Solve 2/5-[4/3+8/4-4/5)

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

Evaluate

$$-\frac{32}{15}\approx -2.133333333$$

Solution Steps

Divide 8 by 4 to get 2.

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

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{4}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add 4 and 6 to get 10.

$$\frac{2}{5}-\left(\frac{10}{3}-\frac{4}{5}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{10}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{2}{5}-\left(\frac{50}{15}-\frac{12}{15}\right)$$

Since \frac{50}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}-\frac{50-12}{15}$$

Subtract 12 from 50 to get 38.

$$\frac{2}{5}-\frac{38}{15}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{38}{15} to fractions with denominator 15.

$$\frac{6}{15}-\frac{38}{15}$$

Since \frac{6}{15} and \frac{38}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-38}{15}$$

Subtract 38 from 6 to get -32.

$$-\frac{32}{15}$$

Factor

$$-\frac{32}{15} = -2\frac{2}{15} = -2.1333333333333333$$