# Proportionality

This follows from the fact that for all rational numbers x, y and z, if x = y, then xz = yz. So, we start with $x=\frac{a}{b}$ and $y=\frac{a'}{b'}$ and multiply both sides of $x = y$ by $z = bb'$. It follows that $\frac{a}{b}bb'=\frac{a'}{b'}bb'$. Since $\frac{a}{b}b=a$ and $\frac{a'}{b'}b'=a'$, we get $ab'=a'b$.