To divide \( 5 \frac{2}{9} \) by 13, let's follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \( 5 \frac{2}{9} \) can be converted as follows:

\[
5 \frac{2}{9} = \frac{(5 \times 9) + 2}{9} = \frac{45 + 2}{9} = \frac{47}{9}
\]

### Step 2: Divide the improper fraction by 13.
Dividing by 13 is the same as multiplying by the reciprocal of 13, which is \( \frac{1}{13} \):

\[
\frac{47}{9} \div 13 = \frac{47}{9} \times \frac{1}{13} = \frac{47}{117}
\]

### Final answer:
\[
5 \frac{2}{9} \div 13 = \frac{47}{117}
\]

This fraction can be simplified further if possible, but since 47 and 117 have no common factors, this is the simplified answer.

Would you like further clarification or have any questions?

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Here are 5 related questions:
1. How do you convert a mixed number to an improper fraction?
2. What is the reciprocal of a number, and how is it used in division?
3. Can you simplify fractions that don't have common factors?
4. How do you multiply two fractions together?
5. How would you convert \( \frac{47}{117} \) into a decimal?

**Tip:** Always check if a fraction can be simplified by finding common factors between the numerator and denominator.

Learn how to divide the mixed number 5 2/9 by 13 with a step-by-step guide. This problem covers key concepts such as converting mixed numbers to improper fractions and dividing fractions using reciprocals. Suitable for students in Grades 5-7.

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