Solve 1/2+2/5/frac{2{9}-5/6}

$$\frac { \frac { 1 } { 2 } + \frac { 2 } { 5 } } { \frac { 2 } { 9 } - \frac { 5 } { 6 } }$$

Evaluate

$$-\frac{81}{55}\approx -1.472727273$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{\frac{5}{10}+\frac{4}{10}}{\frac{2}{9}-\frac{5}{6}}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4}{10}}{\frac{2}{9}-\frac{5}{6}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{9}{10}}{\frac{2}{9}-\frac{5}{6}}$$

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

$$\frac{\frac{9}{10}}{\frac{4}{18}-\frac{15}{18}}$$

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

$$\frac{\frac{9}{10}}{\frac{4-15}{18}}$$

Subtract 15 from 4 to get -11.

$$\frac{\frac{9}{10}}{-\frac{11}{18}}$$

Divide \frac{9}{10} by -\frac{11}{18} by multiplying \frac{9}{10} by the reciprocal of -\frac{11}{18}.

$$\frac{9}{10}\left(-\frac{18}{11}\right)$$

Multiply \frac{9}{10} times -\frac{18}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-18\right)}{10\times 11}$$

Do the multiplications in the fraction \frac{9\left(-18\right)}{10\times 11}.

$$\frac{-162}{110}$$

Reduce the fraction \frac{-162}{110} to lowest terms by extracting and canceling out 2.

$$-\frac{81}{55}$$

Factor

$$-\frac{81}{55} = -1\frac{26}{55} = -1.4727272727272727$$