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ing towards each other, one at the rate of 3 miles an hour, the other 2 miles; how much do they approach each other in an hour ! How much in 2 hours ? In how many hours will they meet At what distance from each place from which they set out 1
A. l. If you give 4 of an orange to one boy, and } to another, how much more do you give the first, than the second 7 2. 3 of an orange is how many # of an orange? 3. If you give # of an orange to one boy, and ; to another, how many + would you give away ? How many + would you have left? 4. 4 and 4 are how many # 1 5. A man gave to one labourer 4 of a bushel of wheat, and # to another; how many # of a bushel did he give to both 1 How many bushels? 6. , and ; are how many # 1 How many times 1 7 7. A man gave 4 of a barrel of flour to one man, and of a barrel to another; to which did he give the most 1 8. 4 is how many # 1 9. A man bought 4 of a bushel of wheat at one time, and # of a bushel at another; at which time did he buy the most 1 10. # is how many # 7 11. A man bought 4 of a yard of cloth at one time, and # of a yard at another; at which time did he buy the most 12. # are how many # 1 13. A man wished to give 4 of a bushel of wheat to one man, and 4 of a bushel to another; but he could not tell how to divide it. Another man stand ing by advised him to divide the whole bushel into six equal parts first, and then take # of them fol one, and , of them for the other. How many parts did he give to each 1 How many to both 1 How many had he left 1 14. is how many # 1 % is how many # 1 + 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 1 16. What is the difference between 4 and # 1 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 1 18. What is the difference between # and + 2 19. A boy distributing some nuts among his companions, gave 4 of a quart to one, and # 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 #2 21. A man having two bushels of grain to distribute among his labourers, wished to give # of a bushel to one, and 4 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 # 1 23. A man had a horse, and a cow, and a sheep. The horse would eat 3 of a load of hay in the winter, the cow +, and the sheep #. How many # of a load would each eat? How many # would they all eat 1 How many loads 7 w
24. A boy having a quart of nuts, wished to divide them, so as to give one companion #, another f, 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 1 How many eighths had he left for himself 25. # is how many # 1 + is how many # 1 ; and # and 4 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 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. 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 of 1 + is how many to 1 # and + are how many to 2 30. Mr. Goodman having a pound of raisins, said me would give Sarah 4, 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 ; and # of them. How many twelfths would each have 1 31. 4 and # and are how many or ? 32. George bought a pine apple, and said he would give 4 of it to his papa, and # to his mamma, and so, to his brother James, if he could divide it James took it, and cut it into twenty equal pieces
When the denominators in two or more frae. tions are the same, the fractions are said to have a common denominator. Thus # and 3 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 3 and # to a common denominator.
80. Reduce # and # to a common denominator.