Question

Use the additive inverse to find −12 2/3 − (−8 5/6)
−
12
2
3
−
(
−
8
5
6
)
. Write the answer as a mixed number.(

Answer 1

To solve the expression \(-12 \frac{2}{3} - (-8 \frac{5}{6})\), we can first rewrite it using the additive inverse.

The additive inverse of \(-8 \frac{5}{6}\) is \(8 \frac{5}{6}\). Therefore, the expression becomes:

\[
-12 \frac{2}{3} + 8 \frac{5}{6}
\]

Now, we need to add these two mixed numbers together. First, we can convert them to improper fractions.

1. **Convert \(-12 \frac{2}{3}\) to an improper fraction**:
\[
-12 \frac{2}{3} = -\left(12 \cdot 3 + 2\right)/3 = -\left(36 + 2\right)/3 = -\frac{38}{3}
\]

2. **Convert \(8 \frac{5}{6}\) to an improper fraction**:
\[
8 \frac{5}{6} = \left(8 \cdot 6 + 5\right)/6 = \frac{48 + 5}{6} = \frac{53}{6}
\]

Now, we will add \(-\frac{38}{3}\) and \(\frac{53}{6}\).

Before adding, we need a common denominator. The least common multiple of 3 and 6 is 6.

Convert \(-\frac{38}{3}\) to have a denominator of 6:
\[
-\frac{38}{3} = -\frac{38 \cdot 2}{3 \cdot 2} = -\frac{76}{6}
\]

Now we can add the fractions:
\[
-\frac{76}{6} + \frac{53}{6} = \frac{-76 + 53}{6} = \frac{-23}{6}
\]

Now, we convert \(\frac{-23}{6}\) back to a mixed number:
\(-23 \div 6 = -3\) remainder \(-5\), so this can be written as:
\[
-3 \frac{5}{6}
\]

Thus, the final answer is:
\[
\boxed{-3 \frac{5}{6}}
\]