To solve the expression \( \frac{2}{9} - \left( \frac{3}{4} - \frac{2}{3} \right) \), we first need to simplify the expression in the parentheses.
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Find a common denominator for \( \frac{3}{4} \) and \( \frac{2}{3} \):
- The least common multiple (LCM) of 4 and 3 is 12.
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Convert \( \frac{3}{4} \) and \( \frac{2}{3} \) to have a denominator of 12:
- \( \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \)
- \( \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
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Subtract the two fractions: \[ \frac{3}{4} - \frac{2}{3} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12} \]
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Now substitute back into the original expression: \[ \frac{2}{9} - \left( \frac{3}{4} - \frac{2}{3} \right) = \frac{2}{9} - \frac{1}{12} \]
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Find a common denominator for \( \frac{2}{9} \) and \( \frac{1}{12} \):
- The least common multiple (LCM) of 9 and 12 is 36.
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Convert \( \frac{2}{9} \) and \( \frac{1}{12} \) to have a denominator of 36:
- \( \frac{2}{9} = \frac{2 \times 4}{9 \times 4} = \frac{8}{36} \)
- \( \frac{1}{12} = \frac{1 \times 3}{12 \times 3} = \frac{3}{36} \)
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Now subtract the two fractions: \[ \frac{2}{9} - \frac{1}{12} = \frac{8}{36} - \frac{3}{36} = \frac{5}{36} \]
So, the final answer is: \[ \frac{5}{36} \]