# $a/b=c$, how to move the numerator to the right side of the equation

Given an equation of the form $a/b=c$, how do you move $a$, the numerator, over to the other side so that you get $b =c?$ (where $?$ denotes my ignorance of what the right side should look like).

\begin{align*} a/b &= c\\ a &= bc\\ b &= a/c \end{align*}
\begin{align} \frac{a}{b} & = c \\ \\ b \cdot \frac{a}{b} & = c \cdot b \\ \require{cancel} \\ \cancel{b} \cdot \frac{a}{\cancel{b}} & = c \cdot b \\ \\ a & = cb \\ \\ \frac{a}{c} & = \frac{cb}{c} \\ \\ \frac{a}{c} & = \frac{\cancel{c}b}{\cancel{c}} \\ \\ \frac{a}{c} & = b \end{align}
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