Solve (1/6-2/3+(-1/2))^2*(3/4divfrac{1}{4}+frac{3}{8})

$$( \frac { 1 } { 6 } - \frac { 2 } { 3 } + ( - \frac { 1 } { 2 } ) ) ^ { 2 } \times ( \frac { 3 } { 4 } \div \frac { 1 } { 4 } + \frac { 3 } { 8 } )$$

Evaluate

$$\frac{27}{8}=3.375$$

Solution Steps

Subtract \frac{2}{3} from \frac{1}{6} to get -\frac{1}{2}.

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

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

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

Calculate -1 to the power of 2 and get 1.

$$1\left(\frac{\frac{3}{4}}{\frac{1}{4}}+\frac{3}{8}\right)$$

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

$$1\left(\frac{3}{4}\times 4+\frac{3}{8}\right)$$

Multiply \frac{3}{4} and 4 to get 3.

$$1\left(3+\frac{3}{8}\right)$$

Add 3 and \frac{3}{8} to get \frac{27}{8}.

$$1\times \frac{27}{8}$$

Multiply 1 and \frac{27}{8} to get \frac{27}{8}.

$$\frac{27}{8}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {3}} = 3\frac{3}{8} = 3.375$$