Solve (-4/5):(+8/5)-(+2)*(+5/4)

$$( - \frac { 4 } { 5 } ) : ( + \frac { 8 } { 5 } ) - ( + 2 ) \cdot ( + \frac { 5 } { 4 } )$$

Evaluate

$$-3$$

Solution Steps

Divide -\frac{4}{5} by \frac{8}{5} by multiplying -\frac{4}{5} by the reciprocal of \frac{8}{5}.

$$-\frac{4}{5}\times \frac{5}{8}-2\times \frac{5}{4}$$

Multiply -\frac{4}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4\times 5}{5\times 8}-2\times \frac{5}{4}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-4}{8}-2\times \frac{5}{4}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{2}-2\times \frac{5}{4}$$

Express 2\times \frac{5}{4} as a single fraction.

$$-\frac{1}{2}-\frac{2\times 5}{4}$$

Multiply 2 and 5 to get 10.

$$-\frac{1}{2}-\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}-\frac{5}{2}$$

Since -\frac{1}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-5}{2}$$

Subtract 5 from -1 to get -6.

$$\frac{-6}{2}$$

Divide -6 by 2 to get -3.

$$-3$$

Factor

$$-3$$