To solve \( 4 \frac{2}{4} \div 1 \frac{6}{9} \), let's first convert the mixed numbers into improper fractions.

1. Convert \( 4 \frac{2}{4} \) to an improper fraction:
   \[
   4 \frac{2}{4} = \frac{4 \times 4 + 2}{4} = \frac{16 + 2}{4} = \frac{18}{4}
   \]

2. Convert \( 1 \frac{6}{9} \) to an improper fraction:
   \[
   1 \frac{6}{9} = \frac{1 \times 9 + 6}{9} = \frac{9 + 6}{9} = \frac{15}{9}
   \]

Now, perform the division:
\[
\frac{18}{4} \div \frac{15}{9}
\]

To divide fractions, multiply by the reciprocal of the second fraction:
\[
\frac{18}{4} \times \frac{9}{15}
\]

Simplify the fractions:
\[
\frac{18}{4} = \frac{9}{2} \quad \text{and} \quad \frac{9}{15} = \frac{3}{5}
\]

Now multiply the simplified fractions:
\[
\frac{9}{2} \times \frac{3}{5} = \frac{9 \times 3}{2 \times 5} = \frac{27}{10}
\]

Convert back to a mixed number:
\[
\frac{27}{10} = 2 \frac{7}{10}
\]

So, \( 4 \frac{2}{4} \div 1 \frac{6}{9} = 2 \frac{7}{10} \).

Would you like further details or clarifications?

### Related Questions:
1. How do you multiply and divide mixed numbers?
2. Can you explain the process of converting improper fractions to mixed numbers?
3. What are the rules for simplifying fractions?
4. How do you handle addition or subtraction with mixed numbers?
5. Can you explain how to find the reciprocal of a fraction?

**Tip:** Always simplify fractions at each step to make calculations easier!

Learn how to divide mixed numbers like 4 2/4 ÷ 1 6/9 by converting them into improper fractions and applying division rules. This detailed solution simplifies fractions and explains each step for Grades 5-7 students.

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