1. **State the problem:** Add and simplify the fractions $\frac{1}{14} + \frac{2}{14} + \frac{8}{14}$. 2. **Formula and rules:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{d} + \frac{b}{d} = \frac{a+b}{d}$$ 3. **Add the numerators:** $$\frac{1}{14} + \frac{2}{14} + \frac{8}{14} = \frac{1+2+8}{14} = \frac{11}{14}$$ 4. **Simplify the fraction:** The fraction $\frac{11}{14}$ cannot be simplified further because 11 and 14 have no common factors other than 1. 5. **Final answer:** $$\boxed{\frac{11}{14}}$$