Solve (+1/5)+(-21/3)-(-24/5)-(+32/3)

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

Evaluate

$$-3$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{1}{5}-\frac{6+1}{3}-\left(-\frac{2\times 5+4}{5}\right)-\frac{3\times 3+2}{3}$$

Add 6 and 1 to get 7.

$$\frac{1}{5}-\frac{7}{3}-\left(-\frac{2\times 5+4}{5}\right)-\frac{3\times 3+2}{3}$$

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

$$\frac{3}{15}-\frac{35}{15}-\left(-\frac{2\times 5+4}{5}\right)-\frac{3\times 3+2}{3}$$

Since \frac{3}{15} and \frac{35}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-35}{15}-\left(-\frac{2\times 5+4}{5}\right)-\frac{3\times 3+2}{3}$$

Subtract 35 from 3 to get -32.

$$-\frac{32}{15}-\left(-\frac{2\times 5+4}{5}\right)-\frac{3\times 3+2}{3}$$

Multiply 2 and 5 to get 10.

$$-\frac{32}{15}-\left(-\frac{10+4}{5}\right)-\frac{3\times 3+2}{3}$$

Add 10 and 4 to get 14.

$$-\frac{32}{15}-\left(-\frac{14}{5}\right)-\frac{3\times 3+2}{3}$$

The opposite of -\frac{14}{5} is \frac{14}{5}.

$$-\frac{32}{15}+\frac{14}{5}-\frac{3\times 3+2}{3}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{32}{15} and \frac{14}{5} to fractions with denominator 15.

$$-\frac{32}{15}+\frac{42}{15}-\frac{3\times 3+2}{3}$$

Since -\frac{32}{15} and \frac{42}{15} have the same denominator, add them by adding their numerators.

$$\frac{-32+42}{15}-\frac{3\times 3+2}{3}$$

Add -32 and 42 to get 10.

$$\frac{10}{15}-\frac{3\times 3+2}{3}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\frac{3\times 3+2}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{2}{3}-\frac{9+2}{3}$$

Add 9 and 2 to get 11.

$$\frac{2}{3}-\frac{11}{3}$$

Since \frac{2}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-11}{3}$$

Subtract 11 from 2 to get -9.

$$\frac{-9}{3}$$

Divide -9 by 3 to get -3.

$$-3$$

Factor

$$-3$$