Reducing Fractions
Pronunciation: /rɪˈdus.ɪŋɡ ˈfræk.ʃənz/ Explain
To reduce a fraction is to cancel
common factors
in the fraction.
Example 1
Step | Equation | Description |
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
Step | Equation | Description |
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
Step | Equation | Description |
1 | | This is the fraction to reduce. |
2 | |
Start by finding the prime factorization of the numerator and the denominator.
x^{2} - x - 2 =
( x + 1 )( x - 2 ),
x^{2} + 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 |
References
- 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.)