Solve (8/3+5/4-3/2+7/8

$$( \frac { 8 } { 3 } + \frac { 5 } { 4 } - \frac { 3 } { 2 } + \frac { 7 } { 8 }$$

Evaluate

$$\frac{79}{24}\approx 3.291666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{8}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{32}{12}+\frac{15}{12}-\frac{3}{2}+\frac{7}{8}$$

Since \frac{32}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{32+15}{12}-\frac{3}{2}+\frac{7}{8}$$

Add 32 and 15 to get 47.

$$\frac{47}{12}-\frac{3}{2}+\frac{7}{8}$$

Least common multiple of 12 and 2 is 12. Convert \frac{47}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{47}{12}-\frac{18}{12}+\frac{7}{8}$$

Since \frac{47}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{47-18}{12}+\frac{7}{8}$$

Subtract 18 from 47 to get 29.

$$\frac{29}{12}+\frac{7}{8}$$

Least common multiple of 12 and 8 is 24. Convert \frac{29}{12} and \frac{7}{8} to fractions with denominator 24.

$$\frac{58}{24}+\frac{21}{24}$$

Since \frac{58}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{58+21}{24}$$

Add 58 and 21 to get 79.

$$\frac{79}{24}$$

Factor

$$\frac{79}{2 ^ {3} \cdot 3} = 3\frac{7}{24} = 3.2916666666666665$$