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

### Step 1: Convert mixed numbers to improper fractions.
- \(2 \frac{1}{6} = \frac{13}{6}\)
  \[
  2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6}
  \]
- \(4 \frac{1}{2} = \frac{9}{2}\)
  \[
  4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}
  \]

### Step 2: Multiply the improper fractions.
\[
\frac{13}{6} \times \frac{9}{2} = \frac{13 \times 9}{6 \times 2} = \frac{117}{12}
\]

### Step 3: Simplify the fraction.
To simplify \(\frac{117}{12}\), divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:
\[
\frac{117 \div 3}{12 \div 3} = \frac{39}{4}
\]

### Step 4: Convert the improper fraction back to a mixed number.
\[
\frac{39}{4} = 9 \frac{3}{4}
\]

### Final Answer:
\[
2 \frac{1}{6} \times 4 \frac{1}{2} = 9 \frac{3}{4}
\]

Would you like any further details on this solution?

Here are 5 related questions to expand your understanding:
1. How do you multiply fractions and mixed numbers in general?
2. How do you find the greatest common divisor (GCD) of two numbers?
3. Can you explain how to simplify fractions step by step?
4. How do you add or subtract mixed numbers?
5. What are improper fractions, and how do you convert them to mixed numbers?

**Tip:** When multiplying mixed numbers, always convert them to improper fractions first for easier calculations.

Learn how to multiply the mixed numbers 2 1/6 and 4 1/2 with a step-by-step solution. This guide includes conversion of mixed numbers to improper fractions, multiplication, simplification, and final conversion to a mixed number. Suitable for students in Grades 5-7.

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