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Factoring to Reduce Fractions Help

based on 2 ratings
By — McGraw-Hill Professional
Updated on Sep 26, 2011

Factor to Reduce Fractions

Among factoring’s many uses is in reducing fractions. If the numerator’s terms and the denominator’s terms have common factors, factor them then cancel. It might not be necessary to factor the numerator and denominator completely.

Examples

Factoring to Reduce Fractions Examples

Find practice problems and solutions at Factoring to Reduce Fractions Practice Problems - Set 1.

Factor Out Negative One

Reducing a fraction or adding two fractions sometimes only requires that −1 be factored from one or more denominators. For instance in Factoring to Reduce Fractions the numerator and denominator are only off by a factor of  –1. To reduce this fraction, factor –1 from the numerator or denominator:

Factoring to Reduce Fractions

In the sum Factoring to Reduce Fractions the denominators are off by a factor of –1. Factor –1 from one of the denominators and use the fact that Factoring to Reduce Fractions to write both terms with the same denominator.

Factoring to Reduce Fractions

In the next examples and practice problems a “–1” is factored from the denominator and moved to the numerator.

Examples

Factoring to Reduce Fractions Examples

Find practice problems and solutions at Factoring to Reduce Fractions Practice Problems - Set 2.

Cancel Like Terms

To reduce a fraction to its lowest terms, factor the numerator and denominator. Cancel any like factors.

Examples

Factoring To Reduce Fractions Examples

Find practice problems and solutions at Factoring To Reduce Fractions Practice Problems - Set 3.

Factor the Denominator & Find the LCD

Before adding or subtracting fractions factor the denominator. Once the denominator is factored you can determine the LCD.

Examples

Factoring To Reduce Fractions Examples

From the first fraction we see that the LCD needs x – 4 and x + 1 as factors. From the second fraction we see that the LCD needs x – 1 and x + 1, but x + 1 has been accounted for by the first fraction. The LCD is ( x – 4)( x – 1)( x + 1).

Factoring To Reduce Fractions

Find practice problems and solutions at Factoring To Reduce Fractions Practice Problems - Set 4.

"Missing" Factors

Once the LCD is found rewrite each fraction in terms of the LCD—multiply each fraction by the “missing” factors over themselves. Then add or subtract the numerators.

Examples

Factoring To Reduce Fractions Examples

LCD = ( x + 3)( x – 1)( x – 3)

The factor x – 3 is “missing” in the first denominator so multiply the first fraction by Factoring To Reduce Fractions . An x – 1 is “missing” from the second denominator so multiply the second fraction by Factoring To Reduce Fractions .

Factoring To Reduce Fractions

 

Find practice problems and solutions at Factoring To Reduce Fractions Practice Problems  - Set 5.

More practice problems for this concept can be found at: Algebra Factoring Practice Test.

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