To solve the division of a fraction by a mixed number \( \frac{1}{6} \div 2 \frac{2}{9} \), follow these steps:

### Step 1: Convert the Mixed Number to an Improper Fraction
First, convert \( 2 \frac{2}{9} \) into an improper fraction:
\[
2 \frac{2}{9} = \frac{2 \times 9 + 2}{9} = \frac{18 + 2}{9} = \frac{20}{9}
\]

### Step 2: Perform the Division by Multiplying by the Reciprocal
Next, divide \( \frac{1}{6} \) by \( \frac{20}{9} \) by multiplying by the reciprocal of \( \frac{20}{9} \):
\[
\frac{1}{6} \div \frac{20}{9} = \frac{1}{6} \times \frac{9}{20} = \frac{1 \times 9}{6 \times 20} = \frac{9}{120}
\]

### Step 3: Simplify the Fraction
Finally, simplify the fraction \( \frac{9}{120} \):
\[
\frac{9}{120} = \frac{3}{40} \quad \text{(Divide both numerator and denominator by 3)}
\]

So, \( \frac{1}{6} \div 2 \frac{2}{9} = \frac{3}{40} \).

Would you like any details or have any further questions?

### Related Questions:
1. How do you divide a whole number by a fraction?
2. What is the importance of finding the reciprocal in division problems?
3. How do you simplify complex fractions?
4. What steps should you follow when converting mixed numbers to improper fractions?
5. Can you explain why multiplying by the reciprocal works in division?
6. How do you convert improper fractions back to mixed numbers?
7. What is the process to multiply fractions and simplify the result?
8. How can you handle division problems involving decimal fractions?

### Tip:
When dividing by a mixed number, always convert it to an improper fraction first to simplify the process.

Learn how to divide the fraction 1/6 by the mixed number 2 2/9 with a step-by-step solution. This problem covers key concepts including fractions, division of fractions, mixed numbers, and the use of reciprocals in division. Suitable for students in Grades 6-8.

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