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 į of them for one, and į of tliem for the other. How many parts did he give to each ? How many to both ? How many had he left ? 14. į is how many ? } is how many : ? 1 and į are how many ? 15. A man paying some money to his labourers, gave each man į of a dollar, and each boy i of a dollar; how much more did he give to a man than to a boy? 16. What is the difference between 1 and ? 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 ? 18. What is the difference between and ? 19. A boy distributing some nuts among his companions, gave į 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. 21. A man having two bushels of grain to distribute among his labourers, wislied to give į of a bushiel 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 equel parts, or sixths, and then to distribute those parts. How many sixthis did he give to cach? 22. is how many ? 23. Ä 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 á. How many of a load would each eat? How many å would they all eat ? How many loads ? 24. A boy having a quart of nuts, wished to divide them, so as to give one companion ļ, another 1, 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 i them as he wished. How many eighths did he give to each ? How many eighths had he ieft for himself ? 25. is how many }? } is how many ; ? 1/ 를 and And i are how many ś? 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 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 O yes I can said he, I will first divide them into twelve equal parts, and then I can diviile them well enough. Pray how many twelfths did he give to each ? 29. { is how many iz ? } is how many i'a ? } and are how many 'z? 30. Mr. Goodman having a pound of raisins, said he would give Sarah ḥ, 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 1 and 1 and of them. How many twelfths would each have ? 31. and and are how many 's ? 32. George bought a pine apple, and said he would give of it to his papa, and į to his mamma, and % to'bis brother James, if he could divide it. James took it, and cut it into twenty equal pieces, them so. and then distributed them as George had desired. How many twentieths did he give to each ? 33. 'is how many zó? } is how many zó? } is how many zło? ij is how many z'o ? 34. is how many to ? 35. 1 is how many 14 ?? 36. į is how many ☆ ? 37. į is how many i's? 38. are how many ? 39. are how many a'i 40. is how many to? 41. are how many t's ? 42. are how many is ? 43. are how many zi 44. are how many 3'5 45. are how many 56 46. - are how many 36 47. i. are how many z ? 48. Reduce į to sixths and { to sixths. 49. i and i are how many š? 50. Reduce, and to eighths. 51. , and I are how many š? 52. į and į are how many ? 53. and į are how many ; ? 54. and are how many š? 55. and are how many ? 56. į and are how many 'a ? 57. and and 1 are how many į? 58. į and and are how many it? 59. and are how many 's ? 60. and and į are how many i'z ? 61. and in and are how many zo ? 62. and 1 and 2 and 1 and 1 are how many y's? 63. and are how many is ? 64. and į are how many 1'5 ?? 65. and are how many 1'5 ?? 66. less ; are how many ? 70. 67. and less are how many? ? ? 71. į and \, and }, and , less are how many 72. and }, and, and to, and zo, less are how many as ? 73. 4 and 2 are how many t's ? 74. i and are how many ;' 75. and į are how many o'z 'When the denominators in two or more fractions are the same, the fractions are said to have a common denominator. Thus and i 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 denominator. 79. Reduce ; and to a common denominator. 80. Reduce and to a common denominator 81. Reduce 1 and 1 and to a common denominator. 82. Add together and . E 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 11 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 2} at another. How much did he buy in the whole ? 4. A man bought 74 yards of one kind of cloth, and 62 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 6 at another ; how much did he buy in the whole ? 6. A man bought one sheep for 4ş dollars, and another for 5 dollars; how much' did he give for both ? 7. There is a pole standing, so that į 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? |