Rule 10: Reducing Fractions

To reduce a simple fraction, follow the following three steps:

1.: Factor the numerator.
2.: Factor the denominator.
3.: Find the fraction mix that equals 1.

For example, reduce .

First: Rewrite the fraction with the numerator and the denominator factored.

Note all factors in the numerator and denominator are separated by multiplication signs.

Second: Find the fraction that equals 1. can be written which in turn can be written which in turn can be written .

Third: We have just illustrated that tex2html_wrap_inline101 . Although the left side of the equal sign does not look identical to the right side of the equal sign, both fractions are equivalent because they have the same value. Check it with your calculator. and . This proves that the fraction can be reduced to the equivalent fraction .

Example 1: Reduce the fraction .

Answer. Factor the numerator and factor the denominator and look for the fractions in the mix that have a value of 1.

and

The fraction has been reduced into the equivalent fraction .
Now prove to yourself with your calculator that both fractions are equivalent. When you divide 120 by 180, you will get the same answer as when you divide 2 by 3.