To divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply by the reciprocal of the second fraction:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
Now, when you multiply two negative numbers, the result is positive:
\[ \frac{10}{11} \times \frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now, simplify \(\frac{50}{22}\):
\[ \frac{50}{22} = \frac{25}{11} \quad (\text{dividing both numerator and denominator by 2}) \]
Now, we can convert \(\frac{25}{11}\) to a mixed number. Divide 25 by 11:
25 divided by 11 is 2 with a remainder of 3. So:
\[ \frac{25}{11} = 2 \frac{3}{11} \]
Thus, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
2 \(\frac{3}{11}\).