Solve (2/3+5/12-7/9)*9/11+(frac{1}{4}-frac{1}{3}-frac{1}{2}):3frac{1}{2}=?

$$( \frac { 2 } { 3 } + \frac { 5 } { 12 } - \frac { 7 } { 9 } ) \cdot \frac { 9 } { 11 } + ( \frac { 1 } { 4 } - \frac { 1 } { 3 } - \frac { 1 } { 2 } ) : 3 \frac { 1 } { 2 } = ?$$

Evaluate

$$\frac{1}{12}\approx 0.083333333$$

Solution Steps

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{5}{12} to fractions with denominator 12.

$$\left(\frac{8}{12}+\frac{5}{12}-\frac{7}{9}\right)\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Since \frac{8}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\left(\frac{8+5}{12}-\frac{7}{9}\right)\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Add 8 and 5 to get 13.

$$\left(\frac{13}{12}-\frac{7}{9}\right)\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Least common multiple of 12 and 9 is 36. Convert \frac{13}{12} and \frac{7}{9} to fractions with denominator 36.

$$\left(\frac{39}{36}-\frac{28}{36}\right)\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Since \frac{39}{36} and \frac{28}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-28}{36}\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Subtract 28 from 39 to get 11.

$$\frac{11}{36}\times \frac{9}{11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Multiply \frac{11}{36} times \frac{9}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 9}{36\times 11}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Cancel out 11 in both numerator and denominator.

$$\frac{9}{36}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Reduce the fraction \frac{9}{36} to lowest terms by extracting and canceling out 9.

$$\frac{1}{4}+\frac{\frac{1}{4}-\frac{1}{3}-\frac{1}{2}}{\frac{3\times 2+1}{2}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 3 to get -1.

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

Least common multiple of 12 and 2 is 12. Convert -\frac{1}{12} and \frac{1}{2} to fractions with denominator 12.

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

Since -\frac{1}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from -1 to get -7.

$$\frac{1}{4}+\frac{-\frac{7}{12}}{\frac{3\times 2+1}{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{1}{4}+\frac{-\frac{7}{12}}{\frac{6+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{1}{4}+\frac{-\frac{7}{12}}{\frac{7}{2}}$$

Divide -\frac{7}{12} by \frac{7}{2} by multiplying -\frac{7}{12} by the reciprocal of \frac{7}{2}.

$$\frac{1}{4}-\frac{7}{12}\times \frac{2}{7}$$

Multiply -\frac{7}{12} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}+\frac{-7\times 2}{12\times 7}$$

Do the multiplications in the fraction \frac{-7\times 2}{12\times 7}.

$$\frac{1}{4}+\frac{-14}{84}$$

Reduce the fraction \frac{-14}{84} to lowest terms by extracting and canceling out 14.

$$\frac{1}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

$$\frac{1}{12}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$$