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\frac{1}{6}\times 9
Divide \frac{1}{6} by \frac{1}{9} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{9}.
\frac{9}{6}
Multiply \frac{1}{6} and 9 to get \frac{9}{6}.
\frac{3}{2}
Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.