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

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

Evaluate

$$-\frac{1}{15}\approx -0.066666667$$

Solution Steps

Divide 4 by 2 to get 2.

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

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{1}{3}\left(\frac{2}{5}-2\left(\frac{5}{10}-\frac{2}{10}\right)\right)$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\left(\frac{2}{5}-2\times \frac{5-2}{10}\right)$$

Subtract 2 from 5 to get 3.

$$\frac{1}{3}\left(\frac{2}{5}-2\times \frac{3}{10}\right)$$

Express 2\times \frac{3}{10} as a single fraction.

$$\frac{1}{3}\left(\frac{2}{5}-\frac{2\times 3}{10}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{1}{3}\left(\frac{2}{5}-\frac{6}{10}\right)$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

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

Since \frac{2}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{2-3}{5}$$

Subtract 3 from 2 to get -1.

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

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

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 5}.

$$\frac{-1}{15}$$

Fraction \frac{-1}{15} can be rewritten as -\frac{1}{15} by extracting the negative sign.

$$-\frac{1}{15}$$

Factor

$$-\frac{1}{15} = -0.06666666666666667$$