Let $a,b,c,d \in \mathbb{Z}-\{0\}$ A mnemonic device for calculating

$$\frac{a}{b} \div \frac{c}{d}$$

is KFC. This stands for "keep-flip-change". This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem. Thus, the expression above becomes

$$\frac{a}{b} \cdot \frac{d}{c}.$$

This yields that

$$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b} \cdot \frac{d}{c}=\frac{ad}{bc}.$$