To solve the division of mixed numbers \(3 \frac{1}{3} \div 1 \frac{2}{9}\), we first need to convert the mixed numbers into improper fractions.

### Step 1: Convert Mixed Numbers to Improper Fractions
- \(3 \frac{1}{3}\) can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator:
  \[
  3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
  \]
- \(1 \frac{2}{9}\) can be converted similarly:
  \[
  1 \frac{2}{9} = \frac{1 \times 9 + 2}{9} = \frac{9 + 2}{9} = \frac{11}{9}
  \]

### Step 2: Perform the Division of Fractions
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{10}{3} \div \frac{11}{9} = \frac{10}{3} \times \frac{9}{11} = \frac{10 \times 9}{3 \times 11} = \frac{90}{33}
\]

### Step 3: Simplify the Fraction
Now, simplify \(\frac{90}{33}\):
\[
\frac{90}{33} = \frac{30}{11} \quad \text{(Divide both numerator and denominator by 3)}
\]

### Step 4: Convert the Improper Fraction to a Mixed Number
Finally, convert \(\frac{30}{11}\) back to a mixed number:
\[
\frac{30}{11} = 2 \frac{8}{11}
\]

So, \(3 \frac{1}{3} \div 1 \frac{2}{9} = 2 \frac{8}{11}\).

Would you like any details or have any further questions?

### Related Questions:
1. How do you convert improper fractions back into mixed numbers?
2. What is the process of finding the reciprocal of a fraction?
3. How do you multiply fractions step by step?
4. How do you simplify fractions with large numerators and denominators?
5. Can you show how to convert a division of fractions into a multiplication problem?
6. What is the significance of simplifying fractions in solving problems?
7. How do you handle division of fractions involving negative numbers?
8. What are other methods to divide mixed numbers?

### Tip:
Always simplify fractions whenever possible to make further calculations easier.

Learn how to divide mixed numbers 3 1/3 ÷ 1 2/9 step-by-step with detailed explanations. This problem covers fractions, mixed numbers, and division of fractions concepts, suitable for Grades 6-8.

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