$$4\frac{1}{5}=\frac{4 \cdot 5 + 1}{5}=\frac{20+1}{5}=\frac{21}{5}$$
$$4\frac{1}{5}:7=\frac{21}{5}:7=\frac{21}{5} \cdot \frac{1}{7}=\frac{21 \cdot 1}{5 \cdot 7}=\frac{3 \cdot 7}{5 \cdot 7}=\frac{3}{5}$$
Ответ: $$\frac{3}{5}$$