Simplifying Fractions
Learning Outcomes
- Simplify fractions by finding common factors between the numerator and denominator
- Simplify fractions containing variables
Simplify Fractions
In working with equivalent fractions, you saw that there are many ways to write fractions that have the same value, or represent the same part of the whole. How do you know which one to use? Often, we’ll use the fraction that is in simplified form. A fraction is considered simplified if there are no common factors, other than , in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.Simplified Fraction
A fraction is considered simplified if there are no common factors in the numerator and denominator.- is simplified because there are no common factors of and .
- is not simplified because is a common factor of and .
Equivalent Fractions Property
If are numbers where , then .Simplify a fraction.
- Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.
- Simplify, using the equivalent fractions property, by removing common factors.
- Multiply any remaining factors.
Example
Simplify: Solution: To simplify the fraction, we look for any common factors in the numerator and the denominator.Notice that is a factor of both and . | |
Factor the numerator and denominator. | |
Remove the common factors. | |
Simplify. |
try it
[ohm_question height="400"]146014[/ohm_question]Example
Simplify:Answer: Solution:
We notice that 18 and 24 both have factors of 6. | |
Rewrite the numerator and denominator showing the common factor. | |
Remove common factors. | |
Simplify. |
Try it
[ohm_question height="400"]146015[/ohm_question]Example
Simplify:Answer: Solution:
Rewrite the numerator and denominator, showing the common factors, 8. | |
Remove common factors. | |
Simplify. |
Try it
[ohm_question height="400"]146017[/ohm_question]Example
Simplify:Answer: Solution:
Use factor trees to factor the numerator and denominator. |
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Rewrite the numerator and denominator as the product of the primes. | |
Remove the common factors. | |
Simplify. | |
Multiply any remaining factors. |
Try it
[ohm_question height="400"]146018[/ohm_question]Example
Simplify:Answer: Solution:
Rewrite numerator and denominator showing common factors. | |
Remove common factors. | |
Simplify. |