To divide the fraction \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply \(-\frac{10}{11}\) by the reciprocal of \(-\frac{2}{5}\).
The reciprocal of \(-\frac{2}{5}\) is \(-\frac{5}{2}\). So, the operation becomes:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
When you multiply the two fractions, the negative signs cancel out:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now, you can simplify \(\frac{50}{22}\). The greatest common divisor of 50 and 22 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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