8. \( 1 \frac{6}{7}+\left(4 \frac{13}{14}-3 \frac{1}{2}\right) \)

To tackle this expression, let's simplify it step by step. First, we convert the mixed numbers into improper fractions: 1. \( 1 \frac{6}{7} = \frac{7 \cdot 1 + 6}{7} = \frac{13}{7} \) 2. \( 4 \frac{13}{14} = \frac{14 \cdot 4 + 13}{14} = \frac{56 + 13}{14} = \frac{69}{14} \) 3. \( 3 \frac{1}{2} = \frac{2 \cdot 3 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \) Next, compute \( 4 \frac{13}{14} - 3 \frac{1}{2} \): To perform the subtraction, we need a common denominator. The least common multiple of 14 and 2 is 14. Convert \( 3 \frac{1}{2} \): \[ 3 \frac{1}{2} = \frac{7}{2} = \frac{7 \cdot 7}{2 \cdot 7} = \frac{49}{14} \] Now we subtract: \[ \frac{69}{14} - \frac{49}{14} = \frac{69 - 49}{14} = \frac{20}{14} = \frac{10}{7} \] Now, add \( 1 \frac{6}{7} \) to the result: \[ 1 \frac{6}{7} + \frac{10}{7} = \frac{13}{7} + \frac{10}{7} = \frac{23}{7} \] Finally, convert \( \frac{23}{7} \) back to a mixed number: \[ \frac{23}{7} = 3 \frac{2}{7} \] So, the final answer is: \[ 3 \frac{2}{7} \]