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 E B R A. 83 A L G ties, exprefles the quotient of the former divided by the Rule. Multiply each numerator, feparately taken, into all the denominators but its own, and the produds latter. Thus, a-- b -r- a — xis the quotient oi a b, (hall give the new numerators. Then multiply all the divided by a — x. denominators into one another, and the produd (hall give the common denominator. Thus, Chap. V. 0/'Fractions. —» are refpedively equal to In the laft chapter it was faid, that the quotient of any The fradions 4-’ C quantity a, divided by b, is exprelfed by placing a a- thefe fradions --bed -’ bed bed -r—f bed which have the bove a fmall line, and b under it, thus, —. 0 Thefe denominator bed. And the fradions y, y, £, are quotients are alfo called frattivns; and the dividend, or fame refpedively equal to thefe £•§, £§• quantity placed above the line, is called the numerator of the fraction, and the divifor, or quantity placed unPROBLEM IV. der the line, is called the denominator, 7b A d d and Subtract fradions. “ If the numerator of a fradion be equal to the de“ nominator, then the fradion is equal to unity. Thus, Rule. Reduce them to a common denominator, and add or fubtrad the numerators; the fum or difference “ and — are equal to unit. If the numerator is fet over the common denominator, is the fum or re*? greater than the denominator, then the fradion is mainder “ greater than unit.” In both thefe cafes, the fradion a c required. % d a de--bce--dlb a is called improper. But “ if the numerator is lels than “ the denominator, then the fradion is lefs than unit,” b d e b de » b d 2 3 _ 8 + 9 __ 17 11 _3 and is called proper. Thus, is an improper frac- ad—be. b d ’ ■$ 4 12 12 4 J tion; but-3-and-j- are proper fradions. A mixt _ 9—8 _ J_. j_ 3_ _ 16—-1; _ J_. 12 12 ’ 5 4 20 20 ’ a quantity is that whereof one part is an integert and the x _ 3 X ■— 2 X _ X ■ other a frattion. As 3 -j- and 5 and a -13 6 6‘ PROBLEM V. PROBLEM I. To Multiply fradions. To reduce « M 1 x t quantity /<? «» I m p a o P E R Fraction. Rule. Multiply their numerators one into another to the numerator of the produd ; and their denoRule. Multiply the part that is an integer by the de- obtain minators multiplied into one another (hall give the denominator of the fradional part; and to the produd nominator of the produd. Thus, add the numerator ; under their fum place the former denominator; 5 Thus1 2 j- reduced to an improper1 fradion gives V» ab+a*, a ax a1 x* a +.a-r— If a mixt quantity is to be multiplied, firfl: reduce it b b ; and a — x + x = —=—. x to the form of a fradion (by Prob. I.) And, if an integer is to be multiplied by a fradion, you may reduce PROBLEM II. it to the form of a fradion by placing unit under it. To reduce in Improper fraction to a Examp. 5 JLx J- = LI x JL = iJ-. Mixt Qu a n t i t y. 3 4 3 4 12 Rule. Divide the numerator of the fradion by the denominator, and the quotient (hall give the integral PROBLEM VI. part; the remainder fet over the denominator (hall To Divide Fradions. be the fradional part. Rule. Multiply the numerator of the dividend by the Thus il= 2 a2±£. = * + ll. denominator of the divifor, their produd (hall give S S b b the numerator of the quotient. Then multiply the denominator of the dividend by the numerator of the PROBLEM III. divifor, and their produd (hall give the denominator. To reduce frafiions of different denominations to Thus, ± (if. J_ J_( 35 . fratiions of equal value that Jhall have the fame de5 / 3 V12’ 7/8 V 24’ d) b c b’ nominator. To,