EXAMPLES. 3 66. Reduce, 2, and 1⁄2 to a common denominator. 9 , and to a common denom 67. Reduce, 7 inator. 12 10 15 68. Reduce 11, 13, 12, and 14 to a common denominator. 69. Reduce 2, 12, 17, and to a common denominator. 72 70. Reduce,,, and to a inator. to a common denom 7 77 24 71. Reduce of 4, 4 of 8, and of 161 to a common denominator. 72. Reduce of 11, of, and 9 to a common denominator. 73. Reduce, &, 11, 3 9 and to a common denom inator. 13 74. Reduce of 21, 24, and to a common de nominator. 19 75. Reduce 11, 26, and 191 to a common denominator. 4, and to a common denom 77. Reduce of 9 and 3 of 24 to a common denominator. 8 78. Reduce 4, 23, 30, and 22 to a common denominator. 79. Reduce 11, 11, 13, and to a common denominator, 80. Reduce 13' 11' 17' 4 8 15, and 19 to a common denom inator. 81. Reduce of 7 and & of 91 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. 9 EXAMPLES. 83. Reduce to a fraction with 15 for a numerator. 13 84. Reduce to a fraction with 21 for a numerator. 17 24 85. Reduce to a fraction with 31 for a numerator. 86. Reduce 12 to a fraction with 21 for a numerator. 20 87. Reduce 2 to a fraction with 41 for a numerator. 37 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. to a fraction with 13 for a denom 88. Reduce Since both terms are multiplied and divided by the same 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 ? 9 EXAMPLES. 89. Reduce to a fraction with 19 for a denominator. 17 90. Reduce to a fraction with 21 for a denominator. 21 91. Reduce to a fraction with 19 for a denominator. 3 1 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, and ? The fractions, reduced to a common denominator, are 28, 15, 24; 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. EXAMPLES. 3 9 ? 97. What is the sum of 2, 2, and ? 98. What is the sum of %, %, and 99. What is the sum of 3, 2, and ? 100. What is the sum of %, %, and § ? 101. What is the sum of 4, 3, and 11? 102. What is the sum of §, 13, and 17 ? 103. What is the sum of 1, 1, and 14? 104. What is the sum of 105. What is the sum of 4 13 of and 7 of ? of 11 and 13 of 1? 11 19 106. What is the sum of 2 of 4 and 7 of 9? of 51, and § of 111? off and of 25? 110. What is the sum of 1, 19, 18, and } ? 111. What is the sum of 1, 2, 1, 4, and §? 112. What is the sum of 211, 14%, and 7 of 40? 113. What is the sum of 7, 10, 11, and 18? 9 114. What is the sum of, 18, 18, and 5? 115. What is the sum of 116. What is the sum of of 10 and & of 301? of 93 and 1⁄2 of 64? MULTIPLICATION OF FRACTIONS. 94. RULE. Multiply the numerators together for a numerator, and the denominators for a denominator. OBS. 1. Whole and mixed nnmbers must first be changed to im→ proper fractions. OBS. 2. Cancel all factors common to the numerators and denominators. The principle of this rule is the same as that for the reduction of compound fractions. What is the rule for the multiplication of fractions? F 117. Multiply by . First multiply by 4, which is X4; but since the multiplier is not 4, but of 4, the product is 9 times This product must therefore be divided too large. by 9. 9 Cancel the two factors common to the numerator and divisor; the product of the remaining figures is 4. EXAMPLES. 119. Multiply by §. 1 SUBTRACTION OF FRACTIONS. 95. RULE. Reduce the fractions as in addition, subtract the less numerator from the greater, and write the difference over the common denominator. OBS. 1. All whole and mixed numbers must first be reduced to improper fractions, and compound fractions to simple ones. What is the rule for the subtraction of fractions? |