To solve \(-4 \frac{5}{1} - 2 \frac{4}{11}\), we first convert these mixed numbers to improper fractions.
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Convert \(-4 \frac{5}{1}\) to an improper fraction:
\[ -4 \frac{5}{1} = -\left(4 \cdot 1 + 5\right) = -\left(4 + 5\right) = -9 \quad \text{(since \(5/1 = 5\))} \]
Therefore, \(-4 \frac{5}{1} = -9\).
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Convert \(2 \frac{4}{11}\) to an improper fraction:
\[ 2 \frac{4}{11} = 2 \cdot 11 + 4 = 22 + 4 = 26 \quad \text{(so it becomes \(\frac{26}{11}\))} \]
Therefore, \(2 \frac{4}{11} = \frac{26}{11}\).
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Now perform the subtraction:
We want to calculate:
\[ -9 - \frac{26}{11} \]
To subtract these two values, we write \(-9\) as a fraction:
\[ -9 = -\frac{9 \cdot 11}{11} = -\frac{99}{11} \]
Now we can combine the two fractions:
\[ -\frac{99}{11} - \frac{26}{11} = -\frac{99 + 26}{11} = -\frac{125}{11} \]
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Final answer:
The result is:
\[ -\frac{125}{11} \]
Thus, the final answer is \(\boxed{-\frac{125}{11}}\).