To divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\), we can multiply by the reciprocal of the divisor.
So, we have:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
The negatives cancel out:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now, we can simplify \(\frac{50}{22}\):
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Now, \( \frac{25}{11} \) is already in simplest form.
To express \( \frac{25}{11} \) as a mixed number:
\[ 25 \div 11 = 2 \quad \text{remainder } 3 \]
So, \( \frac{25}{11} = 2 \frac{3}{11} \).
Thus, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
2 \( \frac{3}{11} \)