Oral Exercises. 48. In 12 sixths how many units? 49. In 27 fifths how many units? Ans. 2. Ans. 5 and 2 fifths. 50. Reduce to integers or mixed numbers; 17; 4; 27; 133. Hence, to reduce an improper fraction to an integer or mixed number, Rule. Divide the numerator by the denominator; if there is any remainder, place it over the divisor, and annex the fraction so formed to the quotient. 135. To reduce fractions to fractions having a common denominator. Fractions have a Common Denominator when their denominators are equal. Fractions have their Least Common Denominator when the common denominator is the least possible. 65. Reduce and to fractions having a common denominator. 66. Reduce and to fractions having a common denominator. 67. Reduce the following pairs of fractions to fractions having a common denominator: and; and ; and † ; † and ✈ ; and; and ; and ; and ; and ; and 68. Reduce the following pairs of fractions to fractions having their least common denominator: and; and ; and ; and; and ; and ; and ; and ; and ; fr and 69. Reduce 1, 2, and to fractions having their least common denominator, that is, to eighths. 70. Reduce §, §, and to fractions having their least common denominator. 71. Reduce†,§, and to fractions having their least common denominator. NOTE. When the denominators are mutually prime, the least common denominator is the product of all the denominators, and the new numerators are found by multiplying each numerator by all the denominators except its own. 72. Reduce,, and to fractions having their least common denominator. 73. Reduce,, and to fractions having their least common denominator. 137. From these examples, to reduce fractions to fractions having their least common denominator, we derive the following Rule. Reduce each fraction to its lowest terms. Find the least common multiple of the denominators for the common denominator. For the new numerators multiply each numerator by the quotient arising from dividing this multiple by its denominator. 138. Written Exercises. Reduce the following sets of fractions to fractions having their least common denominator: 74. 4, 3, and 4. 76. f,,, and ‡. 75. f, f, and 4. 77. §, 13, 12, and 1. NOTE. As we know the factors of the least common multiple and of each denominator, we can tell what "the quotient arising from dividing this multiple" is, without actually performing the division. 88. James had 2 quarters of a dollar, and his father gave him another quarter; how many quarters did he have? 89. William had half a dollar, and his father gave him a quarter; how much money did William have then? 140. From these examples in addition of fractions we derive the following Rule. Reduce the fractions, if necessary, to fractions having a common denominator; then write the sum of the new numerators over the common denominator. 117. A man had seven horses sold at auction. The first brought $141, the second $1733, the third $1314, the fourth $217, the fifth $1837, the sixth $ 2243, the seventh $257. What did he receive for all? 118. A merchant bought five hogsheads of sugar weighing respectively, 417, 487, 516, 4192, and 502 pounds. How many pounds of sugar did he buy? SUBTRACTION OF FRACTIONS. 142. Oral Exercises. 119. John had 3 quarters of a dollar and lost 2 of them; how many quarters had he left? -4=1 120. Henry had half a dollar and spent a quarter; how much 127. If a boy who has of a dollar gives away how much has he left? of a dollar, 128. If of a pole is above the surface of the water, and † of it is in the mud, what part of it is in the water? 143. From these examples in subtraction of fractions we derive the following Rule. Reduce the fractions, if necessary, to fractions having a common denominator; then subtract the numerator of the subtrahend from that of the minuend, and write the result over the common denominator. OPERATION. 1872 = 18712 =? 137. T6-88=! Reduce the fractions to fractions having a common denominator; as we cannot take 19 from, we take a unit from the 7 units of 187, and reduce it to twelfths; adding this to the, we have 11, from which subtracting we have ; then we proceed as in simple subtraction. |