To find the quotient when you 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, the negatives cancel each other out:
\[ \frac{10}{11} \times \frac{5}{2} \]
Next, multiply the numerators and denominators:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
Now, simplify \(\frac{50}{22}\). Both 50 and 22 can be divided by 2:
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
We can express this as:
\[ 2 \frac{3}{11} \]
The whole number part is 2 and the fraction part is \(\frac{3}{11}\). Therefore, the quotient is:
\[ 2 \frac{3}{11} \]
So, the correct answer is \(2 \frac{3}{11}\).
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