3. Reduce 6531, to its equivalent improper fraction. Anf. 2163 I 7 Anf. 12410 19 To reduce a whole number to an equivalent fraction, having a given denominator. RULE. Multiply the whole number by the given denominator: Place the product over the faid denominator, and it will form the fraction required. EXAMPLES. 1. Reduce 6 to a fraction, whofe denominator shall be 8. 6x8=48, and 48 the Anf.-Proof 45 = 48÷8= 6. 2. Reduce G 2. Reduce 15 to a fraction, whose denominator fhall be 12. Anf. 180 To reduce an improper fraction to its equivalent whole, or mixed number. RULE.* Divide the numerator by the denominator; the quotient will be the whole number, and the remainder, if any, will be the numerator to the given denominator. EXAMPLES. 1. Reduce 293 to its equivalent whole, or mixed number. 8)293(36 Anf. 24 53 48 Or, 293293+8=361⁄2 as before. 5 2. Reduce 2163 to its equivalent whole, or mixed number. 27 Anf. 1277. 3. Reduce 45 to its equivalent whole number. CASE V. Anf. 9. To reduce a compound fraction to an equivalent fimple one. RULE. Multiply all the numerators continually together for a new numerator, and all the denominators, for a This rule is evidently the reverse of cafe 2d. new new denominator, and they will form the fimple fraction required. If part of the compound fraction be a whole or mixed number, it must be reduced to an improper fraction, by cafe 2d, or 3d. If the denominator of any member of a compound fraction be equal to the numerator of another member thereof, these equal numerators and denominators may be expunged, and the other members continually multiplied, (as by the rule) will produce the fractions required in lower terms. EXAMPLES. 1. Reduce of of of to a fimple fraction. IX2X3X4 2X3 X4 X5 == the Aafwer. Or, by expunging the equal numerators and denomi nators, it will give as before. 2. Reduce of off of 1 to a fimple fraction. 3X4×5X11 =4000 = 14 Anf. Or, by expung. 4×5×6×12 660 ing the equal numerators and denominators, it will be 3XII 6×12 as before. To reduce fractions of different denominators to equivalent fractions, having a common denominator. RULE Multiply each numerator into all the denominators, except its own, for a new numerator, and all the the denominators into each other, continually, for a common de: ominator. EXAMPLES. 1. Reduce, and to equivalent fractions, having a common denominator. 40 6 4 Therefore the new equivalent fractions are 185 and 10, the Anf. 2 3 2. Reduce, 4, and to fractions having a common denominator. 5 ST, FITT TITT TITI. of 5, 74, and, to a common de 936 1040 14508 432 Ans. 145 78729 7877, 7875° RULE II. To reduce any given fractions to others, which fhall have the leaft common denominator. 1. By Prob. 2, page 70, find the leaft common multiple of all the denominators of the given fractions, and it will be the common denominator required. 2. Divide the common denominator by the denominator of each fraction, and multiply the quotient by the numerator, and the product will be the numerator of the fraction required. EXAMPLES. 24÷3X18 the firft numerator; 24÷4×3=18 the fecond numerator; 24-8x7=21 the third numerator. Whence, the required fractions are 24, 14, 24.. CASE VII. 8 To reduce a fraction of one denomination to the fraction of another, but greater, retaining the fame value. RULE. Reduce the given fraction to a compound one by comparing it with all the denominations between it and that denomination you would reduce it to; laftly, reduce this compound fraction to a tingle one, by cafe 5th, and you will have a fraction of the required denomination, equal in value to the given fraction. EXAMPLE S. 1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of of; which, reduced by cafe 5th, will be 3XIXI=3. And 5 X 12 X 20=1200—35. 2. Reduce |