algebra precalculus - Given $frac {acdot y}{bcdot x} = frac CD$, find $y$.

That's a pretty easy one... I have the following equality : $\dfrac {a\cdot y}{b\cdot x} = \dfrac CD$ and I want to leave $y$ alone so I move "$b\cdot x$" to the other side

$$a\cdot y= \dfrac {(C\cdot b\cdot x)}{D}$$

and then "$a$"

$$y=\dfrac {\dfrac{(C\cdot b\cdot x)}D} a.$$

Where is my mistake? I should be getting $y= \dfrac {(b\cdot C\cdot x)}{(a\cdot D)}$.

I know that the mistake I am making is something very stupid, but can't work it out. Any help? Cheers!

Answer

No mistake was made. Observe that:
$$y=\dfrac{\left(\dfrac{Cbx}{D}\right)}{a}=\dfrac{Cbx}{D} \div a = \dfrac{Cbx}{D} \times \dfrac{1}{a}=\dfrac{Cbx}{Da}=\dfrac{bCx}{aD}$$
as desired.