Solve (-3)^2-(11/2)^3*2/9-6div|-2/3|+|-11/8|divfrac{3}{4}*frac{4}{3}*|-frac{1}{2}|

$$( - 3 ) ^ { 2 } - ( 1 \frac { 1 } { 2 } ) ^ { 3 } \times \frac { 2 } { 9 } - 6 \div | - \frac { 2 } { 3 } | + | - 1 \frac { 1 } { 8 } | \div \frac { 3 } { 4 } \times \frac { 4 } { 3 } \times | - \frac { 1 } { 2 } |$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$9-\left(\frac{1\times 2+1}{2}\right)^{3}\times \frac{2}{9}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply 1 and 2 to get 2.

$$9-\left(\frac{2+1}{2}\right)^{3}\times \frac{2}{9}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Add 2 and 1 to get 3.

$$9-\left(\frac{3}{2}\right)^{3}\times \frac{2}{9}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$9-\frac{27}{8}\times \frac{2}{9}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply \frac{27}{8} and \frac{2}{9} to get \frac{3}{4}.

$$9-\frac{3}{4}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Subtract \frac{3}{4} from 9 to get \frac{33}{4}.

$$\frac{33}{4}-\frac{6}{|-\frac{2}{3}|}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{2}{3} is \frac{2}{3}.

$$\frac{33}{4}-\frac{6}{\frac{2}{3}}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Divide 6 by \frac{2}{3} by multiplying 6 by the reciprocal of \frac{2}{3}.

$$\frac{33}{4}-6\times \frac{3}{2}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply 6 and \frac{3}{2} to get 9.

$$\frac{33}{4}-9+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Subtract 9 from \frac{33}{4} to get -\frac{3}{4}.

$$-\frac{3}{4}+\frac{|-\frac{1\times 8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply 1 and 8 to get 8.

$$-\frac{3}{4}+\frac{|-\frac{8+1}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Add 8 and 1 to get 9.

$$-\frac{3}{4}+\frac{|-\frac{9}{8}|}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{9}{8} is \frac{9}{8}.

$$-\frac{3}{4}+\frac{\frac{9}{8}}{\frac{3}{4}}\times \frac{4}{3}|-\frac{1}{2}|$$

Divide \frac{9}{8} by \frac{3}{4} by multiplying \frac{9}{8} by the reciprocal of \frac{3}{4}.

$$-\frac{3}{4}+\frac{9}{8}\times \frac{4}{3}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply \frac{9}{8} and \frac{4}{3} to get \frac{3}{2}.

$$-\frac{3}{4}+\frac{3}{2}\times \frac{4}{3}|-\frac{1}{2}|$$

Multiply \frac{3}{2} and \frac{4}{3} to get 2.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

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

Multiply 2 and \frac{1}{2} to get 1.

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

Add -\frac{3}{4} and 1 to get \frac{1}{4}.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$