Reducing Fractions

Pronunciation: /rɪˈdus eɪ ˈfræk ʃən/ ?

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)=4/5Calculate the numerator and denominator. The fraction is reduced.
512/15=4/5We 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)=6/5Calculate the numerator and denominator. The fraction is reduced.
584/70=6/5We 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.
5(x^2-x-2)/(x^2+4x+3)=(x-2)/(x+3),x!=1We can now conclude that x^2-x-2)/(x^2+4x+3)=(x-2)/(x+3),x!=1.
Table 3

More Information

  • McAdams, David. Complex Fraction. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Complex%20Fraction.

Cite this article as:


Reducing Fractions. 2009-01-15. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/reducingfractions.html.

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2009-01-15: Initial version (McAdams, David.)

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