# Reducing Fractions

Pronunciation: /rɪˈdus.ɪŋɡ ˈfræk.ʃənz/ Explain

To reduce a fraction is to cancel common factors in the fraction.

Example 1
StepEquationDescription
1 This is the fraction to reduce.
2 Start by finding the prime factorization of the numerator and the denominator. 12 = 2 · 2 · 3, 15 = 3 · 5. Use the substitution property of equality to substitute the prime factorization in for the original value.
3 Cancel any common factors.
4 Calculate the numerator and denominator. The fraction is reduced.
5 We can now conclude that .
Table 1

Example 2
StepEquationDescription
1 This is the fraction to reduce.
2 Start by finding the prime factorization of the numerator and the denominator. 84 = 2 · 2 · 3 · 7, 70 = 2 · 5 · 7. Use the substitution property of equality to substitute the prime factorization in for the original value.
3 Cancel any common factors.
4 Calculate the numerator and denominator. The fraction is reduced.
5 We can now conclude that .
Table 2

Example 3
StepEquationDescription
1 This is the fraction to reduce.
2 Start by finding the prime factorization of the numerator and the denominator. x2 - x - 2 = ( x + 1 )( x - 2 ), x2 + 4x + 3 = ( x + 1 )( x + 3 ). Use the substitution property of equality to substitute the prime factorization in for the original value.
3 Cancel any common factors.
5 We can now conclude that .
Table 3
1. McAdams, David E.. All Math Words Dictionary, reduce a fraction. 2nd Classroom edition 20150108-4799968. pg 153. Life is a Story Problem LLC. January 8, 2015. Buy the book

• McAdams, David E.. Complex Fraction. allmathwords.org. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/c/complexfraction.html.

McAdams, David E. Reducing Fractions. 5/3/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/reducingfractions.html.

### Revision History

5/3/2019: Changed equations and expressions to new format. (McAdams, David E.)