Solve 23/4-(1/3+1/2)

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

Evaluate

$$\frac{23}{12}\approx 1.916666667$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 3 to get 11.

$$\frac{11}{4}-\left(\frac{1}{3}+\frac{1}{2}\right)$$

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

$$\frac{11}{4}-\left(\frac{2}{6}+\frac{3}{6}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{11}{4}-\frac{2+3}{6}$$

Add 2 and 3 to get 5.

$$\frac{11}{4}-\frac{5}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{11}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{33}{12}-\frac{10}{12}$$

Since \frac{33}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-10}{12}$$

Subtract 10 from 33 to get 23.

$$\frac{23}{12}$$

Factor

$$\frac{23}{2 ^ {2} \cdot 3} = 1\frac{11}{12} = 1.9166666666666667$$