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I use the rule that:

(a/b)x(c/d)=(ab/cd)

and

(a/b)divided by(c/d)= (ac/bd)

The reason they change is that when you have to find the lowest common factor, you not only have to change the denominator, but also the numerator.

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Q: Why do denominators change as you simplify the fraction?
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How you multiply fractions?

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