Adding Fractions with Different Denominators: 1/3 and 5/9

Let's solve the problem by finding the sum of $\frac{1}{3}$ and $\frac{5}{9}$.

• Step 1: Convert $\frac{1}{3}$ to have the same denominator as $\frac{5}{9}$.
  To convert $\frac{1}{3}$ to a fraction with a denominator of $9$, multiply both the numerator and the denominator by $3$:
  $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$.
• Step 2: Add the numerators of the two fractions now that they have the same denominator:
  $\frac{3}{9} + \frac{5}{9} = \frac{3 + 5}{9} = \frac{8}{9}$.
• Step 3: Simplify the result if possible. In this case, $\frac{8}{9}$ is already in its simplest form.
• Step 4: Verify the result against the given choices. The correct choice is $\frac{8}{9}$, which matches the given choice $2$.

Therefore, the solution to the problem is $\frac{8}{9}$.