Solve the Fraction Addition: 2/3 + 2/9 Step-by-Step

To solve this problem, we need to add the fractions $\frac{2}{3}$ and $\frac{2}{9}$.

Step 1: Find a common denominator.

Given fractions have denominators 3 and 9. The least common multiple of 3 and 9 is 9. Therefore, we use 9 as the common denominator.

Step 2: Convert fractions to have the same denominator.

The second fraction, $\frac{2}{9}$, already has 9 as its denominator. We need to convert $\frac{2}{3}$ to have a denominator of 9.

To convert $\frac{2}{3}$:
Multiply both the numerator and the denominator by 3:
$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$.

Step 3: Add the fractions $\frac{6}{9}$ and $\frac{2}{9}$.

Since the denominators are the same, add the numerators:
$\frac{6}{9} + \frac{2}{9} = \frac{6+2}{9} = \frac{8}{9}$.

Therefore, the sum of $\frac{2}{3}$ and $\frac{2}{9}$ is $\frac{8}{9}$, which corresponds to choice number 3.