Solve [(0-4/6)^2*3/6]+[(1-4/6)^2*2/6]+[(2-frac{4}{6})^2*frac{1}{6}]

$$[ ( 0 - \frac { 4 } { 6 } ) ^ { 2 } \times \frac { 3 } { 6 } ] + [ ( 1 - \frac { 4 } { 6 } ) ^ { 2 } \times \frac { 2 } { 6 } ] + [ ( 2 - \frac { 4 } { 6 } ) ^ { 2 } \times \frac { 1 } { 6 } ]$$

Evaluate

$$\frac{5}{9}\approx 0.555555556$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\left(0-\frac{2}{3}\right)^{2}\times \frac{3}{6}+\left(1-\frac{4}{6}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Subtract \frac{2}{3} from 0 to get -\frac{2}{3}.

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

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

$$\frac{4}{9}\times \frac{3}{6}+\left(1-\frac{4}{6}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{4}{9}\times \frac{1}{2}+\left(1-\frac{4}{6}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Multiply \frac{4}{9} and \frac{1}{2} to get \frac{2}{9}.

$$\frac{2}{9}+\left(1-\frac{4}{6}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{9}+\left(1-\frac{2}{3}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

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

$$\frac{2}{9}+\left(\frac{1}{3}\right)^{2}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

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

$$\frac{2}{9}+\frac{1}{9}\times \frac{2}{6}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{9}+\frac{1}{9}\times \frac{1}{3}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Multiply \frac{1}{9} and \frac{1}{3} to get \frac{1}{27}.

$$\frac{2}{9}+\frac{1}{27}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Add \frac{2}{9} and \frac{1}{27} to get \frac{7}{27}.

$$\frac{7}{27}+\left(2-\frac{4}{6}\right)^{2}\times \frac{1}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{27}+\left(2-\frac{2}{3}\right)^{2}\times \frac{1}{6}$$

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

$$\frac{7}{27}+\left(\frac{4}{3}\right)^{2}\times \frac{1}{6}$$

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

$$\frac{7}{27}+\frac{16}{9}\times \frac{1}{6}$$

Multiply \frac{16}{9} and \frac{1}{6} to get \frac{8}{27}.

$$\frac{7}{27}+\frac{8}{27}$$

Add \frac{7}{27} and \frac{8}{27} to get \frac{5}{9}.

$$\frac{5}{9}$$

Factor

$$\frac{5}{3 ^ {2}} = 0.5555555555555556$$