1. The problem is to add the fractions $\frac{14}{35}$, $\frac{9}{35}$, and $\frac{2}{35}$ and simplify the result. 2. Since all fractions have the same denominator, we can add the numerators directly: $$\frac{14}{35} + \frac{9}{35} + \frac{2}{35} = \frac{14 + 9 + 2}{35}$$ 3. Calculate the sum of the numerators: $$14 + 9 + 2 = 25$$ 4. So the sum is: $$\frac{25}{35}$$ 5. To simplify, find the greatest common divisor (GCD) of 25 and 35, which is 5. 6. Divide numerator and denominator by 5: $$\frac{\cancel{25}^5}{\cancel{35}^5} = \frac{5}{7}$$ 7. The simplified form of the sum is $\frac{5}{7}$. Therefore, the answer is $\frac{5}{7}$.