Multiply Mixed Numbers: 1 4/5 × 2 1/2 Step-by-Step Solution

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the resulting fraction, if needed, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed numbers to improper fractions.
For $1\frac{4}{5}$:
$1\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}$.
For $2\frac{1}{2}$:
$2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$.

Step 2: Multiply the improper fractions:
$\frac{9}{5} \times \frac{5}{2} = \frac{9 \times 5}{5 \times 2} = \frac{45}{10}$.

Step 3: Simplify the fraction and convert it back to a mixed number:
$\frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}$.

Therefore, the product of $1\frac{4}{5} \times 2\frac{1}{2}$ is $4\frac{1}{2}$, which corresponds to choice 2.