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\frac{4}{9}\times \frac{3}{2}
Divide \frac{4}{9} by \frac{2}{3} by multiplying \frac{4}{9} by the reciprocal of \frac{2}{3}.
\frac{4\times 3}{9\times 2}
Multiply \frac{4}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{12}{18}
Do the multiplications in the fraction \frac{4\times 3}{9\times 2}.
\frac{2}{3}
Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.