in which the dividend is the numerator, and the divisor the denominator of a complex fraction. 135. A complex fraction has a fraction in either its numerator or denominator, or in both of them. The reduction of complex to simple fractions is similar to division of fractions. Reduce to a simple fraction. Multiply both terms by 4 and we have. Reduce to a simple fraction. Multiply both terms by 12, which is the L. C. M. of 4 and 6, and we have at once. 136. To express one number as a fraction of another. The number which follows "of" is the denominator, and the other number the numerator of the required fraction. 137. To reduce a decimal to a common fraction. Reduce 0.25 to a common fraction. 0.25=251. 138. Hence, to reduce a decimal to a common fraction, Write the figures of the decimal for the numerator; and 1, with as many zeros as there are figures in the decimal, for the denominator. 139. To reduce a common fraction to a decimal. Change to a decimal. 8) 3.000 140. Hence, to reduce a common fraction to a decimal, Divide the numerator by the denominator. 141. If a fraction, when reduced to its lowest terms, contains in the denominator any other factor than 2 or 5 (the prime factors of 10), the division of the numerator by the denominator will not terminate. In general, it will be sufficient to obtain five decimal places in the quotient. But the number in the fifth place of the quotient must be increased by 1 if the number in the next place of the quotient is five, or greater than five. Ex. 95. Solve the following problems, first changing the common fractions to decimals: 1. A person owed $24,560. When he has paid $8345,8%, $7234, $6472, how much does he still owe? 2. A man sold 4617 acres of land, at the rate of $94 an acre, and 54 acres at the rate of $218. How much did he receive for the whole? 3. A merchant purchases 346 pieces of cloth, each containing 32 yards, at $1 a yard, and sells the whole for $2 a yard. What does he gain? 4. A merchant purchased 8 yards of cloth at $6 a yard. What sum will he gain per yard if he sells the whole piece for $5624? 5. A man bought a piece of land for $1046 at the rate of $15 an acre. He sells it for $17 an acre. How much does he gain on the whole? 6. A merchant purchased 15 casks of wine of 25 gallons each. He paid $980 for the wine, $78 tax, $33g for transportation. He sold it for $3 a gallon. How much did he gain? 7. A speculator purchased 738 acres of land for $21,294. He sells of his land at the rate of $34 an acre, and the rest at the rate of $35 per acre. What does he gain? 8. A piece of cloth is 29 yards in length. How many pieces, each containing 155 yards, can be cut from it? |