Solve (-2/3)*(-3/5)-(-4/5):(3/5)*(-frac{3}{4})

$$( - \frac { 2 } { 3 } ) \cdot ( - \frac { 3 } { 5 } ) - ( - \frac { 4 } { 5 } ) : ( \frac { 3 } { 5 } ) \cdot ( - \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{3}{5}=-0.6$$

Solution Steps

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

$$\frac{-2\left(-3\right)}{3\times 5}-\frac{-\frac{4}{5}}{\frac{3}{5}}\left(-\frac{3}{4}\right)$$

Do the multiplications in the fraction \frac{-2\left(-3\right)}{3\times 5}.

$$\frac{6}{15}-\frac{-\frac{4}{5}}{\frac{3}{5}}\left(-\frac{3}{4}\right)$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}-\frac{-\frac{4}{5}}{\frac{3}{5}}\left(-\frac{3}{4}\right)$$

Divide -\frac{4}{5} by \frac{3}{5} by multiplying -\frac{4}{5} by the reciprocal of \frac{3}{5}.

$$\frac{2}{5}-\left(-\frac{4}{5}\times \frac{5}{3}\left(-\frac{3}{4}\right)\right)$$

Multiply -\frac{4}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{-4\times 5}{5\times 3}\left(-\frac{3}{4}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{2}{5}-\frac{-4}{3}\left(-\frac{3}{4}\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{2}{5}-\left(-\frac{4}{3}\left(-\frac{3}{4}\right)\right)$$

Multiply -\frac{4}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{-4\left(-3\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{-4\left(-3\right)}{3\times 4}.

$$\frac{2}{5}-\frac{12}{12}$$

Divide 12 by 12 to get 1.

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

Convert 1 to fraction \frac{5}{5}.

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

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

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

Subtract 5 from 2 to get -3.

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

Factor

$$-\frac{3}{5} = -0.6$$