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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?

Note. By dividing a line into halves, and then into fourths, it will be seen that is the same as, a line divided into halves and then into sixths, will show that is the same as, and as ; 4, &, can therefore be reduced to , and to . This is called reducing fractions to their lowest terms. It is done by dividing the greatest number that will divide it without a remainder.

1. Reduce to its lowest terms.* 2. Reduce to its lowest terms.

3. Reduce & to its lowest terms.

Ans. 2.

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9. Reduce

to its lowest terms. 10. Reduce to its lowest terms.

11. Reduce

8

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to its lowest terms.

12. Reduce

to its lowest terms.

to its lowest terms.

13. Reduce 14. Reduce

to its lowest terms.

Note. It will be seen by the above section that if both the numerator and denominator be multi plied 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 of that, what part of the whole orange did he give away?

2. What is of } ?

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 ?

9. A man having

a barrel of flour, sold of

that; how much did he sell?

10. What is 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

of a quart of chestnuts

gave away of what he had.

whole quart did he give away?

14. What is of } ?

15. What is of } ?

What part of the

16. A man owning of a ship, sold of his share; what part of the ship did he sel!, and what part did

he then own?

17. What is

of } ?

18. What is

of?

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28. What is of ? 29. A boy having pieces,) gave his sister many thirds did he give her? 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, therefore I shall have 3 of the whole pine apple. 32. What is of 2? 33. A man owning of his part.

of an orange, (that is, 2 of what he had; how

bank, sold

he sell?

142

34. What is of ??

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 ?

37. What is

38. What is

39. What is

40. What is

of ?

号?

?

of is ?

41. What is of ?

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

share did he sell?

43. What is of { ?

44. What is 1 of 3 ? 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

?

1

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65. What is

66. What is & of

67 What is

68. What is of & ?

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

70. What is of 21 ?

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

did not know now 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 34 dollars; what part of a dollar did 1 bushel cost? Change the 33 to thirds, and then find

above.

74. What is of 54?

fas

75. If 5 bushels of wheat cost 72 dollars, wha is that a bushel ?

76. What is of 72?

77. A man bought 6 gallons of alcohol for 83 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 ?

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89. A man bought 7 yards of cloth for 183 do lars; 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 dol lars; what was it a barrel? What would 7 bariels cost at that rate?

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

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