Sure, let's simplify the given expression step-by-step.
The expression to simplify is:
[tex]\[
\frac{2}{3} \div (-4) - \left( \frac{1}{6} - \frac{8}{6} \right)
\][/tex]
### Step 1: Simplify the division part
First, we simplify [tex]\(\frac{2}{3} \div (-4)\)[/tex].
We can rewrite the division as a multiplication by the reciprocal:
[tex]\[
\frac{2}{3} \div (-4) = \frac{2}{3} \times \frac{1}{-4}
\][/tex]
Multiplying the fractions:
[tex]\[
\frac{2}{3} \times \frac{1}{-4} = \frac{2 \times 1}{3 \times -4} = \frac{2}{-12} = -\frac{1}{6}
\][/tex]
So, the result of [tex]\(\frac{2}{3} \div (-4)\)[/tex] is [tex]\(-\frac{1}{6}\)[/tex].
### Step 2: Simplify the subtraction inside the parentheses
Next, we simplify [tex]\(\frac{1}{6} - \frac{8}{6}\)[/tex].
Since the denominators are the same, we can subtract the numerators directly:
[tex]\[
\frac{1}{6} - \frac{8}{6} = \frac{1 - 8}{6} = \frac{-7}{6}
\][/tex]
So, [tex]\(\frac{1}{6} - \frac{8}{6}\)[/tex] simplifies to [tex]\(-\frac{7}{6}\)[/tex].
### Step 3: Perform the final subtraction
Finally, we subtract [tex]\(-\frac{7}{6}\)[/tex] from [tex]\(-\frac{1}{6}\)[/tex]:
[tex]\[
-\frac{1}{6} - \left( -\frac{7}{6} \right)
\][/tex]
Subtracting a negative number is the same as adding the positive:
[tex]\[
-\frac{1}{6} + \frac{7}{6} = \frac{7}{6} - \frac{1}{6} = \frac{7 - 1}{6} = \frac{6}{6} = 1
\][/tex]
Therefore, the simplified expression is [tex]\(1\)[/tex].
### Conclusion
The simplified form of the expression [tex]\(\frac{2}{3} \div (-4) - \left( \frac{1}{6} - \frac{8}{6} \right)\)[/tex] is [tex]\(1\)[/tex].
