To add the fractions \( \frac{1}{6} \) and \( \frac{7}{8} \), we first need to find a common denominator. The least common multiple (LCM) of 6 and 8 is 24.
Next, we convert both fractions to have this common denominator:
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Convert \( \frac{1}{6} \) to a fraction with a denominator of 24: \[ \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \]
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Convert \( \frac{7}{8} \) to a fraction with a denominator of 24: \[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \]
Now we can add the two fractions: \[ \frac{4}{24} + \frac{21}{24} = \frac{4 + 21}{24} = \frac{25}{24} \]
So, \( \frac{1}{6} + \frac{7}{8} = \frac{25}{24} \), which is an improper fraction. It can also be expressed as: \[ 1 \frac{1}{24} \]
Thus, the final answer is: \[ \frac{25}{24} \text{ or } 1 \frac{1}{24} \]