Solve 2/3-3/4+5/2-1/2

$$2 / 3 - 3 / 4 + 5 / 2 - 1 / 2$$

Evaluate

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

Solution Steps

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

$$\frac{8}{12}-\frac{9}{12}+\frac{5}{2}-\frac{1}{2}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-9}{12}+\frac{5}{2}-\frac{1}{2}$$

Subtract 9 from 8 to get -1.

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

Least common multiple of 12 and 2 is 12. Convert -\frac{1}{12} and \frac{5}{2} to fractions with denominator 12.

$$-\frac{1}{12}+\frac{30}{12}-\frac{1}{2}$$

Since -\frac{1}{12} and \frac{30}{12} have the same denominator, add them by adding their numerators.

$$\frac{-1+30}{12}-\frac{1}{2}$$

Add -1 and 30 to get 29.

$$\frac{29}{12}-\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{29}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{29}{12}-\frac{6}{12}$$

Since \frac{29}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-6}{12}$$

Subtract 6 from 29 to get 23.

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

Factor

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