Question

What is −6 7/12 − 4 1/3

Answer 1

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

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

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

Next, we will need a common denominator to add these two fractions. The denominators 12 and 3 have a least common multiple of 12.

We convert \( -\frac{13}{3} \) to have the same denominator as \( -\frac{79}{12} \):
\[
-\frac{13}{3} = -\frac{13 \times 4}{3 \times 4} = -\frac{52}{12}
\]

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

Finally, we can convert \( -\frac{131}{12} \) back to a mixed number:
\[
-\frac{131}{12} = -10 \frac{11}{12} \quad \text{(since } 131 \div 12 = 10 \text{ remainder } 11\text{)}
\]

Therefore, the final result is:
\[
-10 \frac{11}{12}
\]