One pattern that arises frequently in working with fractions is
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$\displaystyle \,a\cdot \frac{b}{c}\,$.
It's important to realize that this expression can be
written in many different ways:
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$$
a\cdot\frac{b}{c}
\ =\ \frac{ab}{c}
\ =\ \frac{ba}c
\ =\ b\cdot\frac{a}{c}
\ =\ ab\cdot\frac{1}{c}
\ =\ ba\cdot\frac{1}{c}
\ =\ a\cdot\frac{1}{c}\cdot b
\ =\ \frac{1}{c}\cdot ba
\ =\ b\cdot\frac{1}{c}\cdot a
\ =\ \frac{1}{c}\cdot ab
\ =\ \cdots
$$
Note that a factor in the numerator can optionally be centered next to the fraction.
If everything is moved out of the numerator, then a $\,1\,$ is inserted as a ‘placeholder’.
A factor centered next to the fraction can be moved into the numerator.
A factor in the denominator must stay in the denominator.
Assume that all variables are nonzero, so there's no concern about division by zero.