Standardize the expression

The given expression is $\frac{11}{18} + \frac{7}{-27}$. Move the negative sign to the numerator to simplify calculation: $\frac{11}{18} - \frac{7}{27}$.

$\frac{11}{18} - \frac{7}{27}$

Find the common denominator

The LCM of the denominators $18$ ($2 \times 3^2$) and $27$ ($3^3$) is $2 \times 3^3 = 54$.

$LCM(18, 27) = 54$

Convert fractions to common denominator

Convert $\frac{11}{18}$ to $\frac{11 \times 3}{18 \times 3} = \frac{33}{54}$ and $\frac{7}{27}$ to $\frac{7 \times 2}{27 \times 2} = \frac{14}{54}$.

$\frac{33}{54} - \frac{14}{54}$

Calculate the final result

Subtract the numerators while keeping the common denominator: $(33 - 14) / 54 = 19 / 54$.

$\frac{19}{54}$