Factoring to Reduce Fractions Help
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.
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 the numerator and denominator are only off by a factor of –1. To reduce this fraction, factor –1 from the numerator or denominator:
In the sum the denominators are off by a factor of –1. Factor –1 from one of the denominators and use the fact that to write both terms with the same denominator.
In the next examples and practice problems a “–1” is factored from the denominator and moved to the numerator.
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.
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.
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).
Find practice problems and solutions at Factoring To Reduce Fractions Practice Problems - Set 4.
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.
LCD = ( x + 3)( x – 1)( x – 3)
The factor x – 3 is “missing” in the first denominator so multiply the first fraction by . An x – 1 is “missing” from the second denominator so multiply the second fraction by .
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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