Unit 7  Objective 1  Equivalent Fractions
Multiplying or dividing both the numerator and
denominator of a fraction by the same numbers, except zero, results in a fraction that is
equivalent to the original fraction. Equivalent means they represent the same
number. We want to reduce the fraction to lowest terms or simplest terms.
Note:
because and
if we have x/y the negative can be with the numerator as in x/y or
in the denominator as in x/y but the negative cannot be with both. General procedure for
reducing a fraction is to factor numerator and denominator then divide out factors they have in common. 

Examples:
1. 
Reduce to lowest
terms
The numerator and denominator have a common
factor of 8xyz^{3}. We can rewrite the fraction as
Since 8xyz^{3}
cancel we are left with 3x/y^{2} which is equivalent to
which is equal to (3x)/y^2


2. 
Reduce
Notice that x^{2} is
a factor in the numerator but it is not a factor for both terms in the denominator.
We need to factor the denominator which is the difference of two squares. The
numerator cannot be factored farther.
We can now cancel the x  4
term and we are left with 2x^{2}/(x+4) as an equivalent
fraction. (answer: (2x^2)/(x+y) 

Note:
(factor out a (1) changes the signs) 

Examples:
1. 
Reduce to lowest
terms
We do not have a common factor for the
numerator and denominator so we have to factor them separately.
Notice that (5  b) and (b
 5) differ by a negative 1 so we can rewrite either one.
We can now cancel the quantity (b
 5).
= a/3


2. 
Reduce to lowest terms.
Notice that (2x  1) and (1
 2x) differ by a negative 1 so we can rewrite either one..
We can now cancel the quantity (1 
2x).
or


Unit 7 Outline // Course Outline // Home Page
Copyright © 1996 by B. Chambers and P. Lowry. All Rights
Reserved.