Solve (6/2+5/2-2/3):(3/2)=

$$( \frac { 6 } { 2 } + \frac { 5 } { 2 } - \frac { 2 } { 3 } ) : ( \frac { 3 } { 2 } ) =$$

Evaluate

$$\frac{29}{9}\approx 3.222222222$$

Solution Steps

Since \frac{6}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6+5}{2}-\frac{2}{3}}{\frac{3}{2}}$$

Add 6 and 5 to get 11.

$$\frac{\frac{11}{2}-\frac{2}{3}}{\frac{3}{2}}$$

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

$$\frac{\frac{33}{6}-\frac{4}{6}}{\frac{3}{2}}$$

Since \frac{33}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{33-4}{6}}{\frac{3}{2}}$$

Subtract 4 from 33 to get 29.

$$\frac{\frac{29}{6}}{\frac{3}{2}}$$

Divide \frac{29}{6} by \frac{3}{2} by multiplying \frac{29}{6} by the reciprocal of \frac{3}{2}.

$$\frac{29}{6}\times \frac{2}{3}$$

Multiply \frac{29}{6} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 2}{6\times 3}$$

Do the multiplications in the fraction \frac{29\times 2}{6\times 3}.

$$\frac{58}{18}$$

Reduce the fraction \frac{58}{18} to lowest terms by extracting and canceling out 2.

$$\frac{29}{9}$$

Factor

$$\frac{29}{3 ^ {2}} = 3\frac{2}{9} = 3.2222222222222223$$