Solve (11/2+1/3-1/6)*(6/4*frac{2}{3})=

$$( \frac { 11 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 6 } ) \times ( \frac { 6 } { 4 } \times \frac { 2 } { 3 } ) =$$

Evaluate

$$\frac{17}{3}\approx 5.666666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{11}{2} and \frac{1}{3} to fractions with denominator 6.

$$\left(\frac{33}{6}+\frac{2}{6}-\frac{1}{6}\right)\times \frac{6}{4}\times \frac{2}{3}$$

Since \frac{33}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{33+2}{6}-\frac{1}{6}\right)\times \frac{6}{4}\times \frac{2}{3}$$

Add 33 and 2 to get 35.

$$\left(\frac{35}{6}-\frac{1}{6}\right)\times \frac{6}{4}\times \frac{2}{3}$$

Since \frac{35}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-1}{6}\times \frac{6}{4}\times \frac{2}{3}$$

Subtract 1 from 35 to get 34.

$$\frac{34}{6}\times \frac{6}{4}\times \frac{2}{3}$$

Reduce the fraction \frac{34}{6} to lowest terms by extracting and canceling out 2.

$$\frac{17}{3}\times \frac{6}{4}\times \frac{2}{3}$$

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

$$\frac{17}{3}\times \frac{3}{2}\times \frac{2}{3}$$

Multiply \frac{17}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 3}{3\times 2}\times \frac{2}{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{17}{2}\times \frac{2}{3}$$

Multiply \frac{17}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{17}{3}$$

Factor

$$\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667$$