Answer
See proof.
Work Step by Step
Take 2 rational numbers, $\dfrac{a}{b}$ and $\dfrac{c}{d}$ where $a,b,c,d$ are integers and neither $b$ nor $d$ is equal to 0. The product of these two numbers is $\dfrac{ac}{bd}$, and $ac$ and $bd$ are integers. By definition, this fraction is rational. Thus, the product of two rational numbers is also rational.
