1. Problem: Calculate $\frac{1}{9} + \frac{4}{9}$. 2. Since the denominators are the same, add the numerators: $$\frac{1}{9} + \frac{4}{9} = \frac{1+4}{9}$$ 3. Simplify the numerator: $$\frac{5}{9}$$ 4. Final answer: $\frac{5}{9}$. This is a simple addition of fractions with the same denominator, so you just add the numerators and keep the denominator.