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