To add the fractions \( \frac{7}{9} \) and \( \frac{5}{18} \), we first need a common denominator.
The least common multiple (LCM) of the denominators 9 and 18 is 18.
Now, let's convert \( \frac{7}{9} \) to the equivalent fraction with a denominator of 18:
\[ \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \]
Now we can add the fractions:
\[ \frac{14}{18} + \frac{5}{18} = \frac{14 + 5}{18} = \frac{19}{18} \]
Since \( \frac{19}{18} \) is already in simplest form, the answer can be expressed as:
\[ [19] [1]/[18] \]
Thus, the final answer is:
\[ \frac{19}{18} \]