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, and that is the same as ;,, can therefore be reduced to, and to . This is called reducing fractions to their lowest terms.

1. Reduce & to its lowest terms.* 2. Reduce to its lowest terms. 3. Reduce to its lowest terms.

Ans.

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 emit 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 ?

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 1?

of a

13. A boy, having gave away of what he had. whole quart did he give away? 14. What is of ?

15. What is of 1 ?

quart of chestnuts, What part of the

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 of ? 18. What is } of į♪

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

28. What is of ž? 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 of the whole pine-apple. 32. What is of ? 33. A man, owning Bank, sold of his part; } he sell?

34. What is of 4? 35. A man, owning share; what part of the What part had he left? 36. What is of ? 37. What is of

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

of a ship, sold of his whole ship 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 of ?

47. What is

of

68. What is of ?

69. If a yard of cloth cost 24 dollars, what will of a yard cost?

70. What is of 21?

71. A boy had 24 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 5%?

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

76. What is of 72?

77. A man bought 6 gallons of brandy for 8 dollars; what was that a gallon?

78. What is of 82 ?

79. A man bought 7 gallons of wine for 84 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 72 dollars, what is that a bushel ?

88. What is of 94 ?

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

90. What is of 183? What is of 188?

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 of 273? What is 7 of 274 ?