6/11:(-1 4/11)

To divide \( \frac{6}{11} \) by \( -1 \frac{4}{11} \), we first need to convert the mixed number \( -1 \frac{4}{11} \) into an improper fraction.

1. Convert the mixed number: \[ -1 \frac{4}{11} = -\left(1 \cdot 11 + 4\right)/11 = -\frac{11 + 4}{11} = -\frac{15}{11} \]

2. Now we can perform the division: \[ \frac{6}{11} \div -\frac{15}{11} \]

3. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{6}{11} \times -\frac{11}{15} \]

4. Multiply the fractions: \[ = \frac{6 \times -11}{11 \times 15} = \frac{-66}{165} \]

5. Now, simplify the fraction: The greatest common divisor (GCD) of 66 and 165 is 33. \[ \frac{-66 \div 33}{165 \div 33} = \frac{-2}{5} \]

So, \( \frac{6}{11} \div \left(-1 \frac{4}{11}\right) = -\frac{2}{5} \).