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

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

Evaluate

$$-\frac{5}{2}=-2.5$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}-\frac{2}{1}-\left(\frac{1}{3}+\frac{2}{3}\right)$$

Anything divided by one gives itself.

$$\frac{1}{2}-2-\left(\frac{1}{3}+\frac{2}{3}\right)$$

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 1 to get -3.

$$-\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)$$

Since \frac{1}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$-\frac{3}{2}-\frac{1+2}{3}$$

Add 1 and 2 to get 3.

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

Divide 3 by 3 to get 1.

$$-\frac{3}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

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

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

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

Subtract 2 from -3 to get -5.

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

Factor

$$-\frac{5}{2} = -2\frac{1}{2} = -2.5$$