Explanation:
A "reduced" fraction is one that has mutually prime numerator and denominator. That is, the numerator and denominator have no common factors.
A fraction is "reduced" by canceling common factors from numerator and denominator. If "a" is a factor common to the numerator and denominator of a fraction, that fraction can be written with "a" canceled from each:
[tex]\dfrac{ab}{ac}=\dfrac{a}{a}\cdot\dfrac{b}{c}=1\cdot\dfrac{b}{c}=\dfrac{b}{c}[/tex]
Here is a numerical example:
[tex]\dfrac{2}{4}=\dfrac{2\cdot 1}{2\cdot 2}=\dfrac{2}{2}\cdot\dfrac{1}{2}=\dfrac{1}{2}[/tex]
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A numerator factor and a denominator factor "cancel" because their ratio is 1, the identity element for multiplication. Anything times 1 is just that thing.
