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To find the quotient of the given expression:

\[
3 \frac{2}{9} \div 19
\]

### Step-by-Step Solution:

1. **Convert the mixed number to an improper fraction**:
   - \( 3 \frac{2}{9} \) is a mixed number. To convert it to an improper fraction:
   \[
   3 \frac{2}{9} = \frac{3 \times 9 + 2}{9} = \frac{29}{9}
   \]

2. **Rewrite the division as multiplication**:
   - Dividing by a number is the same as multiplying by its reciprocal. So, we can rewrite the division as:
   \[
   \frac{29}{9} \div 19 = \frac{29}{9} \times \frac{1}{19}
   \]

3. **Multiply the fractions**:
   \[
   \frac{29}{9} \times \frac{1}{19} = \frac{29 \times 1}{9 \times 19} = \frac{29}{171}
   \]

So, the quotient is:

\[
\frac{29}{171}
\]

This fraction can be simplified if there is a common factor, but in this case, 29 and 171 share no common factors, so this is the simplified result.

Would you like further clarification or additional details?

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Here are 5 related questions to expand your understanding:

1. How do you convert any mixed number to an improper fraction?
2. How can you simplify fractions after multiplication?
3. What is the difference between dividing fractions and multiplying their reciprocals?
4. Can you rewrite any division of fractions as multiplication?
5. How can you check if a fraction is in its simplest form?

**Tip**: Always simplify your answer whenever possible, and double-check for any common factors between the numerator and denominator!

Learn how to divide a mixed number, 3 2/9, by 19. This step-by-step guide explains the conversion of mixed numbers to improper fractions and dividing using reciprocal multiplication. Ideal for students in Grades 5-7.

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