Solve (1/2-1)^2:{-3-[2/3-(1/3+1)^2:8/9]}-frac{1}{10}

$$( \frac { 1 } { 2 } - 1 ) ^ { 2 } : \{ - 3 - [ \frac { 2 } { 3 } - ( \frac { 1 } { 3 } + 1 ) ^ { 2 } : \frac { 8 } { 9 } ] \} - \frac { 1 } { 10 }$$

Evaluate

$$-\frac{1}{4}=-0.25$$

Solution Steps

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

$$\frac{\left(-\frac{1}{2}\right)^{2}}{-3-\left(\frac{2}{3}-\frac{\left(\frac{1}{3}+1\right)^{2}}{\frac{8}{9}}\right)}-\frac{1}{10}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}}{-3-\left(\frac{2}{3}-\frac{\left(\frac{1}{3}+1\right)^{2}}{\frac{8}{9}}\right)}-\frac{1}{10}$$

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

$$\frac{\frac{1}{4}}{-3-\left(\frac{2}{3}-\frac{\left(\frac{4}{3}\right)^{2}}{\frac{8}{9}}\right)}-\frac{1}{10}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{\frac{1}{4}}{-3-\left(\frac{2}{3}-\frac{\frac{16}{9}}{\frac{8}{9}}\right)}-\frac{1}{10}$$

Divide \frac{16}{9} by \frac{8}{9} by multiplying \frac{16}{9} by the reciprocal of \frac{8}{9}.

$$\frac{\frac{1}{4}}{-3-\left(\frac{2}{3}-\frac{16}{9}\times \frac{9}{8}\right)}-\frac{1}{10}$$

Multiply \frac{16}{9} and \frac{9}{8} to get 2.

$$\frac{\frac{1}{4}}{-3-\left(\frac{2}{3}-2\right)}-\frac{1}{10}$$

Subtract 2 from \frac{2}{3} to get -\frac{4}{3}.

$$\frac{\frac{1}{4}}{-3-\left(-\frac{4}{3}\right)}-\frac{1}{10}$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{\frac{1}{4}}{-3+\frac{4}{3}}-\frac{1}{10}$$

Add -3 and \frac{4}{3} to get -\frac{5}{3}.

$$\frac{\frac{1}{4}}{-\frac{5}{3}}-\frac{1}{10}$$

Divide \frac{1}{4} by -\frac{5}{3} by multiplying \frac{1}{4} by the reciprocal of -\frac{5}{3}.

$$\frac{1}{4}\left(-\frac{3}{5}\right)-\frac{1}{10}$$

Multiply \frac{1}{4} and -\frac{3}{5} to get -\frac{3}{20}.

$$-\frac{3}{20}-\frac{1}{10}$$

Subtract \frac{1}{10} from -\frac{3}{20} to get -\frac{1}{4}.

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

Factor

$$-\frac{1}{4} = -0.25$$