Solve 31/2-13/4+5/6

$$3 \frac{ 1 }{ 2 } -1 \frac{ 3 }{ 4 } + \frac{ 5 }{ 6 }$$

Evaluate

$$\frac{31}{12}\approx 2.583333333$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-\frac{1\times 4+3}{4}+\frac{5}{6}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\frac{1\times 4+3}{4}+\frac{5}{6}$$

Multiply 1 and 4 to get 4.

$$\frac{7}{2}-\frac{4+3}{4}+\frac{5}{6}$$

Add 4 and 3 to get 7.

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

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{14}{4}-\frac{7}{4}+\frac{5}{6}$$

Since \frac{14}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-7}{4}+\frac{5}{6}$$

Subtract 7 from 14 to get 7.

$$\frac{7}{4}+\frac{5}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{21}{12}+\frac{10}{12}$$

Since \frac{21}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{21+10}{12}$$

Add 21 and 10 to get 31.

$$\frac{31}{12}$$

Factor

$$\frac{31}{2 ^ {2} \cdot 3} = 2\frac{7}{12} = 2.5833333333333335$$