 13. Reduce 43 to its lowest terms.

14. Reduce to its lowest terms.

Ans. 2.

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 of an orange gave away t of that, what part of the whole orange did he give away?

2. What is

of 1 ?

14

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 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 ?

8. What is of 1 ?

A man having

2

a barrel of flour, sold of

that; how much did he sell?

10. What is 1 of 1 ?

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 ¦ ?

quart of chestnuts, What part of the

gave away of what he had.

whole quart did he give away?

14. What is of } ?

15. What is 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?

29. A boy having

2

3

of an orange, (that is, 2

1

her?

pieces,) gave his sister of what he had; how
many thirds did he give
30. What is 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 me of them. But of is 4,
therefore I shall have 3 of the whole pine apple.
32. What is of ??
33. A man owning
bank, sold of his part.
he sell?

35. A man owning

of a share in the Boston
What part of a share did

of a ship, sold of his

share; what part of the whole ship did he sell?

What part had he left?

36. What is of 1⁄2 ?

37. What is

of 4 ?

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

3

of ‡ ?

44. What is 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

of ?

47. What is

48. What is

49. What is 50. What is

of ?

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

70. What is of 21 ?

14

71. A boy had 2 oranges, and wished to give

of them to his sister, and 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 of 21 ?

73. A man bought 4 bushels of corn for 3 dollars; what part of a dollar did 1 bushel cost? Change the 33 to thirds, and then find of as above.

74. What is of 51

75. If 5 bushels of wheat cost 73 dollars, what is that a bushel

76. What is of 73 ?

77. A man bought 6 gallons of brandy for 34 dollars; what was that a gallon?

78. What is of 83 ?

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

80. What is of 84 ?

81. A man bought 10 pieces of nankin for 63 dollars; how much was it a piece?

82. What is of 63 ?

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

89. A man bought 7 yards of cloth for 183 dollars; what was that a yard? What would 3 yards cost at that rate?

90. What is of 183? What is of 183 ?

91. A man bought 5 barrels of cider for 273 dollars; what was it a barrel? What would 7 barrels cest at that rate?

92. What is of 273? What is 7 of 273?