Let's simplify the expression step by step:
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We have the expression: \[ \frac{2}{3} \div (-4) - \left(\frac{1}{6} - \frac{8}{6}\right) \]
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First, let's simplify \( \frac{1}{6} - \frac{8}{6} \): \[ \frac{1}{6} - \frac{8}{6} = \frac{1 - 8}{6} = \frac{-7}{6} \]
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Now we can rewrite the expression as: \[ \frac{2}{3} \div (-4) - \left(\frac{-7}{6}\right) \]
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The division \( \frac{2}{3} \div (-4) \) can be rewritten as: \[ \frac{2}{3} \div -4 = \frac{2}{3} \cdot \frac{1}{-4} = \frac{2}{-12} = -\frac{1}{6} \]
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Now substituting this back into the expression: \[ -\frac{1}{6} - \left(-\frac{7}{6}\right) = -\frac{1}{6} + \frac{7}{6} \]
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Combining the fractions: \[ -\frac{1}{6} + \frac{7}{6} = \frac{-1 + 7}{6} = \frac{6}{6} = 1 \]
So the simplified expression is: \[ \boxed{1} \]
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