Solve 5/9div(7/9+11/18)

$$\frac{ 5 }{ 9 } \div ( \frac{ 7 }{ 9 } + \frac{ 11 }{ 18 } )$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Least common multiple of 9 and 18 is 18. Convert \frac{7}{9} and \frac{11}{18} to fractions with denominator 18.

$$\frac{\frac{5}{9}}{\frac{14}{18}+\frac{11}{18}}$$

Since \frac{14}{18} and \frac{11}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{9}}{\frac{14+11}{18}}$$

Add 14 and 11 to get 25.

$$\frac{\frac{5}{9}}{\frac{25}{18}}$$

Divide \frac{5}{9} by \frac{25}{18} by multiplying \frac{5}{9} by the reciprocal of \frac{25}{18}.

$$\frac{5}{9}\times \frac{18}{25}$$

Multiply \frac{5}{9} times \frac{18}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 18}{9\times 25}$$

Do the multiplications in the fraction \frac{5\times 18}{9\times 25}.

$$\frac{90}{225}$$

Reduce the fraction \frac{90}{225} to lowest terms by extracting and canceling out 45.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$