Solve {-[1/3+1/2*(1-1/2)-1/9]-(-frac{1}{3})^2}-{[(-1-frac{1}{2})^2-frac{1}{4}]+frac{1}{2}}

$$\{ - [ \frac { 1 } { 3 } + \frac { 1 } { 2 } \cdot ( 1 - \frac { 1 } { 2 } ) - \frac { 1 } { 9 } ] - ( - \frac { 1 } { 3 } ) ^ { 2 } \} - \{ [ ( - 1 - \frac { 1 } { 2 } ) ^ { 2 } - \frac { 1 } { 4 } ] + \frac { 1 } { 2 } \}$$

Evaluate

$$-\frac{37}{12}\approx -3.083333333$$

Solution Steps

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$-\left(\frac{1}{3}+\frac{1}{2}\times \frac{1}{2}-\frac{1}{9}\right)-\left(-\frac{1}{3}\right)^{2}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$-\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{9}\right)-\left(-\frac{1}{3}\right)^{2}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Add \frac{1}{3} and \frac{1}{4} to get \frac{7}{12}.

$$-\left(\frac{7}{12}-\frac{1}{9}\right)-\left(-\frac{1}{3}\right)^{2}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Subtract \frac{1}{9} from \frac{7}{12} to get \frac{17}{36}.

$$-\frac{17}{36}-\left(-\frac{1}{3}\right)^{2}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$-\frac{17}{36}-\frac{1}{9}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Subtract \frac{1}{9} from -\frac{17}{36} to get -\frac{7}{12}.

$$-\frac{7}{12}-\left(\left(-1-\frac{1}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Subtract \frac{1}{2} from -1 to get -\frac{3}{2}.

$$-\frac{7}{12}-\left(\left(-\frac{3}{2}\right)^{2}-\frac{1}{4}+\frac{1}{2}\right)$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-\frac{7}{12}-\left(\frac{9}{4}-\frac{1}{4}+\frac{1}{2}\right)$$

Subtract \frac{1}{4} from \frac{9}{4} to get 2.

$$-\frac{7}{12}-\left(2+\frac{1}{2}\right)$$

Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$-\frac{7}{12}-\frac{5}{2}$$

Subtract \frac{5}{2} from -\frac{7}{12} to get -\frac{37}{12}.

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

Factor

$$-\frac{37}{12} = -3\frac{1}{12} = -3.0833333333333335$$