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

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

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{9}{12}-\frac{4}{12}+\frac{5}{6}-\frac{1}{2}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-4}{12}+\frac{5}{6}-\frac{1}{2}$$

Subtract 4 from 9 to get 5.

$$\frac{5}{12}+\frac{5}{6}-\frac{1}{2}$$

Least common multiple of 12 and 6 is 12. Convert \frac{5}{12} and \frac{5}{6} to fractions with denominator 12.

$$\frac{5}{12}+\frac{10}{12}-\frac{1}{2}$$

Since \frac{5}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{5+10}{12}-\frac{1}{2}$$

Add 5 and 10 to get 15.

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

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{5}{4}-\frac{2}{4}$$

Since \frac{5}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{4}$$

Subtract 2 from 5 to get 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$