Solve (-1/2)(5/3)-(2/3)(-3/2)(frac{5}{6})

$$( - \frac { 1 } { 2 } ) ( \frac { 5 } { 3 } ) - ( \frac { 2 } { 3 } ) ( - \frac { 3 } { 2 } ) ( \frac { 5 } { 6 } )$$

Evaluate

$$0$$

Solution Steps

Multiply -\frac{1}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5}{2\times 3}-\frac{2}{3}\left(-\frac{3}{2}\right)\times \frac{5}{6}$$

Do the multiplications in the fraction \frac{-5}{2\times 3}.

$$\frac{-5}{6}-\frac{2}{3}\left(-\frac{3}{2}\right)\times \frac{5}{6}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$-\frac{5}{6}-\frac{2}{3}\left(-\frac{3}{2}\right)\times \frac{5}{6}$$

Multiply \frac{2}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{6}-\frac{2\left(-3\right)}{3\times 2}\times \frac{5}{6}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{5}{6}-\frac{-3}{3}\times \frac{5}{6}$$

Divide -3 by 3 to get -1.

$$-\frac{5}{6}-\left(-\frac{5}{6}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$-\frac{5}{6}+\frac{5}{6}$$

Add -\frac{5}{6} and \frac{5}{6} to get 0.

$$0$$

Factor

$$0$$