To subtract the mixed numbers \(-6 \frac{7}{12}\) and \(4 \frac{1}{3}\), we first convert them into improper fractions.
-
Convert \(-6 \frac{7}{12}\): \[ -6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\frac{72 + 7}{12} = -\frac{79}{12} \]
-
Convert \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = 4 \times 3 + 1 / 3 = \frac{12 + 1}{3} = \frac{13}{3} \]
-
To subtract these two improper fractions, 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: \[ \frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12} \]
-
Now, perform the subtraction: \[ -\frac{79}{12} - \frac{52}{12} = -\frac{79 + 52}{12} = -\frac{131}{12} \]
-
Finally, convert \(-\frac{131}{12}\) back to a mixed number: \[ -\frac{131}{12} = -10 \frac{11}{12} \quad (\text{since } 131 \div 12 = 10 \text{ R } 11) \]
So, the answer to \(-6 \frac{7}{12} - 4 \frac{1}{3}\) is: \[ -10 \frac{11}{12} \]