Solve 1/18:(11/9+1/27)

$$\frac { 1 } { 18 } : ( \frac { 11 } { 9 } + \frac { 1 } { 27 } )$$

Evaluate

$$\frac{3}{68}\approx 0.044117647$$

Solution Steps

Least common multiple of 9 and 27 is 27. Convert \frac{11}{9} and \frac{1}{27} to fractions with denominator 27.

$$\frac{\frac{1}{18}}{\frac{33}{27}+\frac{1}{27}}$$

Since \frac{33}{27} and \frac{1}{27} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{18}}{\frac{33+1}{27}}$$

Add 33 and 1 to get 34.

$$\frac{\frac{1}{18}}{\frac{34}{27}}$$

Divide \frac{1}{18} by \frac{34}{27} by multiplying \frac{1}{18} by the reciprocal of \frac{34}{27}.

$$\frac{1}{18}\times \frac{27}{34}$$

Multiply \frac{1}{18} times \frac{27}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 27}{18\times 34}$$

Do the multiplications in the fraction \frac{1\times 27}{18\times 34}.

$$\frac{27}{612}$$

Reduce the fraction \frac{27}{612} to lowest terms by extracting and canceling out 9.

$$\frac{3}{68}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 17} = 0.04411764705882353$$