To evaluate the expression \( 24 \cdot 11 - 5 \cdot 117 \), we need to perform the operations step by step.
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Calculate \( 24 \cdot 11 \): \[ 24 \cdot 11 = 264 \]
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Calculate \( 5 \cdot 117 \): \[ 5 \cdot 117 = 585 \]
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Subtract the second result from the first: \[ 264 - 585 = -321 \]
Thus, the final answer is: \[ \boxed{-321} \]