Solve 4/9*((9/11+2/11)div(5/6-frac{3}{4}))

$$\frac{ 4 }{ 9 } \times (( \frac{ 9 }{ 11 } + \frac{ 2 }{ 11 } ) \div ( \frac{ 5 }{ 6 } - \frac{ 3 }{ 4 } ))$$

Evaluate

$$\frac{16}{3}\approx 5.333333333$$

Solution Steps

Since \frac{9}{11} and \frac{2}{11} have the same denominator, add them by adding their numerators.

$$\frac{4}{9}\times \frac{\frac{9+2}{11}}{\frac{5}{6}-\frac{3}{4}}$$

Add 9 and 2 to get 11.

$$\frac{4}{9}\times \frac{\frac{11}{11}}{\frac{5}{6}-\frac{3}{4}}$$

Divide 11 by 11 to get 1.

$$\frac{4}{9}\times \frac{1}{\frac{5}{6}-\frac{3}{4}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{4}{9}\times \frac{1}{\frac{10}{12}-\frac{9}{12}}$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{9}\times \frac{1}{\frac{10-9}{12}}$$

Subtract 9 from 10 to get 1.

$$\frac{4}{9}\times \frac{1}{\frac{1}{12}}$$

Divide 1 by \frac{1}{12} by multiplying 1 by the reciprocal of \frac{1}{12}.

$$\frac{4}{9}\times 1\times 12$$

Multiply 1 and 12 to get 12.

$$\frac{4}{9}\times 12$$

Express \frac{4}{9}\times 12 as a single fraction.

$$\frac{4\times 12}{9}$$

Multiply 4 and 12 to get 48.

$$\frac{48}{9}$$

Reduce the fraction \frac{48}{9} to lowest terms by extracting and canceling out 3.

$$\frac{16}{3}$$

Factor

$$\frac{2 ^ {4}}{3} = 5\frac{1}{3} = 5.333333333333333$$