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

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

Evaluate

$$-\frac{1}{5}=-0.2$$

Solution Steps

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

$$\frac{3}{6}-\frac{4}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

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

$$\frac{3-4}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Subtract 4 from 3 to get -1.

$$-\frac{1}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{1}{6} and \frac{4}{5} to fractions with denominator 30.

$$-\frac{5}{30}+\frac{24}{30}-\frac{1}{2}-\frac{1}{3}$$

Since -\frac{5}{30} and \frac{24}{30} have the same denominator, add them by adding their numerators.

$$\frac{-5+24}{30}-\frac{1}{2}-\frac{1}{3}$$

Add -5 and 24 to get 19.

$$\frac{19}{30}-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 30 and 2 is 30. Convert \frac{19}{30} and \frac{1}{2} to fractions with denominator 30.

$$\frac{19}{30}-\frac{15}{30}-\frac{1}{3}$$

Since \frac{19}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-15}{30}-\frac{1}{3}$$

Subtract 15 from 19 to get 4.

$$\frac{4}{30}-\frac{1}{3}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{2}{15}-\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{2}{15} and \frac{1}{3} to fractions with denominator 15.

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

Since \frac{2}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 2 to get -3.

$$\frac{-3}{15}$$

Reduce the fraction \frac{-3}{15} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{5} = -0.2$$