To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can rewrite the division as a multiplication by the reciprocal:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
Multiplying two negative numbers gives a positive result:
\[ -\frac{10}{11} \times -\frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now, simplify \(\frac{50}{22}\):
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Now, we can look at the answer choices:
- \( \frac{34}{2} \) (not relevant)
- \( \frac{2311}{2} \) (not relevant)
- \( -\frac{2311}{2} \) (not relevant)
- \( \frac{411}{1} \) (not relevant)
It appears none of the given options match \(\frac{25}{11}\) directly, but \(\frac{50}{22}\) gives us \(\frac{25}{11}\) when simplified.
Let’s confirm the conversion of options again to cross-check. The correct answer from the calculated quotient \(\frac{25}{11}\) seems like it’s related to an option like "negative" but none directly fits.
Please check for clearer guidance as specific notations or variations could potentially have styles affecting the understood outputs. If seeking purely, the final quotient indeed is \(\frac{25}{11}\).