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

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

Evaluate

$$-\frac{85}{12}\approx -7.083333333$$

Solution Steps

Divide \frac{1}{4} by \frac{1}{2} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{2}.

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

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

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

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

$$\frac{\frac{9}{4}}{\frac{2}{3}-\frac{1}{4}-\frac{3}{4}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Subtract \frac{1}{4} from \frac{2}{3} to get \frac{5}{12}.

$$\frac{\frac{9}{4}}{\frac{5}{12}-\frac{3}{4}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Subtract \frac{3}{4} from \frac{5}{12} to get -\frac{1}{3}.

$$\frac{\frac{9}{4}}{-\frac{1}{3}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Divide \frac{9}{4} by -\frac{1}{3} by multiplying \frac{9}{4} by the reciprocal of -\frac{1}{3}.

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

Multiply \frac{9}{4} and -3 to get -\frac{27}{4}.

$$-\frac{27}{4}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

$$-\frac{27}{4}+\frac{1}{6}-\frac{1}{2}$$

Add -\frac{27}{4} and \frac{1}{6} to get -\frac{79}{12}.

$$-\frac{79}{12}-\frac{1}{2}$$

Subtract \frac{1}{2} from -\frac{79}{12} to get -\frac{85}{12}.

$$-\frac{85}{12}$$

Factor

$$-\frac{85}{12} = -7\frac{1}{12} = -7.083333333333333$$