Solve (7/3+9/2*2/3-1/2)div(frac{1}{2}-frac{1}{3})

$$( \frac { 7 } { 3 } + \frac { 9 } { 2 } \times \frac { 2 } { 3 } - \frac { 1 } { 2 } ) \div ( \frac { 1 } { 2 } - \frac { 1 } { 3 } )$$

Evaluate

$$29$$

Solution Steps

Multiply \frac{9}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{3}+\frac{9\times 2}{2\times 3}-\frac{1}{2}}{\frac{1}{2}-\frac{1}{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{7}{3}+\frac{9}{3}-\frac{1}{2}}{\frac{1}{2}-\frac{1}{3}}$$

Since \frac{7}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+9}{3}-\frac{1}{2}}{\frac{1}{2}-\frac{1}{3}}$$

Add 7 and 9 to get 16.

$$\frac{\frac{16}{3}-\frac{1}{2}}{\frac{1}{2}-\frac{1}{3}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{16}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{32}{6}-\frac{3}{6}}{\frac{1}{2}-\frac{1}{3}}$$

Since \frac{32}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{32-3}{6}}{\frac{1}{2}-\frac{1}{3}}$$

Subtract 3 from 32 to get 29.

$$\frac{\frac{29}{6}}{\frac{1}{2}-\frac{1}{3}}$$

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

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

$$\frac{\frac{29}{6}}{\frac{1}{6}}$$

Divide \frac{29}{6} by \frac{1}{6} by multiplying \frac{29}{6} by the reciprocal of \frac{1}{6}.

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

Cancel out 6 and 6.

$$29$$

Factor

$$29$$