To subtract the mixed numbers \(-4 \frac{5}{11}\) and \(2 \frac{4}{11}\), follow these steps:
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Convert Mixed Numbers to Improper Fractions:
- For \(-4 \frac{5}{11}\): \[ -4 \frac{5}{11} = - \left(4 \times 11 + 5\right)/11 = - \frac{44 + 5}{11} = - \frac{49}{11} \]
- For \(2 \frac{4}{11}\): \[ 2 \frac{4}{11} = \frac{2 \times 11 + 4}{11} = \frac{22 + 4}{11} = \frac{26}{11} \]
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Perform the Subtraction: \[
- \frac{49}{11} - \frac{26}{11} = - \frac{49 + 26}{11} = - \frac{75}{11} \]
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Convert Back to a Mixed Number:
- Divide \(75\) by \(11\): \[ 75 \div 11 = 6 \quad \text{remainder } 9 \]
- Thus, \(- \frac{75}{11} = -6 \frac{9}{11}\).
The final answer is: \[ \text{-} 6 \frac{9}{11} \]