To solve \(-6 \frac{7}{12} - 4 \frac{1}{3}\), we first need to convert both mixed numbers into improper fractions.
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Convert \(-6 \frac{7}{12}\): \[ -6 \frac{7}{12} = -\left(6 \cdot 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -\frac{79}{12} \]
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Convert \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = \left(4 \cdot 3 + 1\right)/3 = (12 + 1)/3 = \frac{13}{3} \]
Now, we need to subtract \(\frac{13}{3}\) from \(-\frac{79}{12}\). To do that, we need a common denominator. The least common multiple of \(12\) and \(3\) is \(12\).
Convert \(\frac{13}{3}\) to have a denominator of \(12\): \[ \frac{13}{3} = \frac{13 \cdot 4}{3 \cdot 4} = \frac{52}{12} \]
Now we can perform the subtraction: \[ -\frac{79}{12} - \frac{52}{12} = \frac{-79 - 52}{12} = \frac{-131}{12} \]
The result is \(-\frac{131}{12}\). If we want to convert this back to a mixed number: \[ -\frac{131}{12} = -10 \frac{11}{12} \]
Thus, the final answer is: \[ \boxed{-10 \frac{11}{12}} \]
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