To add the fractions \( \frac{4}{5} \) and \( \frac{5}{6} \), we first need a common denominator. The least common multiple (LCM) of 5 and 6 is 30.
Next, we convert each fraction to have a denominator of 30:
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Convert \( \frac{4}{5} \): \[ \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \]
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Convert \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \]
Now, we can add the two fractions: \[ \frac{24}{30} + \frac{25}{30} = \frac{24 + 25}{30} = \frac{49}{30} \]
Now we check if \( \frac{49}{30} \) can be simplified. Since 49 (which is \( 7^2 \)) and 30 (which is \( 2 \times 3 \times 5 \)) have no common factors, the fraction is already in simplest form.
Therefore, the final answer is: \[ \frac{49}{30} \]
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