Explanation:
c/x = d/r
to solve for x means that we want to transform the equation, so that at the end we have
x = ...
or
... = x
for any transformation it is important that we do it always on both sides of the equation.
it is like a mechanical balance : when it is in balance, if you change something on one side, you need to make the same change in the other, or the balance will no longer be balanced.
so, what do we need to do to get x from the bottom side of a fraction to the top side ?
well, we multiply by x :
x×c/x = x×d/r
c = x×d/r
ha ! now we want to remove the "attachments" if x.
the easiest first step is multiply both sides by r :
r×c = r×x×d/r
r×c = x×d
the last "disturbing" element is this "×d" on the side of x. so, we simply divide both sides by d :
r×c/d = x×d/d
r×c/d = x
or short
rc/d = x
and there you have it :
x = rc/d