To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction.
So, \( \frac{3}{8} \div \frac{4}{5} \) is the same as \( \frac{3}{8} \times \frac{5}{4} \).
Now, multiply the fractions:
\[ \frac{3 \times 5}{8 \times 4} = \frac{15}{32} \]
Thus, \( \frac{3}{8} \div \frac{4}{5} = \frac{15}{32} \).