To divide fractions, you multiply by the reciprocal of the second fraction.
So, \( \frac{3}{4} \div \frac{2}{5} \) can be rewritten as:
\[ \frac{3}{4} \times \frac{5}{2} \]
Now, multiply the numerators and the denominators:
\[ \frac{3 \times 5}{4 \times 2} = \frac{15}{8} \]
So, \( \frac{3}{4} \div \frac{2}{5} = \frac{15}{8} \).
This can also be expressed as a mixed number:
\[ \frac{15}{8} = 1 \frac{7}{8} \]
Thus, the final answer is \( \frac{15}{8} \) or \( 1 \frac{7}{8} \).