One pattern that arises frequently in working with fractions is
$\displaystyle \,a\cdot \frac{b}{c}\,$.
It's important to realize that this expression can be
written in many different ways:
$$
\cssId{s6}{a\cdot\frac{b}{c}}
\cssId{s7}{\ =\ \frac{ab}{c}}
\cssId{s8}{\ =\ \frac{ba}c}
\cssId{s9}{\ =\ b\cdot\frac{a}{c}}
\cssId{s10}{\ =\ ab\cdot\frac{1}{c}}
\cssId{s11}{\ =\ ba\cdot\frac{1}{c}}
\cssId{s12}{\ =\ a\cdot\frac{1}{c}\cdot b}
\cssId{s13}{\ =\ \frac{1}{c}\cdot ba}
\cssId{s14}{\ =\ b\cdot\frac{1}{c}\cdot a}
\cssId{s15}{\ =\ \frac{1}{c}\cdot ab}
\cssId{s16}{\ =\ \cdots}
$$
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.