Solve (2/3-1/6)-(3/4+5/8-2)

$$( \frac { 2 } { 3 } - \frac { 1 } { 6 } ) - ( \frac { 3 } { 4 } + \frac { 5 } { 8 } - 2 )$$

Evaluate

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

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{4}{6}-\frac{1}{6}-\left(\frac{3}{4}+\frac{5}{8}-2\right)$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{6}-\left(\frac{3}{4}+\frac{5}{8}-2\right)$$

Subtract 1 from 4 to get 3.

$$\frac{3}{6}-\left(\frac{3}{4}+\frac{5}{8}-2\right)$$

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

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

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{1}{2}-\left(\frac{6}{8}+\frac{5}{8}-2\right)$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\left(\frac{6+5}{8}-2\right)$$

Add 6 and 5 to get 11.

$$\frac{1}{2}-\left(\frac{11}{8}-2\right)$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{1}{2}-\left(\frac{11}{8}-\frac{16}{8}\right)$$

Since \frac{11}{8} and \frac{16}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\frac{11-16}{8}$$

Subtract 16 from 11 to get -5.

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

The opposite of -\frac{5}{8} is \frac{5}{8}.

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

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{5}{8} to fractions with denominator 8.

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

Since \frac{4}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

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

Add 4 and 5 to get 9.

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

Factor

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