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to one man, and # of a bushel to another ; but he could not tell how to divide it. Another man standing by advised him to divide the whole bushel into six equal parts first, and then take 4 of them for one, and 4 of them for the other. How many parts did he give to each How many to both How many had he left 14. # is how many # 1 % is how many # 4 g and # are how many # 1 15. A man paying some money to his labourers, gave each man # of a dollar, and each boy # of a dollar; how much more did he give to a man than to a boy? 16. What is the difference between 4 and #3 17. If a man can earn # of a dollar in a day, and a boy # of a dollar, how much does the man earn more than the boy 7 18. What is the difference between # and 4 19. A boy distributing some nuts among his companions, gave # of a quart to one, and 4 of a quart to another; how much more did he give to one, than to the other ? NoTE. Change them to sixths. 20. What is the difference between 4 and #3 21. A man having two bushels of grain to distribute among his labourers, wished to give # of a bushel to one, and # of a bushel to another, and the rest to a third; but was at a loss to tell how to divide it; at last he concluded to divide each bushel into six equal parts, or sixths, and then to distribute those parts. How many sixths did he give to each 22. 4 is how many # 7 23. A man had a horse, and a cow, and a sheep. The horse would eat # of a load of hay in the winter, the cow #, and the sheep #. How many # of a load would each eat 3 How many # would they all eat 3 How many loads 7

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 7 How many eighths had he left for himself 1 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 give 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 + to his brother, and the rest to his mamma. His mam

ma 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 # 1 + and + 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 4 and 4 and # of them. How many twelfths would each have 1 31. 3 and 4 and # are how many T'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, . and then distributed them as George had desired. How many twentieths did he give to each

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is how many for " is how many or ? is how many # is how many to ? are how many # 3 are how many or ? is how many for " | are how many to are how many are how many are how many are how many are how many for are how many or ? Reduce 4 to sixths and 4 to sixths. # and # are how many # 3 | Reduce 4 and # to eighths. and # are how many # 1 and + are how many # 3 and + are how many # 1 and # are how many # 1 and # are how many # 1 and # are how many for " and 4 and are how many # 1 and # and or are how many to 1. and # are how many to 7 and # and # are how many to 1 and for and + are how many # 1 and # and # and # and #3 are how many Ho! and # are how many or ? and # are how many F's and # are how many I's 1 ; less + are how many #

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67. 4 and # less is are how many of 1
68. # less g are how many # t
69. less ; are how many #

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70. # less # are how many #

71. # and #, and #, and #, less are how many *r

72. # and #, and #, and #, and #, less 4 are

how many # 7 73. # and # are how many # 1 74. # and # are how many or ? 75. # and # are how many # 7 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 3 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 3 and # to a common denominator. 78. Reduce 3 and ; and # to a common denominator. 79. Reduce , and # to a common denominator. 89. Reduce 3 and 3 to a common denominator.

81. Reduce # and # and 3 to a common denominator. "

82. Add together # and 3.

83. Add together # and for.

84. Add together # and #.

85. Add together 4 and # and for.

86. Subtract 4 from 4.

87. Subtract for from #.

88. Subtract 4 from 3.

89. Subtract # from #.

B. 1. Mr. F. said he would give 4 of a pine apple to Fanny, and 4 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 3 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 ! 3. A man bought 64 bushels of wheat at one time, and 24 at another. How much did he buy in the whole 7 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, 24 barrels at another, and 63 at another ; how much did he buy in the whole 1 f 6. A man bought one sheep for 44 dollars, and another for 5; 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 7

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