To divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply by the reciprocal of the divisor:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
The negative signs cancel each other out:
\[ \frac{10}{11} \times \frac{5}{2} \]
Now, multiply the numerators and the denominators:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Next, simplify \(\frac{50}{22}\) by finding the greatest common divisor (GCD) of 50 and 22, which is 2:
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Thus, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
\[ \frac{25}{11} \]
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