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To multiply the fractions \( \frac{2}{3} \) and \( \frac{3}{2} \), you multiply the numerators together and the denominators together:

\[ \frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1 \]

So, \( \frac{2}{3} \times \frac{3}{2} = 1 \).