JIEDUCTION OF VULGAR FRACTIONS. 6'f 



CASE IV, 



To reduce a whole number to an equivalent fraction^ having a 

 piven denominator. 



RULE.* 



Multiply the whole number by the given denominator^ 

 and place the product over the said denominator, audit 

 v/ill form the fraction required. 



EXAMPLES. 



J. Reduce 7 to a fraction, whose denominator shall be 9, 



7X9:^:63, and y the answer. 



And y =z63-^9=r7 the proof. 



1. Reduce 13 to a fraction, whose denominator shall 



Ke 12. Ans. Vr'- 



3. Reduce 100 to a fraction, whose denominator shall 



be 90. Ans. 



9 O G 



'9 o 



CASE V. 

 To redu;:e a compound fraction to an equivalent single one, 



RULE.f 



Multiply all the numerator? together for the numerator, 

 and all the denominators together for the denominator, and 

 they will form the single fraction required. 



^ If 



* Multiplication and division are here equally used, and conse- 

 quently the result is the same as the quantity first pro])osed. 



f That a compound fraction may be represented by a single 

 one is very evident, since a part of a part must be equal to some 

 part of the whole. The truth of the rule for this reduction may 

 be shewn as follows. 



I^et the compound fraction to be reduced be y of t. Then y 

 of 4=4-r3=TT? and consequently ^ of 4=AX2=:xt the same 

 as by the rule, and the like will be found to be true in all cases. 



