Solve {-1/2-(-2/5)}+{-(-1/2+2/5)}

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

Evaluate

$$0$$

Solution Steps

The opposite of -\frac{2}{5} is \frac{2}{5}.

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

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

$$-\frac{5}{10}+\frac{4}{10}-\left(-\frac{1}{2}+\frac{2}{5}\right)$$

Since -\frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{-5+4}{10}-\left(-\frac{1}{2}+\frac{2}{5}\right)$$

Add -5 and 4 to get -1.

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

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

$$-\frac{1}{10}-\left(-\frac{5}{10}+\frac{4}{10}\right)$$

Since -\frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$-\frac{1}{10}-\frac{-5+4}{10}$$

Add -5 and 4 to get -1.

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

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$-\frac{1}{10}+\frac{1}{10}$$

Add -\frac{1}{10} and \frac{1}{10} to get 0.

$$0$$

Factor

$$0$$