Solve 2/8*(1-3/2)-1/2div(-2/5)

$$\frac { 2 } { 8 } \times ( 1 - \frac { 3 } { 2 } ) - \frac { 1 } { 2 } \div ( - \frac { 2 } { 5 } )$$

Evaluate

$$\frac{9}{8}=1.125$$

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\left(1-\frac{3}{2}\right)-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{4}\left(\frac{2}{2}-\frac{3}{2}\right)-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}\times \frac{2-3}{2}-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Subtract 3 from 2 to get -1.

$$\frac{1}{4}\left(-\frac{1}{2}\right)-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Multiply \frac{1}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 2}.

$$\frac{-1}{8}-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$-\frac{1}{8}-\frac{\frac{1}{2}}{-\frac{2}{5}}$$

Divide \frac{1}{2} by -\frac{2}{5} by multiplying \frac{1}{2} by the reciprocal of -\frac{2}{5}.

$$-\frac{1}{8}-\frac{1}{2}\left(-\frac{5}{2}\right)$$

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

$$-\frac{1}{8}-\frac{1\left(-5\right)}{2\times 2}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 2}.

$$-\frac{1}{8}-\frac{-5}{4}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$-\frac{1}{8}-\left(-\frac{5}{4}\right)$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$-\frac{1}{8}+\frac{5}{4}$$

Least common multiple of 8 and 4 is 8. Convert -\frac{1}{8} and \frac{5}{4} to fractions with denominator 8.

$$-\frac{1}{8}+\frac{10}{8}$$

Since -\frac{1}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{-1+10}{8}$$

Add -1 and 10 to get 9.

$$\frac{9}{8}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {3}} = 1\frac{1}{8} = 1.125$$