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

$$\begin{align*} a/b &= c\\ a &= bc\\ b &= a/c \end{align*}$$

I know this has been answered but here is it worded. You multiply the denominator out by multiplying both sides so: a/b = c becomes a/bb = cb. As you are multiplying the fraction by the denominator the denominator and the multiplier cancel out and you are left with a = bc. You cannot get rid of a letter but if you wanted b on one side then you would simply move c, to do this you factorise so its a = b(c). You then divide both sides by c, so then a/c = (b(c))/c. Then the c on the numerator and denominator cancel out so you will be left with a/c = b or rearrange to b = a/c.