To express  in simplest form 4 ⅜ x 2 ⅖

To express the product of \(4 \frac{3}{8} \times 2 \frac{2}{5}\) in its simplest form, follow these steps:

1. **Convert the mixed numbers to improper fractions**:
   - \(4 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}\)
   - \(2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}\)

2. **Multiply the improper fractions**:
   \[
   \frac{35}{8} \times \frac{12}{5} = \frac{35 \times 12}{8 \times 5} = \frac{420}{40}
   \]

3. **Simplify the fraction**:
   - Find the greatest common divisor (GCD) of 420 and 40, which is 20.
   - Divide both the numerator and the denominator by their GCD:
   \[
   \frac{420 \div 20}{40 \div 20} = \frac{21}{2}
   \]

4. **Convert the improper fraction back to a mixed number** (if desired):
   \[
   \frac{21}{2} = 10 \frac{1}{2}
   \]

So, the product \(4 \frac{3}{8} \times 2 \frac{2}{5}\) in its simplest form is \(10 \frac{1}{2}\).

Would you like any further details or have any questions?

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**Related Questions**:
1. How do you multiply two improper fractions?
2. What is the process to simplify fractions?
3. How do you convert a mixed number to an improper fraction?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. Can you demonstrate simplifying more complex fractions?

**Tip**: Always check if a fraction can be simplified further by finding the greatest common divisor of the numerator and denominator.

Learn how to simplify the product of 4 3/8 and 2 2/5 into its simplest form with a detailed step-by-step solution. This problem covers fractions, mixed numbers, improper fractions, and the process of simplifying fractions. Suitable for students in Grades 5-6.

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