5. \( 7 \frac{2}{7}+\frac{1}{7}= \)

To solve \( 7 \frac{2}{7} + \frac{1}{7} \), first convert the mixed number into an improper fraction. \( 7 \frac{2}{7} \) is equivalent to \( \frac{7 \times 7 + 2}{7} = \frac{49 + 2}{7} = \frac{51}{7} \). Now, you can add \( \frac{1}{7} \): \[ \frac{51}{7} + \frac{1}{7} = \frac{51 + 1}{7} = \frac{52}{7}. \] This improper fraction can be converted back to a mixed number: \( 7 \frac{3}{7} \). So, \( 7 \frac{2}{7} + \frac{1}{7} = 7 \frac{3}{7} \).