Let's simplify the given expression step by step:

\[
\frac{8}{9} \div \frac{4}{9} + \frac{3}{8}
\]

### Step 1: Convert Division into Multiplication  
Dividing by a fraction is equivalent to multiplying by its reciprocal:

\[
\frac{8}{9} \times \frac{9}{4} + \frac{3}{8}
\]

### Step 2: Multiply Fractions  
Multiply the numerators and denominators:

\[
\frac{8 \times 9}{9 \times 4} = \frac{72}{36} = \frac{2}{1} = 2
\]

So, the expression simplifies to:

\[
2 + \frac{3}{8}
\]

### Step 3: Convert to a Common Denominator  
Rewrite \(2\) with a denominator of 8:

\[
\frac{16}{8} + \frac{3}{8}
\]

### Step 4: Add the Fractions  
\[
\frac{16 + 3}{8} = \frac{19}{8}
\]

### Final Answer:  
\[
\frac{19}{8} \quad \text{or} \quad 2.375
\]

Would you like a detailed breakdown of any step?  

### Related Questions:
1. How do you simplify a complex fraction step by step?
2. What is the rule for dividing fractions?
3. How do you find a common denominator when adding fractions?
4. How can mixed numbers be converted into improper fractions?
5. What are some real-life applications of fraction division?

### **Tip:**  
When dividing fractions, always **multiply by the reciprocal** to simplify the process easily!

Learn how to simplify the expression 8/9 ÷ 4/9 + 3/8 step by step. This solution covers key concepts such as dividing fractions, adding fractions, finding common denominators, and converting to mixed numbers. Ideal for students in Grades 6-8.

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