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81. Reduce and fand & to a common denominator.

82. Add together and .
83. Add together and
84. Add together and te
85. Add together and fand .
86. Subtract from .
87. Subtract * from .
88. Subtract & from .
89. Subtract f from

B. 1. Mr. F. said he would give of a pine-apple to Fanny, and to George, and the rest to the one that could tell how to divide it, and how much there would be left. But neither of them could tell; so he kept it himself. Could you have told if you had been there? How would you divide it? How much would be left ?

2. A man sold 14 bushels of wheat to one man, 44 bushels to another; how many bushels did he sell to both ? *

3. A man bought 67 bushels of wheat at one time, and 23 at another; how much did he buy in the whole ?

4. A man bought. 73 yards of one kind of cloth. and 63 yards of another kind; how many yards in the whole ?

5. A man bought of a barrel of beer at one time, 24 barrels at another, and 6f at another; how much did he buy in the whole ?

6. A man bought one sheep for 44 dollars, and another for 5 dollars; how much did he give for both ?

7. There is a pole standing, so that of it is in the mud, and if of it in the water, and the rest out of the water ; how much of it is out of the water?

Ans. $

8. A man, having undertaken to do a piece of work, did of it the first day, 4 of it the second day, and t 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 f of the work in a day, and the other 1 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 1, and that is the same as t, and that is the same as ; , &, can therefore be reduced to t, and to g. This is called reducing fractions to their lowest terins.

1. Reduce s to its lowest terms. * 2. Reduce B to its lowest terms. 3. Reduce & to its lowest terms. 4. Reduce to its lowest terms. 5. Reduce 14 to its lowest terms. 6. Reduce is to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce je to its lowest terms. 9. Reduce to its lowest terms. 0. Reduce to its lowest terms. 11. Reduce 5 to its lowest terms. 12. Reduce to its lowest terms. 13. Reduce to its lowest terms. 14. Reduce 4z 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 dupil, 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 1 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 į of ?

5. A boy had 7 of a pine-apple, and cut that half into three picces, in order to give away of it. What part of the whole apple did he give away?

6. What is f 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 1 of 4 ?

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

10. What is 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 f of 1?

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?

14. What is of ? 15. What is 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 ?

19. What is of ? 20. What is of 1? 21. What is of +? 22. What is t of ? 23. What is į of +? 24. What is of $? 25. What is & of ? 26. What is of 7 ? 27. What is of ?? 28. What is of f?

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

30. What is 4 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 f of 4 is $; therefore I shall have of the whole pine-apple.

32. What is of f?

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 fof f?

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

36. What is of $?
37. What is of #?
38. What is 1 of f?
39. What is } of
40. What is of ¥?
41. What is of ?

42. A man, owning á 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 į 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 į of 47. What is of 48. What is į of ? 49. What is į of ? 50. What is it of $? 51. What is 4 of 4? 52. What is in 53. What is 54. What is of 55. What is 56. What is 57. What is } 58. What is 59. What is 60. What is 61. What is ģ of 62. What is f of 63. What is $ of 64. What is it off 65. What is To off 66. What is 3 of ? 67. What is } off 68. What is z of ?

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

70. What is f of 21?

71. A boy had 27 oranges, and wished to give of them to his sister, and to his brother, but he

non, non, non, non, n. m. n. colo

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