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81. Reduce j and and to a common denominator.

82. Add together and .
83. Add together and
84. Add together and the
85. Add together and and M.
86. Subtract from į.
87. Subtract from
88. Subtract from se
89. Subtract g 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 yould you divide it ? How inuch would be left ?,

2. A man sold 14 bushels of wheat to one man, 4 bushels to another ; how many bushels did he sell to both ? 679

3. A man bought 61 bushels of wheat at one time, and 2; at another. How much did he buy in the whole ? 676

4. A man bought 7 yards of one kind of cloth, and 6yards of another kind ; how many yards in

the whole bouche

5. A man bought of a barrel of beer at one time, 2; barrels at another, and 6 at another ; how much did he buy in the whole ?

6. A man bought one sheep for 4 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 of it in the water, and the rest out of the water; how much of it was out of the water?

8. A man having undertaken to do a piece of work, did of it the first day, į of it the second day, and į 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 , and that i is the same as ģ, and that f is the same as ; , , can therefore be reduced to 1, and to . This is called reducing fractions to their lowest terms. 1. Reduce to its lowest terms.*

Ans. 2. Reduce to its lowest tèrms. 3. Reduce to its lowest terms. 4. Reduce to its lowest terms. 5. Reduce id to its lowest terms. 6. Reduce is to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce i to its lowest terms. 9. Reduce it to its lowest terms. 10. Reduce to its lowest terms. 11. Reduce já to its lowest terms. 12. Reduce to its lowest terms. 13. Reduce ji 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 { of an orange gave away ; 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 į of į?

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

6. What is į 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 į of ?

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

10. What is of į?

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 į of i?

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 į? 15. What is į of } ?

16. A man owning } of a ship, sold į 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 of į?
20. What is ?
21. What is
22. What is
23. What is į of ?
24. What is of f?
25. What is į of į?
26. What is } {?
27. What is of i?
28. What is of; ?

29. A boy baving 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 į or three pieces, if you cut them all in two, you can give me į of them.

But į of 1 is }, 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 į 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 of f? 37. What is į of f? 3. What is į off 39. What is į of ? 40. What is , of 4 ? 41. What is

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

43. What is į of ? 44. What is į of 4 ?

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 'ó of 51. What is į of 52. What is 53. What is 54. What is it 55. What is 56. What is 57. What is 58. What is 59. What is a 60. What is 61. What is of į? 62. What is 63. What is of 64. What is in 65. What is of 66. What is of jo 67. What is of ? 68. What is şof , ? 69. If a yard of cloth cost 21 dollars, what will of a yard cost ? 70. What is į of 2; ? 71. A boy had 24 oranges, and wished to give ; of them to his sister, and to his brother, but he

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