Solve 1/5-(-1/2+21/5)+(-2/5-1)

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

Evaluate

$$-\frac{29}{10}=-2.9$$

Solution Steps

Multiply 2 and 5 to get 10.

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

Add 10 and 1 to get 11.

$$\frac{1}{5}-\left(-\frac{1}{2}+\frac{11}{5}\right)-\frac{2}{5}-1$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{11}{5} to fractions with denominator 10.

$$\frac{1}{5}-\left(-\frac{5}{10}+\frac{22}{10}\right)-\frac{2}{5}-1$$

Since -\frac{5}{10} and \frac{22}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}-\frac{-5+22}{10}-\frac{2}{5}-1$$

Add -5 and 22 to get 17.

$$\frac{1}{5}-\frac{17}{10}-\frac{2}{5}-1$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{17}{10} to fractions with denominator 10.

$$\frac{2}{10}-\frac{17}{10}-\frac{2}{5}-1$$

Since \frac{2}{10} and \frac{17}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-17}{10}-\frac{2}{5}-1$$

Subtract 17 from 2 to get -15.

$$\frac{-15}{10}-\frac{2}{5}-1$$

Reduce the fraction \frac{-15}{10} to lowest terms by extracting and canceling out 5.

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

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

$$-\frac{15}{10}-\frac{4}{10}-1$$

Since -\frac{15}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-4}{10}-1$$

Subtract 4 from -15 to get -19.

$$-\frac{19}{10}-1$$

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

$$-\frac{19}{10}-\frac{10}{10}$$

Since -\frac{19}{10} and \frac{10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-19-10}{10}$$

Subtract 10 from -19 to get -29.

$$-\frac{29}{10}$$

Factor

$$-\frac{29}{10} = -2\frac{9}{10} = -2.9$$