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\frac{1}{3}\times \frac{1}{2}-\frac{2}{6}
Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.
\frac{1\times 1}{3\times 2}-\frac{2}{6}
Multiply \frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{6}-\frac{2}{6}
Do the multiplications in the fraction \frac{1\times 1}{3\times 2}.
\frac{1-2}{6}
Since \frac{1}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.
-\frac{1}{6}
Subtract 2 from 1 to get -1.