Solve (-1/2)+(+7/3)+(-4/15)+(-2/5)=

$$( - \frac { 1 } { 2 } ) + ( + \frac { 7 } { 3 } ) + ( - \frac { 4 } { 15 } ) + ( - \frac { 2 } { 5 } ) =$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{7}{3} to fractions with denominator 6.

$$-\frac{3}{6}+\frac{14}{6}-\frac{4}{15}-\frac{2}{5}$$

Since -\frac{3}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$\frac{-3+14}{6}-\frac{4}{15}-\frac{2}{5}$$

Add -3 and 14 to get 11.

$$\frac{11}{6}-\frac{4}{15}-\frac{2}{5}$$

Least common multiple of 6 and 15 is 30. Convert \frac{11}{6} and \frac{4}{15} to fractions with denominator 30.

$$\frac{55}{30}-\frac{8}{30}-\frac{2}{5}$$

Since \frac{55}{30} and \frac{8}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-8}{30}-\frac{2}{5}$$

Subtract 8 from 55 to get 47.

$$\frac{47}{30}-\frac{2}{5}$$

Least common multiple of 30 and 5 is 30. Convert \frac{47}{30} and \frac{2}{5} to fractions with denominator 30.

$$\frac{47}{30}-\frac{12}{30}$$

Since \frac{47}{30} and \frac{12}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{47-12}{30}$$

Subtract 12 from 47 to get 35.

$$\frac{35}{30}$$

Reduce the fraction \frac{35}{30} to lowest terms by extracting and canceling out 5.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$