To divide the fractions \( \frac{2}{5} \) by \( \frac{8}{25} \), you can multiply by the reciprocal of the second fraction.
The reciprocal of \( \frac{8}{25} \) is \( \frac{25}{8} \).
So,
\[ \frac{2}{5} \div \frac{8}{25} = \frac{2}{5} \times \frac{25}{8} \]
Now, multiply the fractions:
\[ \frac{2 \times 25}{5 \times 8} = \frac{50}{40} \]
Now, simplify \( \frac{50}{40} \). Both the numerator and the denominator can be divided by 10:
\[ \frac{50 \div 10}{40 \div 10} = \frac{5}{4} \]
Thus, \( \frac{2}{5} \div \frac{8}{25} = \frac{5}{4} \).