Solve 3/4-(11/2+3/4-2)-2/3

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

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

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

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

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

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

Add 6 and 3 to get 9.

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

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

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

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

$$\frac{3}{4}-\frac{9-8}{4}-\frac{2}{3}$$

Subtract 8 from 9 to get 1.

$$\frac{3}{4}-\frac{1}{4}-\frac{2}{3}$$

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

$$\frac{3-1}{4}-\frac{2}{3}$$

Subtract 1 from 3 to get 2.

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

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

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

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

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

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

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

Subtract 4 from 3 to get -1.

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

Factor

$$-\frac{1}{6} = -0.16666666666666666$$