Solve (+2/3)+(-1/5)+(+4/3)+(-4/5)

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

Evaluate

$$1$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

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

Since \frac{10}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 10 to get 7.

$$\frac{7}{15}+\frac{4}{3}-\frac{4}{5}$$

Least common multiple of 15 and 3 is 15. Convert \frac{7}{15} and \frac{4}{3} to fractions with denominator 15.

$$\frac{7}{15}+\frac{20}{15}-\frac{4}{5}$$

Since \frac{7}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{7+20}{15}-\frac{4}{5}$$

Add 7 and 20 to get 27.

$$\frac{27}{15}-\frac{4}{5}$$

Reduce the fraction \frac{27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{9}{5}-\frac{4}{5}$$

Since \frac{9}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-4}{5}$$

Subtract 4 from 9 to get 5.

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

Divide 5 by 5 to get 1.

$$1$$

Factor

$$1$$