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-\frac{2}{27}\times \frac{9}{2}
Divide -\frac{2}{27} by \frac{2}{9} by multiplying -\frac{2}{27} by the reciprocal of \frac{2}{9}.
\frac{-2\times 9}{27\times 2}
Multiply -\frac{2}{27} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{-18}{54}
Do the multiplications in the fraction \frac{-2\times 9}{27\times 2}.
-\frac{1}{3}
Reduce the fraction \frac{-18}{54} to lowest terms by extracting and canceling out 18.