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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 # 1 + is how many # 1 ; and # and # are how many # 1 26. A man gave ; of a barrel of flour to one man, and # of a barrel to another; to which did he ive the most 7 How much 27. Which is the largest 3 or ; ? How much the largest ? 28. A boy having a pound of almonds, said he intended to give # of them to his sister, and 4 to his brother, and the rest to his mamma. His mamma smiling said she did not think he could divide them so. Oyes 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 1 29. is how many to 1 } is how many to 1 : and 4 are how many # 1 30. Mr. Goodman having a pound of raisins, said he would give Sarah #, and Mary 4, 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 3 and 4 and # of them. How many twelfths would each have 1 31. 3 and 4 and # are how many F's 1 . 32. George bought a pine apple, and said he would give # of it to his papa, and # to his mamma, and for to his brother James, if he could divide it. James took it, and cut it into twenty equal pieces,

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When the denominators in two or more fractions are the same, the fractions are said to have a common denominator. Thus 4 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 3 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 4 and # to a common denominator. 78. Reduce # and # and # to a common denominator. 79. Reduce 4 and # to a common denominator. 80. Reduce # and 4 to a common denominator

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B. 1. Mr. F. said he would give 4 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 1. How would you divide it ! How much would be left 2 2. A man sold 14 bushels of wheat to one man, 4; bushels to another; how many bushels did he sell to both 1 3. A man bought 64 bushels of wheat at one time, and 24 at another. How much did he buy in the whole 1 4. A man bought 74 yards of one kind of cloth, and 63 yards of another kind; how many yards in, the whole 1 5. A man bought # of a barrel of beer at one time, 24 barrels at another, and 6; at another; how much did he buy in the whole ! 6. A man bought one sheep for 44 dollars, and another for 54 dollars; how much did he give for both 1 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?

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8. A man having undertaken to do a piece of work, did + of it the first day, 3 of it the second day, and # of it the third day, how much of it did he do in three days 1

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 4 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 3 is the same as #, and that § is the same as #, and that # is the same as # ; #, #, can therefore be reduced to 4, and # to #. This is called reducing fractions to their lowest terms.

1. Reduce # to its lowest terms.” Ans. #. 2. Reduce for to its lowest terms. 3. Reduce # to its lowest terms. 4. Reduce # to its lowest terms.' 5. Reduce #4 to its lowest terms. 6. Reduce for to its lowest terms. 7. Reduce or to its lowest terms. 8. Reduce # to its lowest terms. 9. Reduce #4 to its lowest terms. 10. Reduce for to its lowest terms. . 11. Reduce # to its lowest terms. 12. Reduce 44 to its lowest terms. , 13. Reduce # to its lowest terms. 14. Reduce #4 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.

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