41. Reduce 734.92. 43. Reduce 9010177 42. Reduce 67301412. 45 44. Reduce 70110 45. Reduce 5, 6, 7, 8, 9, 11, to improper fractions. 46. Reduce 36 to thirds, 42 to fourths, 54 to sixths. 47. Reduce 64 to sevenths, 95 to sixteenths, 112 to twelfths. 88. To reduce compound fractions to simple frac tions, - RULE. Multiply the numerators together for a numerator, and the denominators for a denominator. OBS. 1. All factors common to the numerator and denominator should be cancelled before multiplying. OBS. 2. If a part of a compound fraction be a mixed or whole number, it must first be reduced to an improper fraction. 48. Reduce of to a simple fraction. ofis evidently; 15, the simple fraction. is 3 times, which is 49. Reduce of 1⁄2 of 2 to a simple fraction. Cancelling the factors 2 and 3 in the numerators, and also 2 and 3 in the denominators, gives 5 for a numerator, and the product of 3 and 4 for a denominator, which is, the simple fraction. EXAMPLES. 50. Reduce of of to a simple fraction. 용 51. Reduce of of 1 to a simple fraction. of 3 of 2 of 2 of 7 to a simple frac 52. Reduce tion. 53. Reduce of 18 of 5 of 23 to a simple fraction. What is the rule for reducing compound fractions to simple frac 54. Reduce of 29 of of to a simple fraction. 55. Reduce of 27 of 13 of 32 to a simple fraction. 409 56. Reduce 4 of 3 of 7 of 8 to a simple fraction. 57. What is of 7 of 101? 58. What is of 11 of 911? 89. To change fractions which have different denominators to other equivalent fractions which shall have a common denominator, RULE. Multiply both terms of each fraction by the product of the denominators of the other fractions. Or find the least common multiple of the denominators for a common denominator, (ART. 71.) Then multiply each numerator by that number which denotes the number of times its denominator is contained in the common multiple. 65. Reduce, 2, and to a common denominator. 1 X 4 X 5 4 X 4 X 2 5 X 4 X 2 2 X 4 X 5 = 28. 3 X 5 X 2 = 28. It is obvious that the value of the fractions has not been changed, since the numerators and denominators of each have been multiplied by the same number, (Art. 84.) OBS. It is generally best to find the least common multiple of the denominators, as this reduces the fractions to their lowest terms. Recite the rule for changing fractions to a common denominator. 66. Reduce,, EXAMPLES. and 1⁄2 to a common denominator. 67. Reduce, 33, 7 , and to a common denom inator. 68. Reduce, 13, 14, and 1 to a common denominator. 5 69. Reduce 2, 12, 17, and 42 to a common denominator. 24 70. Reduce,,, and to a inator. common denom 71. Reduce of, of 8, and of 161⁄2 to a common denominator. 72. Reduce of 11, 13 of 3, and 9 to a common denominator. 73. Reduce inator. 3 59 79 9 and 6 to a common denom 74. Reduce of 23, 24, and to a common de nominator. 75. Reduce 1, 2, and 191⁄2 to a common, denominator. 76. Reduce,,, and, to a common denominator. 77. Reduce of 9 and 3 of 24 to a common denominator. 7 8 78. Reduce, 23, 30, and 22 to a common denom inator. 79. Reduce 11, 11, 13, and 7 to a common denominator. 8 80. Reduce, 11, 14, and 19 to a common denominator. 81. Reduce of 7 and 2 of 9 to a common denominator. 90. To reduce one fraction to another of the same value, having a given numerator, RULE. Multiply both terms of the fraction by the proposed numerator, and divide both terms by the numerator of the given fraction. 82. Reduce to a fraction with 11 for its numerator. Since both terms are multiplied and divided by the same numbers, the value of the fraction is not changed. 83. Reduce 84. Reduce 85. Reduce 86. Reduce 87. Reduce 19 20 EXAMPLES.' to a fraction with 15 for a numerator. to a fraction with 21 for a numerator. to a fraction with 31 for a numerator. to a fraction with 21 for a numerator. to a fraction with 41 for a numerator. 91. To reduce one fraction to another of the same value, having a given denominator,— RULE. Multiply both terms of the fraction by the proposed denominator, and divide both terms by the denominator of the given fraction. Since both terms are multiplied and divided by the game numbers, the value of the fraction is not changed. What is the rule for reducing one fraction to another of a given numerator? What for reducing one to a given denominator? EXAMPLES. 89. Reduce to a fraction with 19 for a denominator. 90. Reduce to a fraction with 21 for a denominator. 91. Reduce to a fraction with 19 for a denominator. 92. Reduce to a fraction with 45 for a denominator. 93. Reduce 26 to a fraction with 17 for a denominator. 94. Reduce to a fraction with 23 for a denominator. 95. Reduce to a fraction with 96 for a denominator. ADDITION OF FRACTIONS. 92. RULE. Reduce the fractions, when necessary, to their least common denominators; add their numerators, and write their sum over the common denominator. OBS. 1. All whole and mixed numbers must first be changed to improper fractions, and compound fractions to simple fractions. OBS. 2. In mixed and whole numbers, the whole numbers and fractions may be added separately, and their sums united. 96. What is the sum of 1, 1, and ? The fractions, reduced to a common denominator, are 28, 18, 2; which being added together are 8. 93. It is evident that parts of a number of the same kind can be added in the same manner as whole numbers of the same kind. Thus, one sixtieth added to one sixtieth is two sixtieths, and so of any number of sixtieths. Recite the rule for the addition of fractions. |