To subtract the mixed numbers \(-6 \frac{7}{12}\) and \(4 \frac{1}{3}\), we can follow these steps:
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Convert the mixed numbers to improper fractions.
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For \(-6 \frac{7}{12}\): \[ -6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -79/12 \]
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For \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = 4 \times 3 + 1/3 = (12 + 1)/3 = 13/3 \]
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Now, to subtract these two improper fractions, we need a common denominator. The least common multiple of 12 and 3 is 12.
- Convert \(13/3\) to have a denominator of 12: \[ 13/3 = (13 \times 4)/(3 \times 4) = 52/12 \]
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Now we have: \[ -79/12 - 52/12 \]
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Combine the fractions: \[ -79/12 - 52/12 = \frac{-79 - 52}{12} = \frac{-131}{12} \]
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Convert \(-131/12\) back to a mixed number:
- Dividing 131 by 12 gives 10 with a remainder of 11, so: \[ -\frac{131}{12} = -10 \frac{11}{12} \]
Thus, the result of \(-6 \frac{7}{12} - 4 \frac{1}{3}\) is \(-10 \frac{11}{12}\).