Solve 3/4-1/2:2+15/8(-4/5)-1:(-frac{2}{3})

$$\frac { 3 } { 4 } - \frac { 1 } { 2 } : 2 + \frac { 15 } { 8 } ( - \frac { 4 } { 5 } ) - 1 : ( - \frac { 2 } { 3 } )$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Express \frac{\frac{1}{2}}{2} as a single fraction.

$$\frac{3}{4}-\frac{1}{2\times 2}+\frac{15}{8}\left(-\frac{4}{5}\right)-\frac{1}{-\frac{2}{3}}$$

Multiply 2 and 2 to get 4.

$$\frac{3}{4}-\frac{1}{4}+\frac{15}{8}\left(-\frac{4}{5}\right)-\frac{1}{-\frac{2}{3}}$$

Since \frac{3}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-1}{4}+\frac{15}{8}\left(-\frac{4}{5}\right)-\frac{1}{-\frac{2}{3}}$$

Subtract 1 from 3 to get 2.

$$\frac{2}{4}+\frac{15}{8}\left(-\frac{4}{5}\right)-\frac{1}{-\frac{2}{3}}$$

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

$$\frac{1}{2}+\frac{15}{8}\left(-\frac{4}{5}\right)-\frac{1}{-\frac{2}{3}}$$

Multiply \frac{15}{8} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{15\left(-4\right)}{8\times 5}-\frac{1}{-\frac{2}{3}}$$

Do the multiplications in the fraction \frac{15\left(-4\right)}{8\times 5}.

$$\frac{1}{2}+\frac{-60}{40}-\frac{1}{-\frac{2}{3}}$$

Reduce the fraction \frac{-60}{40} to lowest terms by extracting and canceling out 20.

$$\frac{1}{2}-\frac{3}{2}-\frac{1}{-\frac{2}{3}}$$

Since \frac{1}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-3}{2}-\frac{1}{-\frac{2}{3}}$$

Subtract 3 from 1 to get -2.

$$\frac{-2}{2}-\frac{1}{-\frac{2}{3}}$$

Divide -2 by 2 to get -1.

$$-1-\frac{1}{-\frac{2}{3}}$$

Divide 1 by -\frac{2}{3} by multiplying 1 by the reciprocal of -\frac{2}{3}.

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

Multiply 1 and -\frac{3}{2} to get -\frac{3}{2}.

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

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$-1+\frac{3}{2}$$

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

$$-\frac{2}{2}+\frac{3}{2}$$

Since -\frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{-2+3}{2}$$

Add -2 and 3 to get 1.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$