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\frac{1}{2}\times \frac{3}{2}
Divide \frac{1}{2} by \frac{2}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{2}{3}.
\frac{1\times 3}{2\times 2}
Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{3}{4}
Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.