To solve \( 4 \frac{5}{2} \times 6 \frac{1}{3} \), we'll first convert the mixed numbers to improper fractions and then multiply them.

1. **Convert to improper fractions:**

   \[
   4 \frac{5}{2} = \frac{4 \times 2 + 5}{2} = \frac{8 + 5}{2} = \frac{13}{2}
   \]

   \[
   6 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}
   \]

   So, the problem now is:

   \[
   \frac{13}{2} \times \frac{19}{3}
   \]

2. **Multiply the fractions:**

   \[
   \frac{13 \times 19}{2 \times 3} = \frac{247}{6}
   \]

3. **Convert back to a mixed number (if needed):**

   Dividing 247 by 6 gives 41 with a remainder of 1, so:

   \[
   \frac{247}{6} = 41 \frac{1}{6}
   \]

**Answer:**

\[
4 \frac{5}{2} \times 6 \frac{1}{3} = 41 \frac{1}{6}
\]

Would you like more details, or do you have questions?

1. How do you convert a mixed number to an improper fraction?
2. How is multiplying two improper fractions different from multiplying mixed numbers directly?
3. How do you convert an improper fraction back to a mixed number?
4. What are common errors when multiplying mixed numbers?
5. How can this process apply to dividing mixed numbers?

**Tip:** When converting mixed numbers to improper fractions, always multiply the whole number by the fraction’s denominator, then add the numerator.

Learn how to multiply mixed numbers with a detailed solution for 4 5/2 × 6 1/3. This guide explains converting mixed numbers to improper fractions, multiplying them, and converting back to a mixed number. Ideal for students in Grades 5-7.

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