−12 2/3−(−8 5/6)

Answer 1

To solve the expression \(-12 \frac{2}{3} - (-8 \frac{5}{6})\), we first need to simplify it.

1. Remove the parentheses and change the subtraction to addition: \[ -12 \frac{2}{3} + 8 \frac{5}{6} \]

2. Convert the mixed numbers to improper fractions: \[ -12 \frac{2}{3} = -\left(12 \times 3 + 2\right)/3 = -\frac{38}{3} \] \[ 8 \frac{5}{6} = \left(8 \times 6 + 5\right)/6 = \frac{53}{6} \]

3. Now we need a common denominator to add these fractions. The least common multiple of 3 and 6 is 6.

4. Convert \(-\frac{38}{3}\) to a fraction with a denominator of 6: \[ -\frac{38}{3} = -\frac{38 \times 2}{3 \times 2} = -\frac{76}{6} \]

5. Now we can add \(-\frac{76}{6}\) and \(\frac{53}{6}\): \[ -\frac{76}{6} + \frac{53}{6} = \frac{-76 + 53}{6} = \frac{-23}{6} \]

6. Finally, we can convert \(\frac{-23}{6}\) back to a mixed number. The whole number part is \(-3\) and the remainder is \(5\): \[ -3 \frac{5}{6} \]

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