Solve (-3/5+1/2-(-2/5+2)-1)+1/2=

$$(- \frac{ 3 }{ 5 } + \frac{ 1 }{ 2 } -(- \frac{ 2 }{ 5 } +2)-1)+ \frac{ 1 }{ 2 } =$$

Evaluate

$$-\frac{11}{5}=-2.2$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

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

Since -\frac{6}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

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

Add -6 and 5 to get -1.

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

Convert 2 to fraction \frac{10}{5}.

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

Since -\frac{2}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{10}-\frac{-2+10}{5}-1+\frac{1}{2}$$

Add -2 and 10 to get 8.

$$-\frac{1}{10}-\frac{8}{5}-1+\frac{1}{2}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{1}{10} and \frac{8}{5} to fractions with denominator 10.

$$-\frac{1}{10}-\frac{16}{10}-1+\frac{1}{2}$$

Since -\frac{1}{10} and \frac{16}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-16}{10}-1+\frac{1}{2}$$

Subtract 16 from -1 to get -17.

$$-\frac{17}{10}-1+\frac{1}{2}$$

Convert 1 to fraction \frac{10}{10}.

$$-\frac{17}{10}-\frac{10}{10}+\frac{1}{2}$$

Since -\frac{17}{10} and \frac{10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-10}{10}+\frac{1}{2}$$

Subtract 10 from -17 to get -27.

$$-\frac{27}{10}+\frac{1}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{27}{10} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{27}{10}+\frac{5}{10}$$

Since -\frac{27}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{-27+5}{10}$$

Add -27 and 5 to get -22.

$$\frac{-22}{10}$$

Reduce the fraction \frac{-22}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{5}$$

Factor

$$-\frac{11}{5} = -2\frac{1}{5} = -2.2$$