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