81. Reduce and and to a common denominator.

82. Add together and 3.

83. Add together

and

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, Could you have told if you had been there? How would you divide it? How much would be left?

so he kept it himself.

2. A man sold 1 bushels of wheat to one man, 43 bushels to another; how many bushels did he sell to both? 64

3. A man bought 6 bushels of wheat at one time, and 21 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, 2 barrels at another, and 63 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, of it the second day, and of it the third day, how much of it did

he do in three days?

do it.

9. A man having a piece of work to do, hired The first man could two men and a boy to 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 2 is the same as, and that is the same as, and that is the same as ; 2, 3, can therefore be reduced to, and to . This is called reducing fractions to their lowest terms.

6. Reduce

to its lowest terms.

20

14

0

7. Reduce to its lowest terms. 8. Reduce to its lowest terms. 9. Reduce to its lowest terms. 10. Reduce to its lowest terms. 11. Reduce 25 to its lowest terms. 12. Reduce to its lowest terms. 13. Reduce 43 to its lowest terms. 14. Reduce to its lowest terms.

0

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 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 1 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 ?

18

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?

28. What is of } ?

29. A boy having

of an orange, (that is, 2 pieces,) gave his sister of what he had; how 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 ?

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 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 ?

38. What is

39. What is of

40. What 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?

of { ?

of ?

43. What is 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 } ?

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

70. What is of 21⁄2?

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