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? SECTION XIII. A. 1. If you give of an orange to one boy, and to another, how much more do you give the first, than the second? 2. ? 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. and are how many? ? 5. A man gave to one labourer of a bushe. of wheat, and to another; how many of a bushel did he give to both? How many bushels? 6. 1 and 2 are how many? How many times 1 ? 7. A man gave of a barrel of flour to one man, and of a barrel to another; to which did he give the most? 8. is how many ? 9. A man bought time, and of a bushel of wheat at one of a bushel at another; at which time did he buy the most? 10. is how many? 11. A man bought 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? 13. A man wished to give of a bushel of wheat 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 of them for one, and 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? is how many ? and are how many? 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 ¦ 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 4 and ? 19. A boy distributing some nuts among his companions, gave 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 and ? 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. is how many? 23. A man had a horse, and a cow, and a sheep. The horse would eat of a load of hay in the winHow many of a would they all ter, the cow, and the sheep. load would each eat? How many eat! How many loads? 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? is how many } ? 14 and barrel of flour to one 25. is how many? and are how many? 26. A man gave 2 of a 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? ? 3 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 and of them. How many twelfths would each have? 31. and and are how many? and 32. George bought a pine apple, and said he would give of it to his papa, 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 36. is how many? 37. is how many? 38. are how many? 39. are how many 40. is how many? ? 41. are how many 3 42. are how many ? 1 ? 43. are how many 45. are how many? 46. are how many 47. are how many ? ? 48. Reduce to sixths and to sixths. 49. and are how many? 50. Reduce are how many?? 54. and are how many? 55. and are how many? 56. and are how many? 57. and and are how many 58. and and are how many 59. and are how many 60. and and are how many T 61. and and are how many 62. and and and and 67. and 68. less less are how many? 69. less are how many are how many? 70. less are how many ? 71. 1 and 2, and 1, and, less § are how many 24 ? 72. and, and, and, and, less are how many 73. 4 and 2 are how many 74.3 and 75. and ? ? are how many 36 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 3 and 1⁄2 to a common denominator. 79. Reduce and to a common denominator. 80. Reduce and to a common denominator. |