Rule for multiplying rational numbers The rule for multiplying rational numbers is this:
$\space\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$
Can the rule be proven or is it meant to be taken as a given?
Edit: Where $b\neq 0$ and $d\neq 0$.

An approach to make it more clear might be to seperate each rational into a product of its parts ie. $\frac {a}{b}= \frac{a}{1} \cdot \frac{1}{b}$ and $\frac {c}{d}= \frac{c}{1} \cdot \frac{1}{d}$ then use the commutative property to group the "numerator" fractions and the "denominator" fractions seperately: $\frac{a}{b}\cdot \frac{c}{d}=(\frac{a}{1} \cdot \frac{c}{1})\cdot (\frac{1}{b} \cdot \frac{1}{d})=\frac{ac}{1}\cdot\frac{1}{bd}=\frac{ac}{bd}$. 
