Question

Simplify the expression:Two-thirds divided by (negative 4) minus (one-sixth minus StartFraction 8 over 6 EndFraction)
1
StartFraction 29 over 24 EndFraction
StartFraction negative 24 over 17 EndFraction
StartFraction 23 over 24 EndFraction

Answer 1

Let's simplify the expression step by step:

1. We have the expression:
\[
\frac{2}{3} \div (-4) - \left(\frac{1}{6} - \frac{8}{6}\right)
\]

2. First, let's simplify \( \frac{1}{6} - \frac{8}{6} \):
\[
\frac{1}{6} - \frac{8}{6} = \frac{1 - 8}{6} = \frac{-7}{6}
\]

3. Now we can rewrite the expression as:
\[
\frac{2}{3} \div (-4) - \left(\frac{-7}{6}\right)
\]

4. The division \( \frac{2}{3} \div (-4) \) can be rewritten as:
\[
\frac{2}{3} \div -4 = \frac{2}{3} \cdot \frac{1}{-4} = \frac{2}{-12} = -\frac{1}{6}
\]

5. Now substituting this back into the expression:
\[
-\frac{1}{6} - \left(-\frac{7}{6}\right) = -\frac{1}{6} + \frac{7}{6}
\]

6. Combining the fractions:
\[
-\frac{1}{6} + \frac{7}{6} = \frac{-1 + 7}{6} = \frac{6}{6} = 1
\]

So the simplified expression is:
\[
\boxed{1}
\]