Solve 2/5-4/3-(8/4-4/5)+frac{3}{5}-frac{1}{3})

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

Evaluate

$$-\frac{28}{15}\approx -1.866666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{6}{15}-\frac{20}{15}-\left(\frac{8}{4}-\frac{4}{5}\right)+\frac{3}{5}-\frac{1}{3}$$

Since \frac{6}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-20}{15}-\left(\frac{8}{4}-\frac{4}{5}\right)+\frac{3}{5}-\frac{1}{3}$$

Subtract 20 from 6 to get -14.

$$-\frac{14}{15}-\left(\frac{8}{4}-\frac{4}{5}\right)+\frac{3}{5}-\frac{1}{3}$$

Divide 8 by 4 to get 2.

$$-\frac{14}{15}-\left(2-\frac{4}{5}\right)+\frac{3}{5}-\frac{1}{3}$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{14}{15}-\left(\frac{10}{5}-\frac{4}{5}\right)+\frac{3}{5}-\frac{1}{3}$$

Since \frac{10}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{14}{15}-\frac{10-4}{5}+\frac{3}{5}-\frac{1}{3}$$

Subtract 4 from 10 to get 6.

$$-\frac{14}{15}-\frac{6}{5}+\frac{3}{5}-\frac{1}{3}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{14}{15} and \frac{6}{5} to fractions with denominator 15.

$$-\frac{14}{15}-\frac{18}{15}+\frac{3}{5}-\frac{1}{3}$$

Since -\frac{14}{15} and \frac{18}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-14-18}{15}+\frac{3}{5}-\frac{1}{3}$$

Subtract 18 from -14 to get -32.

$$-\frac{32}{15}+\frac{3}{5}-\frac{1}{3}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{32}{15} and \frac{3}{5} to fractions with denominator 15.

$$-\frac{32}{15}+\frac{9}{15}-\frac{1}{3}$$

Since -\frac{32}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{-32+9}{15}-\frac{1}{3}$$

Add -32 and 9 to get -23.

$$-\frac{23}{15}-\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert -\frac{23}{15} and \frac{1}{3} to fractions with denominator 15.

$$-\frac{23}{15}-\frac{5}{15}$$

Since -\frac{23}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-23-5}{15}$$

Subtract 5 from -23 to get -28.

$$-\frac{28}{15}$$

Factor

$$-\frac{28}{15} = -1\frac{13}{15} = -1.8666666666666667$$