To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply by the reciprocal of the second fraction:
\[ -\frac{10}{11} ÷ -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
Multiplying the two fractions:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now simplify \(\frac{50}{22}\):
\[ \frac{50}{22} = \frac{25}{11} \quad \text{(dividing both the numerator and denominator by 2)} \]
Next, convert \(\frac{25}{11}\) into a mixed number:
\[ 25 \div 11 = 2 \quad \text{(which gives a remainder of 3)} \]
So, \(\frac{25}{11} = 2 \frac{3}{11}\).
Thus, the final answer is:
2 3/11.