Solve (1/3-12/5)+[2/5-(-8/15)]

$$( \frac { 1 } { 3 } - 1 \frac { 2 } { 5 } ) + [ \frac { 2 } { 5 } - ( - \frac { 8 } { 15 } ) ]$$

Evaluate

$$-\frac{2}{15}\approx -0.133333333$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{1}{3}-\frac{5+2}{5}+\frac{2}{5}-\left(-\frac{8}{15}\right)$$

Add 5 and 2 to get 7.

$$\frac{1}{3}-\frac{7}{5}+\frac{2}{5}-\left(-\frac{8}{15}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{7}{5} to fractions with denominator 15.

$$\frac{5}{15}-\frac{21}{15}+\frac{2}{5}-\left(-\frac{8}{15}\right)$$

Since \frac{5}{15} and \frac{21}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-21}{15}+\frac{2}{5}-\left(-\frac{8}{15}\right)$$

Subtract 21 from 5 to get -16.

$$-\frac{16}{15}+\frac{2}{5}-\left(-\frac{8}{15}\right)$$

The opposite of -\frac{8}{15} is \frac{8}{15}.

$$-\frac{16}{15}+\frac{2}{5}+\frac{8}{15}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{8}{15} to fractions with denominator 15.

$$-\frac{16}{15}+\frac{6}{15}+\frac{8}{15}$$

Since \frac{6}{15} and \frac{8}{15} have the same denominator, add them by adding their numerators.

$$-\frac{16}{15}+\frac{6+8}{15}$$

Add 6 and 8 to get 14.

$$-\frac{16}{15}+\frac{14}{15}$$

Since -\frac{16}{15} and \frac{14}{15} have the same denominator, add them by adding their numerators.

$$\frac{-16+14}{15}$$

Add -16 and 14 to get -2.

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

Factor

$$-\frac{2}{15} = -0.13333333333333333$$