Solve 1/2*(1-3/4)-2*(3/4-1)

$$\frac { 1 } { 2 } \cdot ( 1 - \frac { 3 } { 4 } ) - 2 \cdot ( \frac { 3 } { 4 } - 1 )$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

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

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

Subtract 3 from 4 to get 1.

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

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

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 4}.

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

Convert 1 to fraction \frac{4}{4}.

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

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

$$\frac{1}{8}-2\times \frac{3-4}{4}$$

Subtract 4 from 3 to get -1.

$$\frac{1}{8}-2\left(-\frac{1}{4}\right)$$

Express 2\left(-\frac{1}{4}\right) as a single fraction.

$$\frac{1}{8}-\frac{2\left(-1\right)}{4}$$

Multiply 2 and -1 to get -2.

$$\frac{1}{8}-\frac{-2}{4}$$

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

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{1}{8}+\frac{1}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

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

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$