Solve 1/5-3/5[4/6+2(1/4)-frac{5}{6}]+(frac{1}{2})^2

$$\frac { 1 } { 5 } - \frac { 3 } { 5 } [ \frac { 4 } { 6 } + 2 ( \frac { 1 } { 4 } ) - \frac { 5 } { 6 } ] + ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$\frac{1}{5}-\frac{3}{5}\left(\frac{2}{3}+2\times \frac{1}{4}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{1}{5}-\frac{3}{5}\left(\frac{2}{3}+\frac{2}{4}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{1}{5}-\frac{3}{5}\left(\frac{2}{3}+\frac{1}{2}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{1}{5}-\frac{3}{5}\left(\frac{4}{6}+\frac{3}{6}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}-\frac{3}{5}\left(\frac{4+3}{6}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

Add 4 and 3 to get 7.

$$\frac{1}{5}-\frac{3}{5}\left(\frac{7}{6}-\frac{5}{6}\right)+\left(\frac{1}{2}\right)^{2}$$

Since \frac{7}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\frac{3}{5}\times \frac{7-5}{6}+\left(\frac{1}{2}\right)^{2}$$

Subtract 5 from 7 to get 2.

$$\frac{1}{5}-\frac{3}{5}\times \frac{2}{6}+\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{1}{5}-\frac{3}{5}\times \frac{1}{3}+\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{3}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}-\frac{3\times 1}{5\times 3}+\left(\frac{1}{2}\right)^{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{5}-\frac{1}{5}+\left(\frac{1}{2}\right)^{2}$$

Subtract \frac{1}{5} from \frac{1}{5} to get 0.

$$0+\left(\frac{1}{2}\right)^{2}$$

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

$$0+\frac{1}{4}$$

Add 0 and \frac{1}{4} to get \frac{1}{4}.

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

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$