To perform the subtraction \(-4 \frac{5}{11} - 2 \frac{4}{11}\), we can first convert these mixed numbers into improper fractions.
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Convert \(-4 \frac{5}{11}\) to an improper fraction: \[ -4 \frac{5}{11} = -\left(4 \cdot 11 + 5\right) / 11 = -\left(44 + 5\right) / 11 = -\frac{49}{11} \]
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Convert \(-2 \frac{4}{11}\) to an improper fraction: \[ -2 \frac{4}{11} = -\left(2 \cdot 11 + 4\right) / 11 = -\left(22 + 4\right) / 11 = -\frac{26}{11} \]
Now we can subtract the two improper fractions: \[ -\frac{49}{11} - \frac{26}{11} = -\frac{49 + 26}{11} = -\frac{75}{11} \]
The fraction \(-\frac{75}{11}\) is already in simplified form. Thus, the final answer is: \[ \boxed{-\frac{75}{11}} \]