ALGEBRA. 



ttiinator of each fraction by the denomi- 

 uators of all the rest, divided respec- 

 tively by their greatest common measure ; 

 and the tractions will be reduced to a 

 common denominator, in lower terms than 

 they would have been by proceeding 1 ac- 

 cording to the former rule. 



Thus, , , , reduced to a com- 



m x m y in z 



ay: b x x 



uion de nominator, are 



E n _ 



' b d bd bd 



cxtf 



mxyz mxyz 



ON T!U ADDITION AND SUBTRACTION OF 

 FBACTION5. 



If the fractions to be added have a com- 

 mon denominator, their sum is found by add- 

 ing the numerators together, and retaining the 

 common denominator. Thus, 



a c q-j-c 



b + h ~ : b ' 



If the fractions have not a common de- 

 nominator, they must be transformed to 

 others of the same value, which have a 

 common denominator, and then the addi- 

 tion may take place as before. 



a c ad be a d-\-b c 



b d b d b d b d 



Ex 3 \ _ / j __ 



' + b~a l b i ' T ' A> 

 a H--f-^ -'" 



Ex.4.a+=-f=. Here 



a is considered as a fraction whose deno- 

 niinator is unity. 



If txo f:-a, n nmmon tlenimi- 



nator, their difference it found by taking!' the 

 difference of the numeratorg f and retaining 

 the common denominator. Thu.-, 



If they have not a common dcnomina* 

 tor, they must be transformed to others 

 of the same value which have a common 

 denominator, and then the subtraction 

 may lake place its abve. 



Ex. 3. a 



c d ab c d a f> c d 



c-\-d a i ad l> c-\-b d 



*' b c d b c b d b c ii d 



a c a d b c b d 



bcbd ' 



The sign of b d is negative, because 

 every part of the latter traction is to be 

 taken from the former. 



ON THE MULTIPLICATION AND DIVISION 

 OF FBACTION8. 



To multiply a fraction by any quantity, 

 multiply the numerator by that quantity, and 

 retain the denominator. 



* >T -Xc=* ^--. For if the quantity 



o b 



to be divided be r times as great as be- 

 fore, and the divisor the same, the quo- 

 tient must be c times as great. 



The product of two fractions is found by 

 mu/tipfyinif tlir numerators together for a new 

 numerator, and t/ie denominators for a new 

 denominator. 



Let and be the two fractions; then 

 6 d 



multiplying the equal quantities and a-, 



by b, o=A a- ; in the same manner, r -/y; 

 therefore a c = b dxy\ dividing these 

 equal quantities, a c and b d x y, by b d, 



To divide a fraction by any quantity, 

 multiply the di-nnn,inator by that quantity, and 

 retain the numerator. 



The fraction 7- divided by r, is. Bc- 

 b be 



a a e , c ., . . a 



cause -:-= , and act h partot tins is r~5 

 b b c * ' 



the quantity to be divided, beinga r h part 

 i>f what it was before, and the divisor the 

 une. 



Tlc result is the same, whetliert 'ede- 

 nominator is multiplied by tin- quantity, 

 or the- numerator divided by it. 



l.-t tbe fraction be ; if the dcn< mi- 



9 m 



