9. I have 50 square yards of cloth; how many yards, of a yard wide, will be sufficient to line it? Ans. 83 yards. 10. A. Poor can walk 37 miles in 60 minutes; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance? Ans. 734 minutes. 161. To divide a mixed number by a whole number. Divide the integral part of the mixed number; and the remainder, re-duced if necessary to a simple fraction, divide as is in Art. 159. 4. Divide 271 by 9. 9. Divide $143 among 7 men. 10. Divide $1067 among 8 boys. 11. What is the value of 1⁄2 of a dollar? Ans. 2. Ans. 617. Ans. 4733. Ans. 3538. Ans. $2. Ans. $135. Ans. $0.341%. 12. Divide $107 among 4 boys and 3 girls, and give each of the girls twice as much as each of the boys? Ans. Boy's share, $ 104; Girl's share, 212. 13. If $14 will purchase of a ton of copperas, what quan tity will $1 purchase? Ans. 1cwt. 161. How do you divide a mixed number by a whole number? 162. To divide a whole number by a mixed number. Ans. 519. Ex. 1. Divide 25 by 43. OPERATION. 42 25 5 5 115 We first reduce the divisor and dividend to fifths, and then divide as in whole numbers. The divisor and dividend were both multiplied 23)125 (518 by the same number, 5; therefore their relation to each other is the same as before, and the quotient is not changed. (Art. 115, Note.) Hence, 10 Reduce the divisor and dividend to the same fractional parts as are denoted by the denominator of the fraction in the divisor, and then divide as in whole numbers. 6. There is a board 19 feet in length, which I wish to saw into pieces 23 feet long; what will be the number of pieces? Since 1 is contained in, times, is contained in 9 times times, or times; and is contained in, of times, which is , or 1, times. That is, we have multiplied the denominator of the dividend by the number denoting the numerator of the divisor, and the numerator of the dividend by the number denoting the denominator of the divisor, hence, for convenience, as in the second operation, we can simply invert the terms of the divisor and proceed as in Art. 156. 162. How do you divide a whole by a mixed number? How does it appear that this process does not alter the quotient?-163. How do you divide a fraction by a fraction? Give the reason why this process divides the fraction of the dividend. RULE. Invert the divisor, and then proceed as in multiplication of fractions. NOTE 1.-Factors common to numerator and denominator should be canceled. NOTE 2. - - When the divisor and dividend have a common denominator their denominations cancel each other, and the division may be performed by simply dividing the numerator of the dividend by that of the divisor. 164. To divide a mixed number by a mixed number. Reduce them to improper fractions, and proceed as in Art. 163. 163 The rule for dividing one fraction by another? How may fractions be divided when they have a common denominator? Does this process differ in principle from the other? - 164. How do you divide a mixed number by a mixed number? COMPLEX FRACTIONS. 165. To reduce complex to simple fractions. Ex. 1. Reduce Since the numerator of a fraction is the dividend, and the denominator the divisor (Art. 132), we simply divide the numerator, by the denominator, g, as in division of fractions. (Art. 163.) OPERATION. = = We reduce the denomi I nator, of, to a simple fraction, and then proceed as before. RULE. Reduce the terms of the complex fraction, if necessary, to the form of a simple fraction. Then divide the numerator of the complex fraction by its denominator. NOTE. Another method is to multiply both terms of the complex fraction by a common multiple of their denominators. 165. The rule for reducing complex to simple fractions? How does this process differ from division of fractions? 91 what 127 11. If 7 is the denominator of the following fraction, is its value when reduced to a simple fraction? Ans. 12. If is the numerator of the following fraction, its value when reduced to a simple fraction? what is Ans.. 166. Complex fractions, after being reduced to simple ones, may be added, subtracted, multiplied, and divided, like them. 166. How do you add, subtract, multiply, and divide complex fractions? |