To divide the fractions \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply the first fraction by the reciprocal of the second.
The reciprocal of \(-\frac{2}{5}\) is \(-\frac{5}{2}\).
Now perform the multiplication:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
The negatives cancel out:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now simplify \(\frac{50}{22}\):
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
So, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is \(\frac{25}{11}\).
Thus, the correct response is: 2311.