Solve Mixed Number Multiplication: 4⁴/₇ × 2½ Step-by-Step

To solve this problem, we'll follow these steps:

• Convert each mixed number to an improper fraction.
• Multiply the two improper fractions.
• Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
For $4\frac{4}{7}$:
Multiply the whole number by the denominator: $4 \times 7 = 28$.
Add the numerator to this product: $28 + 4 = 32$.
Thus, $4\frac{4}{7} = \frac{32}{7}$.

For $2\frac{1}{2}$:
Multiply the whole number by the denominator: $2 \times 2 = 4$.
Add the numerator: $4 + 1 = 5$.
Thus, $2\frac{1}{2} = \frac{5}{2}$.

Step 2: Multiply the two improper fractions:
$\frac{32}{7} \times \frac{5}{2} = \frac{32 \times 5}{7 \times 2} = \frac{160}{14}$.

Step 3: Simplify $\frac{160}{14}$ and convert to a mixed number:
First, simplify the fraction by finding the greatest common divisor of 160 and 14, which is 2.
$\frac{160}{14} = \frac{160 \div 2}{14 \div 2} = \frac{80}{7}$.

Convert $\frac{80}{7}$ to a mixed number:
Divide 80 by 7, which gives a quotient of 11 and a remainder of 3.
Thus, $\frac{80}{7} = 11\frac{3}{7}$.

Therefore, the solution to the problem is $11\frac{3}{7}$.