Find the smaller angle between the hour and minute hands of a clock at $8:18$.

The formula to calculate the angle $\theta$ between the hour and minute hand is:
$$\theta =\left|30H-\frac{11}{2}M\right|$$

Where $H=8$ and $M=18$.

$$\theta =\left|30\times 8-\frac{11}{2}\times 18\right|$$

$$\theta =|240-11\times 9|$$

$$\theta =|240-99|=141^{\circ }$$

Since $141^{\circ }\le 180^{\circ }$, it is the smaller angle.