Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/471

 arithmetics;. 38? Examples. Examp. What is the value of ^L. ? Reduce % and £ to a common denominator, 3 20 4X5=20, the common denominator^ 3X5=15, the firft numerator. 4)60(15$. Here confider 4; L. as ekprelEng the the fecond numerator. 4 fourth part of three pounds Sterling ; So the4X4=16, fra&ions are and -i-J. — fo reduce L 3, the numerator, to ftiil- When thenewdenominator of one fraction happens to be 20 lings, arid divide by. the denominator 4; an aliquot part of the denominator of another fraction, 20 arid as nothing remains, the quot, viz. the former may be reduced to the fame denominator — jy filillings, is the value complete. with the latter, by multiplying both its numerator and denominator by the number which denotes how often the lefler denominator:=:is contained in the greater. Thus, -f- d" rr -rr + -rv 3 is Contained in 12 four times; fo multiply The reafon of this rule is the fame with that in the Here2 and 3 by 4, and preceeding problem. It is by the pra&ice of this pro- bothAgain, = you have blem that remainders in the rule of three are reduced to Sometimes too, the fra&ion that has the greater devalue. ' ( may, in like manner, be reduced to the fame Pros. VII. To reduce a fra&ion to its Joweflf terms. nominator Rule. Divide both numerator and denominator by denominator with =: that which has the lefler, by divifion. their greateft common divifor ; the two quots make the Thus, i. + T T + T* new fra&ion. And 4|+^ reafon ofr+theTv=A+A+A. above rule for reducing fractions The greateft common divifor of the numerator and to The a common denominator is evident from Corollary II.; denominator of a fraition is found by the following Rule. Divide the greater of thefe two numbers by for both numerator and denominator of every fraftion the lefler; and again divide the divifor by the remain- are multiplied by the fame number, or by the fame numder ; and fo on, continually, till o remains. The laft bers. After fra&ions afe reduced to a common denominator, divifor is their greateft common divifor. they may frequently be reduced to lower terms, by diEx amp. Reduce 9^4 to its loweft terms. Firft find the greateft common divifor of the numera- viding all the numerators, and alfo the common denominator, by any divifor that leaves no remainder, or by tor and denominator, as follows cutting off an equal number of ciphers from both. 784)952(1 784 Addition of Vulgar Frati ions. 168)784(4 Rule I. If the given fractions have all the fame 672 denominator, add the numerators, and place the fum 0ver the denominator. 1x2)168(1 Ex. 1. What is the fum of 4 + 4 ? Anf. 4. 112 2. What is the fum of A + rr * -Anf. = 4, by Prob. VII. Greateft common divifor 50) 112(2 Rule II. If the given fraftions have different deno1X2 minators, reduce them to a common denominator, by Q Prob. VIII. then add the numerators, and place the . to its low- fum over the common denominator. Then proceed to reduce the given( IfraftibW cft terms, by dividing both numerator and denominator Ex. What is the fum of 4 + 4 ? by 56, the greaft common divifor. 4-+ 4 = 44+—44,44- by Prob. VIII. 56)784(14 new num. 5^)952(17 new denom. RuleandIII.44 +If44mixt numbers be given, or if mixt 56 56 numbers and fradtior.s be given, reduce the mixt numbers to improper fractions, by Prob. II ; then reduce 224 392 the fractions to a common denominator, by Prob. VIII. 224 392 and add the numerators. Ex. What is the fum of 744"5t(°) ', 74+5t=V by Prob. II. VIII. and V +.y=+V> n + n, by Prob. Pros. VIII. To reduce fractions of different denoand 44+14 = Vt = 13A> by Prob. I. minators to a common denominator. Rule. Multiply the denominators continually for mixt numbers, or mixt numbers and fractions, ' the common denominator ; and multiply each numerator areWhen given, you may, with greater expedition, work by into a the d nominators, except its cwh, for the frivc- the following rule, viz. reduce only the fractions to a ral nu ra r. Vol. I. No. 17. 33 common denominator, and add5 Fthe fum of the frattionsto