Solve (3/2+4/3):17/18/frac{19{12}+frac{1}{4}-frac{2}{6}}

$$\frac { ( \frac { 3 } { 2 } + \frac { 4 } { 3 } ) : \frac { 17 } { 18 } } { \frac { 19 } { 12 } + \frac { 1 } { 4 } - \frac { 2 } { 6 } }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{\frac{9}{6}+\frac{8}{6}}{\frac{17}{18}}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{9+8}{6}}{\frac{17}{18}}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Add 9 and 8 to get 17.

$$\frac{\frac{\frac{17}{6}}{\frac{17}{18}}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Divide \frac{17}{6} by \frac{17}{18} by multiplying \frac{17}{6} by the reciprocal of \frac{17}{18}.

$$\frac{\frac{17}{6}\times \frac{18}{17}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Multiply \frac{17}{6} times \frac{18}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17\times 18}{6\times 17}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Cancel out 17 in both numerator and denominator.

$$\frac{\frac{18}{6}}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Divide 18 by 6 to get 3.

$$\frac{3}{\frac{19}{12}+\frac{1}{4}-\frac{2}{6}}$$

Least common multiple of 12 and 4 is 12. Convert \frac{19}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{3}{\frac{19}{12}+\frac{3}{12}-\frac{2}{6}}$$

Since \frac{19}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{19+3}{12}-\frac{2}{6}}$$

Add 19 and 3 to get 22.

$$\frac{3}{\frac{22}{12}-\frac{2}{6}}$$

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$\frac{3}{\frac{11}{6}-\frac{2}{6}}$$

Since \frac{11}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{\frac{11-2}{6}}$$

Subtract 2 from 11 to get 9.

$$\frac{3}{\frac{9}{6}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{\frac{3}{2}}$$

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

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

Cancel out 3 and 3.

$$2$$

Factor

$$2$$