To solve \( \frac{2}{3} \div -1 \frac{1}{3} \), we first need to convert the mixed number \( -1 \frac{1}{3} \) into an improper fraction.
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Convert \( -1 \frac{1}{3} \): \[ -1 \frac{1}{3} = -1 - \frac{1}{3} = \frac{-3}{3} - \frac{1}{3} = \frac{-4}{3}. \]
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Now, rewrite the division: \[ \frac{2}{3} \div \frac{-4}{3}. \]
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To divide by a fraction, we multiply by its reciprocal: \[ \frac{2}{3} \div \frac{-4}{3} = \frac{2}{3} \times \frac{3}{-4}. \]
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Now, multiply the fractions: \[ \frac{2 \times 3}{3 \times -4} = \frac{6}{-12}. \]
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Simplify \( \frac{6}{-12} \): \[ \frac{6}{-12} = \frac{1}{-2} = -\frac{1}{2}. \]
Thus, the solution to the expression \( \frac{2}{3} \div -1 \frac{1}{3} \) is \[ \boxed{-\frac{1}{2}}. \]