Numbers and Quantities
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Canceling, simplifying or reducing a fraction is the opposite of expanding a fraction. You will cancel fractions throughout your years in school, so you should rehearse this until it’s second nature to you!
When you cancel, the value of the fraction stays the same. For that reason, you can set an equal sign between the two expressions, even though they look different.
Rule
To simplify by canceling
- 1.
- Factorize the numerator.
- 2.
- Factorize the denominator.
- 3.
- Order the factors by value (optional).
- 4.
- Cancel one common factor in the numerator and the denominator at a time until there are no more common factors.
- 5.
- Multiply the remaining factors in the numerator.
- 6.
- Multiply the remaining factors in the denominator.
Example 1
Simplify the fraction by canceling.
because
Example 2
Simplify the fraction by canceling.
because
Example 3
Simplify the fraction by canceling.
because
Example 4
Simplify the fraction by canceling.
because
Example 5
Simplify the fraction by canceling.
because
Example 6
Simplify the fraction by canceling.
because
Example 7
Simplify the fraction by canceling.
because
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