Question

What is -6 7/12 - 4 1/3? Express your answer as a fraction in simplified form.

Answer 1

To solve the expression \(-6 \frac{7}{12} - 4 \frac{1}{3}\), we will first convert both mixed numbers into improper fractions.

1. Convert \(-6 \frac{7}{12}\):
\[
-6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -\frac{79}{12}
\]

2. Convert \(4 \frac{1}{3}\):
\[
4 \frac{1}{3} = 4 \times 3 + 1/3 = (12 + 1)/3 = \frac{13}{3}
\]

Next, we need a common denominator to perform the subtraction. The least common multiple of 12 and 3 is 12. Therefore, we will convert \(\frac{13}{3}\) to have a denominator of 12:
\[
\frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12}
\]

Now, we can subtract the two fractions:
\[
- \frac{79}{12} - \frac{52}{12} = \frac{-79 - 52}{12} = \frac{-131}{12}
\]

Now, we simplify \(-\frac{131}{12}\). Since 131 is a prime number and does not share any common factors with 12 (other than 1), this fraction is already in its simplest form.

Thus, the answer is:
\[
\boxed{-\frac{131}{12}}
\]