To add the fractions \( \frac{7}{9} \) and \( \frac{3}{4} \), we need to find a common denominator.
The denominators are 9 and 4. The least common multiple (LCM) of 9 and 4 is 36.
Next, we convert each fraction to have a denominator of 36:
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For \( \frac{7}{9} \): \[ \frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \]
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For \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36} \]
Now we can add the two fractions: \[ \frac{28}{36} + \frac{27}{36} = \frac{28 + 27}{36} = \frac{55}{36} \]
The fraction \( \frac{55}{36} \) is already in simplest form because 55 and 36 have no common factors other than 1.
Thus, the final answer is: \[ \frac{55}{36} \]
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