Solve 0-(-22/3)+(+11/2)-[(+1/6)-(-5/6)]

$$0 - ( - 2 \frac { 2 } { 3 } ) + ( + 1 \frac { 1 } { 2 } ) - [ ( + \frac { 1 } { 6 } ) - ( - \frac { 5 } { 6 } ) ]$$

Evaluate

$$\frac{19}{6}\approx 3.166666667$$

Solution Steps

Multiply 2 and 3 to get 6.

$$0-\left(-\frac{6+2}{3}\right)+\frac{1\times 2+1}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Add 6 and 2 to get 8.

$$0-\left(-\frac{8}{3}\right)+\frac{1\times 2+1}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

The opposite of -\frac{8}{3} is \frac{8}{3}.

$$0+\frac{8}{3}+\frac{1\times 2+1}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Add 0 and \frac{8}{3} to get \frac{8}{3}.

$$\frac{8}{3}+\frac{1\times 2+1}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Multiply 1 and 2 to get 2.

$$\frac{8}{3}+\frac{2+1}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Add 2 and 1 to get 3.

$$\frac{8}{3}+\frac{3}{2}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{16}{6}+\frac{9}{6}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Since \frac{16}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{16+9}{6}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

Add 16 and 9 to get 25.

$$\frac{25}{6}-\left(\frac{1}{6}-\left(-\frac{5}{6}\right)\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$\frac{25}{6}-\left(\frac{1}{6}+\frac{5}{6}\right)$$

Since \frac{1}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{25}{6}-\frac{1+5}{6}$$

Add 1 and 5 to get 6.

$$\frac{25}{6}-\frac{6}{6}$$

Since \frac{25}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-6}{6}$$

Subtract 6 from 25 to get 19.

$$\frac{19}{6}$$

Factor

$$\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665$$