Solve 41/2+(-2/3)+4/5+(-1/2)+(-frac{1}{3})

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

Evaluate

$$\frac{19}{5}=3.8$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}-\frac{2}{3}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}-\frac{2}{3}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{27}{6}-\frac{4}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Since \frac{27}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-4}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Subtract 4 from 27 to get 23.

$$\frac{23}{6}+\frac{4}{5}-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 6 and 5 is 30. Convert \frac{23}{6} and \frac{4}{5} to fractions with denominator 30.

$$\frac{115}{30}+\frac{24}{30}-\frac{1}{2}-\frac{1}{3}$$

Since \frac{115}{30} and \frac{24}{30} have the same denominator, add them by adding their numerators.

$$\frac{115+24}{30}-\frac{1}{2}-\frac{1}{3}$$

Add 115 and 24 to get 139.

$$\frac{139}{30}-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 30 and 2 is 30. Convert \frac{139}{30} and \frac{1}{2} to fractions with denominator 30.

$$\frac{139}{30}-\frac{15}{30}-\frac{1}{3}$$

Since \frac{139}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{139-15}{30}-\frac{1}{3}$$

Subtract 15 from 139 to get 124.

$$\frac{124}{30}-\frac{1}{3}$$

Reduce the fraction \frac{124}{30} to lowest terms by extracting and canceling out 2.

$$\frac{62}{15}-\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{62}{15} and \frac{1}{3} to fractions with denominator 15.

$$\frac{62}{15}-\frac{5}{15}$$

Since \frac{62}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{62-5}{15}$$

Subtract 5 from 62 to get 57.

$$\frac{57}{15}$$

Reduce the fraction \frac{57}{15} to lowest terms by extracting and canceling out 3.

$$\frac{19}{5}$$

Factor

$$\frac{19}{5} = 3\frac{4}{5} = 3.8$$