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\left(\frac{3}{4}\times \frac{5}{6}-7\right)\times \frac{9}{2}
Divide \frac{3}{4} by \frac{6}{5} by multiplying \frac{3}{4} by the reciprocal of \frac{6}{5}.
\left(\frac{3\times 5}{4\times 6}-7\right)\times \frac{9}{2}
Multiply \frac{3}{4} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.
\left(\frac{15}{24}-7\right)\times \frac{9}{2}
Do the multiplications in the fraction \frac{3\times 5}{4\times 6}.
\left(\frac{5}{8}-7\right)\times \frac{9}{2}
Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.
\left(\frac{5}{8}-\frac{56}{8}\right)\times \frac{9}{2}
Convert 7 to fraction \frac{56}{8}.
\frac{5-56}{8}\times \frac{9}{2}
Since \frac{5}{8} and \frac{56}{8} have the same denominator, subtract them by subtracting their numerators.
-\frac{51}{8}\times \frac{9}{2}
Subtract 56 from 5 to get -51.
\frac{-51\times 9}{8\times 2}
Multiply -\frac{51}{8} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{-459}{16}
Do the multiplications in the fraction \frac{-51\times 9}{8\times 2}.
-\frac{459}{16}
Fraction \frac{-459}{16} can be rewritten as -\frac{459}{16} by extracting the negative sign.