Solve (7/5+1/4)-(1/2-1/8)

$$( \frac { 7 } { 5 } + \frac { 1 } { 4 } ) - ( \frac { 1 } { 2 } - \frac { 1 } { 8 } )$$

Evaluate

$$\frac{51}{40}=1.275$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{7}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{28}{20}+\frac{5}{20}-\left(\frac{1}{2}-\frac{1}{8}\right)$$

Since \frac{28}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{28+5}{20}-\left(\frac{1}{2}-\frac{1}{8}\right)$$

Add 28 and 5 to get 33.

$$\frac{33}{20}-\left(\frac{1}{2}-\frac{1}{8}\right)$$

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

$$\frac{33}{20}-\left(\frac{4}{8}-\frac{1}{8}\right)$$

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

$$\frac{33}{20}-\frac{4-1}{8}$$

Subtract 1 from 4 to get 3.

$$\frac{33}{20}-\frac{3}{8}$$

Least common multiple of 20 and 8 is 40. Convert \frac{33}{20} and \frac{3}{8} to fractions with denominator 40.

$$\frac{66}{40}-\frac{15}{40}$$

Since \frac{66}{40} and \frac{15}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{66-15}{40}$$

Subtract 15 from 66 to get 51.

$$\frac{51}{40}$$

Factor

$$\frac{3 \cdot 17}{2 ^ {3} \cdot 5} = 1\frac{11}{40} = 1.275$$