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\frac{1\times 1}{3\times 2}\times \frac{3}{5}\times \frac{2}{3}
Multiply \frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{6}\times \frac{3}{5}\times \frac{2}{3}
Do the multiplications in the fraction \frac{1\times 1}{3\times 2}.
\frac{1\times 3}{6\times 5}\times \frac{2}{3}
Multiply \frac{1}{6} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{3}{30}\times \frac{2}{3}
Do the multiplications in the fraction \frac{1\times 3}{6\times 5}.
\frac{1}{10}\times \frac{2}{3}
Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.
\frac{1\times 2}{10\times 3}
Multiply \frac{1}{10} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{2}{30}
Do the multiplications in the fraction \frac{1\times 2}{10\times 3}.
\frac{1}{15}
Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.