Solve 11/12+11/8-(7/12-7/12)div(3/2-2/3)

$$11 / 12 + 11 / 8 - ( 7 / 12 - 7 / 12 ) \div ( 3 / 2 - 2 / 3 )$$

Evaluate

$$\frac{55}{24}\approx 2.291666667$$

Solution Steps

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{11}{8} to fractions with denominator 24.

$$\frac{22}{24}+\frac{33}{24}-\frac{\frac{7}{12}-\frac{7}{12}}{\frac{3}{2}-\frac{2}{3}}$$

Since \frac{22}{24} and \frac{33}{24} have the same denominator, add them by adding their numerators.

$$\frac{22+33}{24}-\frac{\frac{7}{12}-\frac{7}{12}}{\frac{3}{2}-\frac{2}{3}}$$

Add 22 and 33 to get 55.

$$\frac{55}{24}-\frac{\frac{7}{12}-\frac{7}{12}}{\frac{3}{2}-\frac{2}{3}}$$

Subtract \frac{7}{12} from \frac{7}{12} to get 0.

$$\frac{55}{24}-\frac{0}{\frac{3}{2}-\frac{2}{3}}$$

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

$$\frac{55}{24}-\frac{0}{\frac{9}{6}-\frac{4}{6}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55}{24}-\frac{0}{\frac{9-4}{6}}$$

Subtract 4 from 9 to get 5.

$$\frac{55}{24}-\frac{0}{\frac{5}{6}}$$

Zero divided by any non-zero number gives zero.

$$\frac{55}{24}+0$$

Add \frac{55}{24} and 0 to get \frac{55}{24}.

$$\frac{55}{24}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {3} \cdot 3} = 2\frac{7}{24} = 2.2916666666666665$$