Solve 5/6-2/9/frac{5{6}+2/9}

$$\frac { \frac { 5 } { 6 } - \frac { 2 } { 9 } } { \frac { 5 } { 6 } + \frac { 2 } { 9 } }$$

Evaluate

$$\frac{11}{19}\approx 0.578947368$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{2}{9} to fractions with denominator 18.

$$\frac{\frac{15}{18}-\frac{4}{18}}{\frac{5}{6}+\frac{2}{9}}$$

Since \frac{15}{18} and \frac{4}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-4}{18}}{\frac{5}{6}+\frac{2}{9}}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{11}{18}}{\frac{5}{6}+\frac{2}{9}}$$

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{2}{9} to fractions with denominator 18.

$$\frac{\frac{11}{18}}{\frac{15}{18}+\frac{4}{18}}$$

Since \frac{15}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{18}}{\frac{15+4}{18}}$$

Add 15 and 4 to get 19.

$$\frac{\frac{11}{18}}{\frac{19}{18}}$$

Divide \frac{11}{18} by \frac{19}{18} by multiplying \frac{11}{18} by the reciprocal of \frac{19}{18}.

$$\frac{11}{18}\times \frac{18}{19}$$

Multiply \frac{11}{18} times \frac{18}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 18}{18\times 19}$$

Cancel out 18 in both numerator and denominator.

$$\frac{11}{19}$$

Factor

$$\frac{11}{19} = 0.5789473684210527$$