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. 41. 42. is how many? are how many 43. 4 are how many 44. ? ? are how many? 45. are how many? 46. are how many? 47. are how many? 이 48. Reduce to sixths and to sixths. 49. and are how many? 50. Reduce and to eighths. 51. and are how many? 52. and are how many? 53. and are how many? 54. and are how many? 55. and are how many? 56. and are how many o ? 57. and and are how many? 58. and and are how many? 59. and are how many? 60. and and are how many ? 61.and and are how many? 62. and and and and are how many? 63. and are how many? 64. and are how many? 65. and are how many? 66. less are how many {! 67. and, less, are how many? 68. less are how many? 69. less are how many? 70. less are how many? 71., and, and, and, less f, are how many 72., and, and 3, and ro, and, less, are how many? 73. and are how many? 74. and are how many? 75. and are how many? When the denominators in two or more frac tions 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 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 80. Reduce and to a common denominator. to a common denominator. B. 1. Mr. F. said he would give of a pine-apple 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 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 ? 4. A man bought 73 yards of one kind of cloth, and 6 yards of another kind; how many yards in the whole? how 5. A man bought of a barrel of flour at one time, 2 barrels at another, and 6 at another; much did he buy in the whole ? 6. A man bought one sheep for 4 dollars, and another for 5 dollars; how much did he give for both? 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 is out of the water? 8. A man having undertaken to do a piece of work, did of it the first day, of it the second day, and of it the third day, how much of it did he do in three days? 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 of it, and the boy of it; how much of it would they all do in a day? Note. By dividing a line into halves, and then into fourths, it will be seen that is the same as, a line divided into halves and then into sixths, will show that is the same as, and as ;,, can therefore be reduced to , and to . This is called reducing fractions to their lowest terms. It is done by dividing the greatest number that will divide it without a remainder. 13. Reduce to its lowest terms. 14. Reduce to its lowest terms. Note. It will be seen by the above section that if both the numerator and denominator be multi plied 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. SECTION XIV. A. I A BOY having of an orange gave away of that, what part of the whole orange did he give away? 2. What is of } ? 3. If you cut an apple into three pieces, and then cut each of those pieces into two pieces, how many pieces will the whole apple be cut into? What part of the whole apple will one of the pieces be? 4. What is of ? 14 5. A boy had of a pine apple, and cut that half into three pieces, in order to give away of it. What part of the whole apple did he give away? 6. What is of ? 7. If an orange be cut into 4 parts, and then each of the parts be cut in two, how many pieces will the whole be cut into? 8. What is of ↓ ? 9. A man having a barrel of flour, sold of that; how much did he sell? 10. What is of ? 11. If an orange be cut into 4 equal parts, and each of those parts be cut into 3 equal parts, how many parts will the whole orange be cut into? 12. What is of ? 13. A boy having of a quart of chestnuts, gave away of what he had. What part of the whole quart did he give away 14. What is of ¦ ? 15. What is of } ? ? 16. A man owning of a ship, sold of his share ; what part of the ship did he sell, and what part did he then own? |
