115. To change a fraction to its smallest terms: Rule. Divide both terms of the fraction by any common divisor; treat the resulting fraction in the same way, and so continue until a fraction is found whose terms are prime to each other. NOTE. The greater the common divisor used, the shorter will be the pro An Integer or Mixed Number to an Improper Fraction. ORAL EXERCISES. 71. In 2 apples how many fourths of an apple? In 5 apples? In 8 apples? 72. Reduce 6 to fourths; 3 to fifths; 7 to sixths. 73. How many fourths of an apple in 32 apples? In 64 apples. Change to improper fractions: 74. 13, 12, 13, 18, 17, 24, 37, 51, 41, 33. 75. 23, 27, 31, 31, 33, 35, 37, 41, 43, 43. 76. 43, 44, 43, 53, 511⁄2, 54, 51, 52, 53, 61. WRITTEN EXERCISES. 79. Change 19 to eighths. 19 8 eighths. 152 Solution. - In 1 there are 8 eighths; in 19 there are 19 times 8 eighths, or 152. 80. Change 197 to the form of a fraction. 81. Change 21 to ninths. 218 9 194 9 Solution. In 1 there are 9 ninths, and in 21 there are 21 times 9 ninths, or 189 ninths; 189 ninths and 5 ninths are 194 ninths, or 184. 82. Change 27 to thirteenths. 83. Change 37 to elevenths. 116. To change an integer or mixed number to an improper fraction: Rule, Multiply the integer by the denominator, and, if there is a fractional part, add its numerator to the product, and write the result over the denominator. 84. Reduce 93 to fifteenths; 107 to twenty-firsts. 85. Reduce 115 to a fraction whose denominator is 13. An Improper Fraction to an Integer or Mixed Number. ORAL EXERCISES. 98. How many dollars in 32 quarter-dollars? In 40 quarterdollars? In $42? In $42? In $54? Change to integers or mixed numbers: 99. §, ⇓, 5, 1, 7, 2, 4, 47, 13, 14. 100. 6, 7, 8, 2, 4, U, V, 46, 17, 18. 101. 19, 20, 21, 22, 23, 24, 25, 26, 27, 28. 102. 29, 30, 31, 32, 33, 34, 35, 11, 11, 3⁄4. 103. 39, 40, 41, 42, 43, 11, 45, 11⁄2, 11, 42. WRITTEN EXERCISES. 104. Change 793 to an integer or mixed number. 411 19) 793 76 33 19 14 Solution. - As 19 nineteenths are 1, 793 nineteenths will be as many ones as times 19 in 793, or 411. Ans. 411. 105. Change 56 to an integer or mixed number. 106. Change 4421 to an integer or mixed number. 117. To change an improper fraction to an integer or mixed number: 3 124. Change and to fractions having the same denomi nator. 125. Change and to fractions having the same denominator. What is a multiple of 6 and 5? 126. Change,, and to fractions having the same denominator. 127. Express, 3, and 76 each as fortieths. 128. Express, §, and § each as eighteenths. 129. What is the least common multiple of 3, 6, and 9? 118. Fractions have a Common Denominator when their denominators are alike. 119. The smallest denominator common to two or more fractions is their Least Common Denominator. 120. A Common Denominator of several fractions must be some common multiple of their denominators. The Least Common Denominator of several fractions must be the Least Common Multiple of their denominators. WRITTEN EXERCISES. 130. Change and to fractions having a common denominator. Solution. As the product of the denominators, 5 × 7, or 35, is their common multiple, 35 must be a common denominator of the fractions. Changing then the fractions to thirty-fifths, we 131. Change and to fractions having a common denominator. 132. Change, 2, and to fractions having the least common denominator. 8 1/2 Solution. The least common multiple of the denominators is 12, which must be the least common denominator of the fractions. Changing then the fractions to twelfths, we have, 19, and 10. 12 = 12 of 12 10 = 12 133. Change, §, and § to fractions having the least common denominator. 134. Reduce 3, 3, and 11 to fractions having the least common denominator. 121. To reduce to fractions having the least common denominator: Rule. Change each fraction to its smallest terms. Divide the least common multiple of the denominators by the denominator of each fraction, and multiply both terms of the fraction by the quotient. NOTE. - When the denominators are mutually prime, take their product for the common denominator, and multiply each numerator by all the denominators except its own for the new numerator. Reduce to fractions having the least common denomina tor: 135. and 15. 139. 14, 21, and 25. 141.,, and . 142.,, and 12. 143. 2, 13, 15, and 75. 144. To, Too, too, and 7. 147. Reduce, g, and to fractions having the least common denominator, and show by the numerators which of the fractions has the greatest value. |