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\frac{\frac{5}{4}\times 2}{-\frac{6}{5}}
Divide \frac{\frac{5}{4}}{-\frac{6}{5}} by \frac{1}{2} by multiplying \frac{\frac{5}{4}}{-\frac{6}{5}} by the reciprocal of \frac{1}{2}.
\frac{\frac{5\times 2}{4}}{-\frac{6}{5}}
Express \frac{5}{4}\times 2 as a single fraction.
\frac{\frac{10}{4}}{-\frac{6}{5}}
Multiply 5 and 2 to get 10.
\frac{\frac{5}{2}}{-\frac{6}{5}}
Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.
\frac{5}{2}\left(-\frac{5}{6}\right)
Divide \frac{5}{2} by -\frac{6}{5} by multiplying \frac{5}{2} by the reciprocal of -\frac{6}{5}.
\frac{5\left(-5\right)}{2\times 6}
Multiply \frac{5}{2} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.
\frac{-25}{12}
Do the multiplications in the fraction \frac{5\left(-5\right)}{2\times 6}.
-\frac{25}{12}
Fraction \frac{-25}{12} can be rewritten as -\frac{25}{12} by extracting the negative sign.