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