REDUCTION OF VULGAR^fRACTIONS. 69 



EXAMPLES. 



1. Reduce -{-y y and -^-, to equivalent fractions, having 

 a common denominator. 



1X5X7 = 35 the new numerator for 4-. 

 3X2X7 = 42 do. for .|.• 



4X2X5=40 do. for i. 



2X5X7 = 70 the common denominator. 

 Therefore the new equivalent fractions are 4---, ~~, and 

 j~y the answer. 



2. Reduce ^j yj |- ^i"^<^ |> ^o fractions, having a com- 

 men denominator/ Ans. ^±, ^|^, ^^, -iXf 



3. l\.educe y, -| of y, 5y and y*^, to a common denomi- 



4. Reduce —, ^- of i-^, y*— and ^ to a common de- 

 nommator. iinb. yToTTj tt^ttj TTTTo"' Td^oT^-' 



RULE II. 



^0 reduce any givsfi fractions to others^ nxjJAch shall have ih^ 

 least common denominator, 



1. Find the least common multiple of all the denomina- 

 tors of the given fractions, and it will be the common de- 

 nominator required. 



2. Divide the common denominator by the denomina- 

 tor of each fraction, and multiply the quotient by the nu- 

 merator, and the product wiU be the numerator of tlie- 

 fraction required, 



EXAMPLES. 



lion are multiplied by the very sarn§ number, and consequently 

 their values are not altered. Xhus in the fust example : 



X5X7 3 



2 I X5X7 5 



X2X7 



X?X5 



X2X5 



X2X7 7 



In the 2d rule, the common denominator is a multiple of all 

 the denominators, and consequently will divide by any of them j- 

 it is manifest, therefore, that proper parts may be talicn for all th ■ 

 aumeratgrs as required. 



