Solve -2/3-[3/4-(11/2+3/4-2)-frac{2}{3}]

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

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

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

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

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

Add 6 and 3 to get 9.

$$-\frac{2}{3}-\left(\frac{3}{4}-\left(\frac{9}{4}-2\right)-\frac{2}{3}\right)$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{2}{3}-\left(\frac{3}{4}-\left(\frac{9}{4}-\frac{8}{4}\right)-\frac{2}{3}\right)$$

Since \frac{9}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}-\left(\frac{3}{4}-\frac{9-8}{4}-\frac{2}{3}\right)$$

Subtract 8 from 9 to get 1.

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

Since \frac{3}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

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

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

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

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

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

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

Subtract 4 from 3 to get -1.

$$-\frac{2}{3}-\left(-\frac{1}{6}\right)$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$-\frac{2}{3}+\frac{1}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$-\frac{4}{6}+\frac{1}{6}$$

Since -\frac{4}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{-4+1}{6}$$

Add -4 and 1 to get -3.

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

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{2} = -0.5$$