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\frac{1}{2}\left(-\frac{4}{3}\right)
Divide \frac{1}{2} by -\frac{3}{4} by multiplying \frac{1}{2} by the reciprocal of -\frac{3}{4}.
\frac{1\left(-4\right)}{2\times 3}
Multiply \frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{-4}{6}
Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 3}.
-\frac{2}{3}
Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.