Solve (21/2--1/4-1/6)

$$( 2 \frac { 1 } { 2 } - - \frac { 1 } { 4 } - \frac { 1 } { 6 } )$$

Evaluate

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

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}-\left(-\frac{1}{4}\right)-\frac{1}{6}$$

Add 4 and 1 to get 5.

$$\frac{5}{2}-\left(-\frac{1}{4}\right)-\frac{1}{6}$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

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

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{10}{4}+\frac{1}{4}-\frac{1}{6}$$

Since \frac{10}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{4}-\frac{1}{6}$$

Add 10 and 1 to get 11.

$$\frac{11}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{11}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{33}{12}-\frac{2}{12}$$

Since \frac{33}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-2}{12}$$

Subtract 2 from 33 to get 31.

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

Factor

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