1. First, rewrite the mixed numbers as improper fractions: $$3\frac{1}{2} = \frac{7}{2}, \quad 1\frac{13}{14} = \frac{27}{14}$$ 2. Rewrite the expression as: $$\frac{7}{2} + \frac{2}{7} - \frac{27}{14}$$ 3. Find the least common denominator (LCD) for 2, 7, and 14; it is 14. 4. Convert each fraction to have denominator 14: $$\frac{7}{2} = \frac{49}{14}, \quad \frac{2}{7} = \frac{4}{14}, \quad \frac{27}{14} = \frac{27}{14}$$ 5. Perform the addition and subtraction: $$\frac{49}{14} + \frac{4}{14} - \frac{27}{14} = \frac{49 + 4 - 27}{14} = \frac{26}{14}$$ 6. Simplify the fraction: $$\frac{26}{14} = \frac{13}{7} = 1\frac{6}{7}$$ Final answer: $1\frac{6}{7}$