If $\frac{a}{b} = \frac{3}{4}$, $\frac{b}{c} = \frac{5}{6}$, and $\frac{c}{d} = \frac{7}{8}$, find $a:d$.

Combine: $a:b = 3:4$, $b:c = 5:6$, $c:d = 7:8$. Make $b$ common: multiply first by 5 to get $15:20$; second by 4 to get $20:24$ so $a:b:c = 15:20:24$. Now make $c$ common: $24$ and $7$ combine to $168$; $c:d = 7:8 = 168:192$. Thus $a:d = 15:192 = 5:64$ after simplification.