$$4\frac{1}{6} : 10 = \frac{4 \cdot 6 + 1}{6} : 10 = \frac{25}{6} : 10 = \frac{25}{6 \cdot 10} = \frac{25}{60} = \frac{5}{12}$$.
Ответ: $$\frac{5}{12}$$.