Solve (4)-3/4+1/6-1/3-1/2

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

Evaluate

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

Solution Steps

Convert 4 to fraction \frac{16}{4}.

$$\frac{16}{4}-\frac{3}{4}+\frac{1}{6}-\frac{1}{3}-\frac{1}{2}$$

Since \frac{16}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-3}{4}+\frac{1}{6}-\frac{1}{3}-\frac{1}{2}$$

Subtract 3 from 16 to get 13.

$$\frac{13}{4}+\frac{1}{6}-\frac{1}{3}-\frac{1}{2}$$

Least common multiple of 4 and 6 is 12. Convert \frac{13}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{39}{12}+\frac{2}{12}-\frac{1}{3}-\frac{1}{2}$$

Since \frac{39}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{39+2}{12}-\frac{1}{3}-\frac{1}{2}$$

Add 39 and 2 to get 41.

$$\frac{41}{12}-\frac{1}{3}-\frac{1}{2}$$

Least common multiple of 12 and 3 is 12. Convert \frac{41}{12} and \frac{1}{3} to fractions with denominator 12.

$$\frac{41}{12}-\frac{4}{12}-\frac{1}{2}$$

Since \frac{41}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41-4}{12}-\frac{1}{2}$$

Subtract 4 from 41 to get 37.

$$\frac{37}{12}-\frac{1}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{37}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{37}{12}-\frac{6}{12}$$

Since \frac{37}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37-6}{12}$$

Subtract 6 from 37 to get 31.

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

Factor

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