To divide the fraction \(-\frac{10}{11}\) by \(-\frac{2}{5}\), we can multiply by the reciprocal of the second fraction:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
The negatives cancel out:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now we simplify \(\frac{50}{22}\) by finding the greatest common divisor of 50 and 22, which is 2:
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Thus, the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
\[ \frac{25}{11} \]
Looking at the provided responses, the correct answer is:
2311