Solve (-2/3+2)-(2/3-2)

$$( \frac { - 2 } { 3 } + 2 ) - ( \frac { 2 } { 3 } - 2 )$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

Since -\frac{2}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add -2 and 6 to get 4.

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

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

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

Since \frac{2}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}-\frac{2-6}{3}$$

Subtract 6 from 2 to get -4.

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

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{4}{3}+\frac{4}{3}$$

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

$$\frac{4+4}{3}$$

Add 4 and 4 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$