Solve 3(2/3b)(3/4q)-bq/2(frac{2{3}b)(3/4q)+3bq}

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

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Cancel out 3 and 3.

$$\frac{2b\times \frac{3}{4}q-bq}{2\times \frac{2}{3}b\times \frac{3}{4}q+3bq}$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{\frac{2\times 3}{4}bq-bq}{2\times \frac{2}{3}b\times \frac{3}{4}q+3bq}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{6}{4}bq-bq}{2\times \frac{2}{3}b\times \frac{3}{4}q+3bq}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}bq-bq}{2\times \frac{2}{3}b\times \frac{3}{4}q+3bq}$$

Combine \frac{3}{2}bq and -bq to get \frac{1}{2}bq.

$$\frac{\frac{1}{2}bq}{2\times \frac{2}{3}b\times \frac{3}{4}q+3bq}$$

Express 2\times \frac{2}{3} as a single fraction.

$$\frac{\frac{1}{2}bq}{\frac{2\times 2}{3}b\times \frac{3}{4}q+3bq}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{1}{2}bq}{\frac{4}{3}b\times \frac{3}{4}q+3bq}$$

Cancel out \frac{4}{3} and its reciprocal \frac{3}{4}.

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

Combine bq and 3bq to get 4bq.

$$\frac{\frac{1}{2}bq}{4bq}$$

Cancel out bq in both numerator and denominator.

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

Express \frac{\frac{1}{2}}{4} as a single fraction.

$$\frac{1}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$