To add the fractions \( \frac{3}{4} \) and \( \frac{5}{6} \), we first need to find a common denominator. The least common multiple (LCM) of 4 and 6 is 12.
Next, we convert each fraction to have the denominator of 12:
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For \( \frac{3}{4} \): \[ \frac{3}{4} \times \frac{3}{3} = \frac{9}{12} \]
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For \( \frac{5}{6} \): \[ \frac{5}{6} \times \frac{2}{2} = \frac{10}{12} \]
Now, we can add the two fractions: \[ \frac{9}{12} + \frac{10}{12} = \frac{19}{12} \]
Next, we convert \( \frac{19}{12} \) into a mixed number. We divide 19 by 12:
- 19 divided by 12 is 1 with a remainder of 7.
Thus, we can express \( \frac{19}{12} \) as: \[ 1 \frac{7}{12} \]
So, the final result is: \[ 1 \frac{7}{12} \]