To divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\), we can multiply by the reciprocal of the second fraction:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
Now, multiplying the two fractions:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Next, we simplify \(\frac{50}{22}\). We can divide both the numerator and the denominator by 2:
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Now, we can express \(\frac{25}{11}\) as a mixed number.
To convert it:
25 divided by 11 is 2 with a remainder of 3. Thus,
\[ \frac{25}{11} = 2 \frac{3}{11} \]
So the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
2 \( \frac{3}{11} \)
The correct response is:
2 3/11