Reducing Fractions

Pronunciation: /rɪˈdus.ɪŋɡ ˈfræk.ʃənz/ Explain

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

Example 1
StepEquationDescription
112/15This is the fraction to reduce.
212/15=(2*2*3)/(3*5) 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(2*2*3)/(3*5)=(2*2)/(5)Cancel any common factors.
4(2*2)/(5)=4/5 Calculate the numerator and denominator. The fraction is reduced.
512/15=4/5 We can now conclude that 12/15=4/5.
Table 1

Example 2
StepEquationDescription
184/70This is the fraction to reduce.
284/70=(2*2*3*7)/(2*5*7) 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(2*2*3*7)/(2*5*7)=(2*3)/(5)Cancel any common factors.
4(2*3)/(5)=6/5 Calculate the numerator and denominator. The fraction is reduced.
584/70=6/5 We can now conclude that 84/70=6/5.
Table 2

Example 3
StepEquationDescription
1(x^2-x-2)/(x^2+4x+3)This is the fraction to reduce.
2(x^2-x-2)/(x^2+4x+3)=((x+1)(x-2))/((x+1)(x+3)) 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((x+1)(x-2))/((x+1)(x+3))=(x-2)/(x+3),x!=1Cancel any common factors.
5x^2-x-2)/(x^2+4x+3)=(x-2)/(x+3),x!=1 We can now conclude that x^2-x-2)/(x^2+4x+3)=(x-2)/(x+3),x!=1.
Table 3

References

  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

More Information

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

Cite this article as:

 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.

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Revision History

5/3/2019: Changed equations and expressions to new format. (McAdams, David E.)
3/29/2019: Added vocabulary links. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
1/15/2009: Initial version. (McAdams, David E.)

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