How to prove an that if $\frac{a}{b}=\frac{c}{d}$ then, $a\cdot \:d=b\cdot \:c$

Question

For example if we simplify $\frac{2+x}{2x}=\frac{1}{2}$ then we get $\left(2+x\right)\cdot \:2=2x\cdot \:1$ (this equation has no solution).

So this means that if $\frac{a}{b}=\frac{c}{d}$ then, $a\cdot \:d=b\cdot \:c$. How can I prove that?

Answer 1

''So this means that if a/b=d/c then, a⋅d=b⋅c. How can I prove that?''

You mean $a/b = c/d$.

Just multiply the equation both with $b$ and $d$. The equality remains valid and gives $ad=bc$.