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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 he 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 3 of a barrel of flour to one man, and of a barrel to another; to which did he give the most? How much?

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

28. A boy having 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

of them.

and

and How many twelfths would each have?

31. and and are how many 1⁄2?

32. George bought a pine apple, and said he would give of it to his pape, and to his mamma, and to his brother James, if he could divide it. James took it, and cut it into twenty equal pieces,

and then distributed them as George had desired. How many twentieths did he give to each?

33. is how many? is how many? is how many? is how many?

34. is how many

35. is how many

is how many?

?

36.

37. is how many?

38.

are how many?

39. are how many

40. is how many? 41. are how many?

42.

are how many?

43.4 are how many

44. are how many 35

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45. are how many

?

46. are how many

?

?

47. Fare how many

48. Reduce to sixths and to sixths.

49. and are how many?

50. Reduce

and to eighths.

51. and

are how many?

[blocks in formation]

are how many?

53. and

are how many?

[blocks in formation]

are how many?

55.1 and

are how many?

56. and

are how many?

57. and

and

are how many?

58. 1 and

and are how many?

59. and

are how many?

60. and

and are how many?

61. and

[blocks in formation]

and are how many

?

and and and are how many?

63.

and

are how many?

64.

and

are how many?

[blocks in formation]

are how many 13

[blocks in formation]

are how many

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are how many?

67. and

less

68. less

are how many?

69.5 less are how many

?

70. less are how many?

71. 1 and 2, and †, and, less are how many 24?

72. and, and 3, and, and, less 7 are

how many 73. and

?

?

?

are how many 74. and are how many? 75.4 and are how many

When the denominators in two or more fractions 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 2 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 2 and to a common denomi

nator.

79. Reduce and to a common denominator. 80. Reduce and to a common denominator

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B. 1. Mr. F. said he would give of a pine ap ple 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 1 bushels of wheat to one man, 42 bushels to another; how many bushels did he sell to both?

3. A man bought 6 time, and 21 at another. the whole?

bushels of wheat at one

How much did he buy in

4. A man bought 74 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?

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 4 to. This is called reducing fractions to their lowest terms.

1. Reduce to its lowest terms.* Ans. 2.
2. Reduce to its lowest terms.
3. Reduce to its lowest terms.
4. Reduce to its lowest terms.

5. Reduce

6. Reduce

12

to its lowest terms.

to its lowest terms.

7. Reduce to its lowest terms.

20

8. Reduce to its lowest terms.

14

9. Reduce to its lowest terms.

35

10. Reduce to its lowest terms.

12. Reduce

11. Reduce 25 to its lowest terms. to its lowest terms. 13. Reduce to its lowest terms. 14. Reduce to its lowest terms.

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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..

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