To divide by a fraction, you multiply by its reciprocal. So, to divide \( \frac{10}{11} \) by \( \frac{2}{5} \), you can follow these steps:
- Take the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \).
- Multiply \( \frac{10}{11} \) by \( \frac{5}{2} \):
\[ \frac{10}{11} \times \frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
- Simplify \( \frac{50}{22} \). Both the numerator and the denominator can be divided by 2:
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Therefore, \( \frac{10}{11} \div \frac{2}{5} = \frac{25}{11} \).