To add the fractions \( \frac{5}{6} \) and \( \frac{7}{9} \), we need a common denominator. The least common denominator (LCD) of 6 and 9 is 18.
Now, we can convert each fraction to have the denominator of 18:
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Convert \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \]
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Convert \( \frac{7}{9} \): \[ \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \]
Now we can add the two fractions: \[ \frac{15}{18} + \frac{14}{18} = \frac{15 + 14}{18} = \frac{29}{18} \]
The result is \( \frac{29}{18} \), which is an improper fraction. It can also be expressed as a mixed number: \[ \frac{29}{18} = 1 \frac{11}{18} \]
So, the final answer is: \[ \frac{29}{18} \text{ or } 1 \frac{11}{18} \]