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To add the fractions \( \frac{8}{11} \) and \( \frac{1}{7} \), we first need to find a common denominator. The least common multiple (LCM) of 11 and 7 is 77.
Now, we can convert each fraction to have a denominator of 77:
1. Convert \( \frac{8}{11} \):
\[
\frac{8}{11} = \frac{8 \times 7}{11 \times 7} = \frac{56}{77}
\]
2. Convert \( \frac{1}{7} \):
\[
\frac{1}{7} = \frac{1 \times 11}{7 \times 11} = \frac{11}{77}
\]
Now we can add the two fractions:
\[
\frac{56}{77} + \frac{11}{77} = \frac{56 + 11}{77} = \frac{67}{77}
\]
Therefore, the sum of \( \frac{8}{11} + \frac{1}{7} \) is \( \frac{67}{77} \).