Solve 9/20div-1/2*(2/5+4/5)?

$$\frac { 9 } { 20 } \div \frac { - 1 } { 2 } \times ( \frac { 2 } { 5 } + \frac { 4 } { 5 } ) ?$$

Evaluate

$$-\frac{27}{25}=-1.08$$

Solution Steps

Divide \frac{9}{20} by \frac{-1}{2} by multiplying \frac{9}{20} by the reciprocal of \frac{-1}{2}.

$$\frac{9\times 2}{20\left(-1\right)}\left(\frac{2}{5}+\frac{4}{5}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{9}{-10}\left(\frac{2}{5}+\frac{4}{5}\right)$$

Fraction \frac{9}{-10} can be rewritten as -\frac{9}{10} by extracting the negative sign.

$$-\frac{9}{10}\left(\frac{2}{5}+\frac{4}{5}\right)$$

Since \frac{2}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$-\frac{9}{10}\times \frac{2+4}{5}$$

Add 2 and 4 to get 6.

$$-\frac{9}{10}\times \frac{6}{5}$$

Multiply -\frac{9}{10} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 6}{10\times 5}$$

Do the multiplications in the fraction \frac{-9\times 6}{10\times 5}.

$$\frac{-54}{50}$$

Reduce the fraction \frac{-54}{50} to lowest terms by extracting and canceling out 2.

$$-\frac{27}{25}$$

Factor

$$-\frac{27}{25} = -1\frac{2}{25} = -1.08$$