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\frac{3}{4}\times 2\times \frac{4}{9}
Divide \frac{3}{4} by \frac{1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{2}.
\frac{3\times 2}{4}\times \frac{4}{9}
Express \frac{3}{4}\times 2 as a single fraction.
\frac{6}{4}\times \frac{4}{9}
Multiply 3 and 2 to get 6.
\frac{3}{2}\times \frac{4}{9}
Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.
\frac{3\times 4}{2\times 9}
Multiply \frac{3}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.
\frac{12}{18}
Do the multiplications in the fraction \frac{3\times 4}{2\times 9}.
\frac{2}{3}
Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.