REDUCTION OF FRACTIONS Reduction of fractions changes their forms without altering their values. We may reduce whole numbers to fractions of the same values. in As the denominator is to be 18, and since 189 × 2, we multiply both terms by 2. 1 indicates equal parts half as large as those in 7, but twice as many parts are taken as in 7. 1. Write five proper fractions; five improper fractions; five mixed numbers. 2. Write five simple fractions; five complex fractions; five compound fractions. 3. Which is the larger amount: of anything or 254 of it? 11⁄2 of anything or 15 of it? 16 9 90 or of anything? 90 100 pk. or 15 pk? 6 Give the reason in each case, or show by drawing. 4. Which is larger: of or 4×2? By how much? REDUCING INTEGERS TO FRACTIONS 1. Reduce 123 to a fraction with 20 as its denominator. 2. Change 17 to a fraction with 29 as its denominator. 3. Reduce 7, 9, 27, and 40 to elevenths. 4. Reduce 2, 207, 440, and 9 to fractions with 109 as denominator. 5. Reduce 22, 47, 69, and 100 to ninety-thirds. 6. Reduce 217, 613, 927, and 4 to thirteenths. REDUCING MIXED NUMBERS TO FRACTIONS 7. Reduce 74 to an improper fraction. Since in 1 there are 9 ninths, in 7 there are 7 times 9 ninths. 7x=63, 63+4= $7. 9 9 9 add the fraction in the mixed number. 9. Reduce to improper fractions : a. 734. f. 64. 75 5280 k. $4%. p. 51 mi. c. 16. b. 1841. 9. 72. 7. 183 pk. h. 93. m. 103 ed. 9. 8211 hr. d. 14%. e. 71%. i. 163. n. 1818 sq. ft. r. IMPROPER FRACTIONS 1. Reduce 29 to a fraction having 12 for its denominator. 2. Reduce 243 to a fraction having 3 for its denominator. 3. Reduce 7, 23, and 101 to fractions having 18 for denominator. 4. Reduce to improper fractions : a. 39ğ. d. 67631. g. 847-385. j. 3758. m. 17895. b. 112. e. 46413. h. 675187. k. 37584. c. 42714. f. 367184. i. 1495. 7. 483457. MIXED NUMBERS 5. Reduce 1 to a mixed number. 111=117 ÷ 5 = 233 5)117 n. 125g. o. 10.75 == 100 Since 5 fifths 1, 117 fifths equal as many 1's as 5 is contained times in 117. 5 is found in 117 23 times. REDUCTION OF DECIMALS TO COMMON FRACTIONS 1. Reduce .95 to a common fraction at its lowest terms. We divide 95 and 100 by the common factor 5. 2. Reduce .0125 to a common fraction at its lowest terms. We divide 125 and 10000 by 5, 5, and 5, the common factors of the numerator and denominator. 3. Reduce to a common fraction at lowest terms: It is very seldom helpful to change a decimal to a common fraction with a denominator larger than one hundred. It is more often helpful to change a common fraction to a decimal than to change a decimal to a common fraction. 4. What is the ratio of 1 to .25? of .25 to 1? 5. What is the ratio of 1 to .3? of .3 to 1? 6. What is the ratio of 1.25 to 10? of 10 to 1.25? 7. What is the difference between a. $575 and $.50? c. $1 and $.66+? b. $3.75 and $1.375? d. $2.50 and $1.166+? 8. What is the sum of $12.33+ and $12.66+ ? 9. Make drawings to illustrate 4, 5, and 6. There is one decimal place in the dividend, and none in the divisor; therefore, there is one decimal place in the quotient. A common fraction whose denominator contains any factor other than 2 or 5 cannot be reduced to a pure deci- · mal without remainder, unless its own numerator contains that other factor. The decimals with remainders in the common fraction form, or of that value, are "approximate decimals. |