24. A boy, having a quart of nuts, wished to divide them so as to give one companion, another †, and a third of them; but, in order to make a proper division, he first divided the whole into eight equal parts, and then he was able to divide them as he wished. How many eighths did be give to each? How many eighths had he left for himself?

25. is how many? is how many ? and and are how many?

26. A man gave

of a barrel of flour to one man, and of a barrel to another; to which did be give the most? How much?

27. Which is the largest, or ? How much the largest ?

28. A ooy, naving a pound of almonds, said he intended to give of them to his sister, and to his brother, and the rest to his mamma. His mamma, smiling, said she did not think he could divide them so. O yes I can, said he; I will first divide them into twelve equal parts, and then I can divide them well enough. Pray how many twelfths did he give to each ?

29.

is how many? is how many? and are how many?

30. Mr. Goodman, having a pound of raisins, said he would give Sarah, and Mary, and James of them; and he told Charles he should have the rest, if he could tell how to divide them. Well, said Charles, I would first divide the whole into twelve equal parts, and then I could take, and, and of them. How many twelfths would each have? 31. and and are how many?

32. George bought a pine-apple, and said he would give of it to his papa. and to his mamma, and to his brother James f he could divide it. James took it, and eut it into twenty equal pieces,

How

and then distributed them as George had destr
many twentieths did he give to each?
33. is how many? is how many
how many? is how many?
34. is how many?

35.

is how many?

36. is how many?

37.

is how many?

38. are how many? 39. are how many?

40.

is how many? 41. are how many? 42. are how many r 43. are how many r 44. are how many 45. are how many? 46. are how many?

47.

are how many?

48. Reduce to sixths and to sixths 49. and are how many?

50. Reduce and to eighths.

51. and

are how many?

52. and

are how many

53. and

are how many

and are how

many

?

56. and are how many? 57.and and are how many? and and are how many?

58.

59. and are how many?

60. and and are how many? 61. and and are how many? 62. and and and and are how many? + 63. and are how many? 2nd are how many?

64.

72., and, and 2, and to, and 2, less, ar now many?

73. and are how many?
74. and are how many
75. and are how many

?

When the denominate two or more frac tions are the same, the fractions are said to have a common denominator. Thus and have a common denominator. We have seen that, when two or more fractions have a common denominator, they may be added and subtracted as well as whole numbers. We add or subtract the numerators, and write their sum or difference over the common denominator. The first part of the process in the above examples was to reduce them to a common denominator.

76. Reduce and to a common denominator. NOTE. They may be reduced to twelfths.

If it cannot be immediately seen what number must be the common denominator, it may be found、 by multiplying all the denominators together; for that will always produce a number divisible by all the denominators.

77. Reduce and to a common denominator. 78. Reduce and and to a common denom inator.

79. Reduce and to a common denominator. 30. Reduce and to a common denominator q

B. 1. Mr F. said he would give of a pine-apple to Fanny, and 3 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, 4 bushels to another; how many bushels did he sell to both?

3. A man bought 6 bushels of wheat at one time, and 24 at another; how much did he buy in the whole?

4. A man bought 74 yards of one kind of cloth, and 64 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 is out of th water?

8. A man, having undertaken to do a piece of ork, did of it the first day, of it the second ay, 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 ali 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.* Ans. j.
2. Reduce to its lowest terms.

3. Reduce to its lowest terms.

to its lowest terms.

4. Reduce

Note. It will be seen by the above section, that, 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 he 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 sill after the next section.