Solve (7/6-5/9)div11/8

$$( \frac { 7 } { 6 } - \frac { 5 } { 9 } ) \div \frac { 11 } { 8 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{7}{6} and \frac{5}{9} to fractions with denominator 18.

$$\frac{\frac{21}{18}-\frac{10}{18}}{\frac{11}{8}}$$

Since \frac{21}{18} and \frac{10}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-10}{18}}{\frac{11}{8}}$$

Subtract 10 from 21 to get 11.

$$\frac{\frac{11}{18}}{\frac{11}{8}}$$

Divide \frac{11}{18} by \frac{11}{8} by multiplying \frac{11}{18} by the reciprocal of \frac{11}{8}.

$$\frac{11}{18}\times \frac{8}{11}$$

Multiply \frac{11}{18} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 8}{18\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$