To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply \(-\frac{10}{11}\) by the reciprocal of \(-\frac{2}{5}\).
- Reciprocal of \(-\frac{2}{5}\) is \(-\frac{5}{2}\).
- Therefore, the calculation becomes:
\[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
- The negatives cancel out:
\[ \frac{10}{11} \times \frac{5}{2} \]
- Now perform the multiplication:
\[ \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
- Simplify \(\frac{50}{22}\):
\[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Now, to express \(\frac{25}{11}\) as a mixed number:
- Divide 25 by 11: \(25 \div 11 = 2\) (quotient) and remainder \(3\).
- Thus, \(\frac{25}{11} = 2 \frac{3}{11}\).
So, the final answer is:
2 3/11 (which corresponds to "2 Start Fraction 3 over 11 End Fraction").