To add $\frac{4}{9}$ and $\frac{2}{3}$, follow these steps:

1. Find a common denominator. The least common denominator (LCD) of 9 and 3 is 9.
2. Convert $\frac{2}{3}$ to a fraction with a denominator of 9:
   $\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.
3. Now, add the fractions:
   $\frac{4}{9} + \frac{6}{9} = \frac{4 + 6}{9} = \frac{10}{9}$.

So, $\frac{4}{9} + \frac{2}{3} = \frac{10}{9}$, or as a mixed number, $1 \frac{1}{9}$.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you subtract fractions with different denominators?
2. What is the least common denominator (LCD) and why is it important in fraction addition?
3. How do you convert improper fractions into mixed numbers?
4. Can you simplify fractions after addition or subtraction?
5. How do you multiply and divide fractions?

Tip: Always simplify your final answer whenever possible!