To divide \( \frac{6}{11} \) by \( -\frac{4}{5} \), you can multiply \( \frac{6}{11} \) by the reciprocal of \( -\frac{4}{5} \). The reciprocal of \( -\frac{4}{5} \) is \( -\frac{5}{4} \).
So, the calculation becomes:
\[ \frac{6}{11} \div -\frac{4}{5} = \frac{6}{11} \times -\frac{5}{4} \]
Now, multiply the fractions:
\[ \frac{6 \times -5}{11 \times 4} = \frac{-30}{44} \]
Next, simplify \( \frac{-30}{44} \). The greatest common divisor (GCD) of 30 and 44 is 2.
So, we can divide both the numerator and the denominator by 2:
\[ \frac{-30 \div 2}{44 \div 2} = \frac{-15}{22} \]
Thus,
\[ \frac{6}{11} \div -\frac{4}{5} = -\frac{15}{22} \]