Solve 21/4-5/6+7/8

$$2 \frac { 1 } { 4 } - \frac { 5 } { 6 } + \frac { 7 } { 8 }$$

Evaluate

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

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+1}{4}-\frac{5}{6}+\frac{7}{8}$$

Add 8 and 1 to get 9.

$$\frac{9}{4}-\frac{5}{6}+\frac{7}{8}$$

Least common multiple of 4 and 6 is 12. Convert \frac{9}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{27}{12}-\frac{10}{12}+\frac{7}{8}$$

Since \frac{27}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-10}{12}+\frac{7}{8}$$

Subtract 10 from 27 to get 17.

$$\frac{17}{12}+\frac{7}{8}$$

Least common multiple of 12 and 8 is 24. Convert \frac{17}{12} and \frac{7}{8} to fractions with denominator 24.

$$\frac{34}{24}+\frac{21}{24}$$

Since \frac{34}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{34+21}{24}$$

Add 34 and 21 to get 55.

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

Factor

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