The expression in the image shows:

$4 \frac{4}{9} + 4 \frac{2}{3}$

Step 1: Convert the mixed numbers to improper fractions.

1. $4 \frac{4}{9}$ becomes $\frac{40}{9}$: $4 \frac{4}{9} = 4 + \frac{4}{9} = \frac{36}{9} + \frac{4}{9} = \frac{40}{9}$

2. $4 \frac{2}{3}$ becomes $\frac{14}{3}$: $4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3}$

Step 2: Find a common denominator.

The denominators are 9 and 3. The least common denominator (LCD) is 9. So, convert $\frac{14}{3}$ to have the same denominator: $\frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9}$

Step 3: Add the fractions.

Now, add $\frac{40}{9}$ and $\frac{42}{9}$: $\frac{40}{9} + \frac{42}{9} = \frac{40 + 42}{9} = \frac{82}{9}$

Step 4: Simplify the result.

$\frac{82}{9} = 9 \frac{1}{9}$

So, the sum of $4 \frac{4}{9} + 4 \frac{2}{3}$ is $9 \frac{1}{9}$.

Would you like more details on any step or further clarification?

Here are 5 related questions to explore:

1. How do you subtract mixed numbers like this?
2. What is the best method to multiply two mixed numbers?
3. Can you explain how to divide fractions with different denominators?
4. How do you convert improper fractions back into mixed numbers?
5. How do you handle adding mixed numbers with different whole parts?

Tip: When dealing with fractions, always look for the least common denominator to make calculations easier!