Rule 10: Reducing Fractions

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

Factor the numerator.
Factor the denominator.
Find the fraction mix that equals 1.

For example, reduce tex2html_wrap_inline89 .

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. tex2html_wrap_inline93 can be written tex2html_wrap_inline95 which in turn can be written tex2html_wrap_inline97 which in turn can be written tex2html_wrap_inline99 .

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. tex2html_wrap_inline103 and tex2html_wrap_inline105 . This proves that the fraction tex2html_wrap_inline89 can be reduced to the equivalent fraction tex2html_wrap_inline99 .

Example 1: Reduce the fraction tex2html_wrap_inline111 .

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




The fraction tex2html_wrap_inline111 has been reduced into the equivalent fraction tex2html_wrap_inline119 .
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.

If you would like to see another example, click on the word Example.

Work the following problems and click on Answer to check your results.

Problem 1: Reduce the fraction tex2html_wrap_inline121 .


Problem 2: Reduce the fraction tex2html_wrap_inline123 .


Problem 3: Reduce the fraction tex2html_wrap_inline125 .


Problem 4: Reduce the fraction tex2html_wrap_inline127 .


Problem 5: Reduce the fraction tex2html_wrap_inline129 .


Menu Back to Simple Fractions

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[Division] [Building Fractions] [Addition] [Subtraction]
[Order of Operation]

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Author: Nancy Marcus

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