Solve (5/4-2/3)-(1/2:2)

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{15}{12}-\frac{8}{12}-\frac{\frac{1}{2}}{2}$$

Since \frac{15}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-8}{12}-\frac{\frac{1}{2}}{2}$$

Subtract 8 from 15 to get 7.

$$\frac{7}{12}-\frac{\frac{1}{2}}{2}$$

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

$$\frac{7}{12}-\frac{1}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{7}{12}-\frac{1}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{7}{12}-\frac{3}{12}$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-3}{12}$$

Subtract 3 from 7 to get 4.

$$\frac{4}{12}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$