To determine which fraction is equivalent to \( \frac{2}{3} \), we can check each option by cross-multiplying.
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For \( \frac{4}{6} \): \[ 2 \times 6 = 12 \quad \text{and} \quad 3 \times 4 = 12 \] Since both products are equal, \( \frac{4}{6} \) is equivalent to \( \frac{2}{3} \).
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For \( \frac{4}{9} \): \[ 2 \times 9 = 18 \quad \text{and} \quad 3 \times 4 = 12 \] Since the products are not equal, \( \frac{4}{9} \) is not equivalent to \( \frac{2}{3} \).
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For \( \frac{3}{9} \): \[ 2 \times 9 = 18 \quad \text{and} \quad 3 \times 3 = 9 \] Since the products are not equal, \( \frac{3}{9} \) is not equivalent to \( \frac{2}{3} \).
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For \( \frac{3}{4} \): \[ 2 \times 4 = 8 \quad \text{and} \quad 3 \times 3 = 9 \] Since the products are not equal, \( \frac{3}{4} \) is not equivalent to \( \frac{2}{3} \).
The only fraction that is equivalent to \( \frac{2}{3} \) is \( \frac{4}{6} \).