Solve Mixed Number Multiplication: 3⁴⁄₅ × 2½

To solve the problem, we'll use the following steps:

• Step 1: Convert both mixed numbers into improper fractions.

• Step 2: Multiply the improper fractions.

• Step 3: Convert the product back to a mixed number.

Now, let’s work through each step:

Step 1: Convert $3\frac{4}{5}$ and $2\frac{1}{2}$ into improper fractions.
For $3\frac{4}{5}$: Multiply the whole number 3 by the denominator 5, and add the numerator 4:
$3 \times 5 + 4 = 15 + 4 = 19$.
The improper fraction is $\frac{19}{5}$.
For $2\frac{1}{2}$: Multiply the whole number 2 by the denominator 2, and add the numerator 1:
$2 \times 2 + 1 = 4 + 1 = 5$.
The improper fraction is $\frac{5}{2}$.

Step 2: Multiply the improper fractions.
$\frac{19}{5} \times \frac{5}{2} = \frac{19 \times 5}{5 \times 2} = \frac{95}{10}$.

Step 3: Simplify $\frac{95}{10}$ and convert to a mixed number.
Divide 95 by 10. The quotient is 9 with a remainder of 5, so:
$\frac{95}{10} = 9\frac{5}{10}$.
Since $\frac{5}{10}$ simplifies to $\frac{1}{2}$, we get:
$9\frac{1}{2}$ as the final answer.

Therefore, the solution to the problem is $9\frac{1}{2}$.