Multiply Mixed Numbers: 1⁴/₅ × 1½ Step-by-Step Solution

To solve the problem of multiplying $1\frac{4}{5}$ and $1\frac{1}{2}$, we will follow these detailed steps:

• Step 1: Convert both mixed numbers to improper fractions.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the result and convert back to a mixed number.

Now let's go through each step in detail:

Step 1: Convert to Improper Fractions
For the number $1\frac{4}{5}$:
- Multiply the whole number by the denominator: $1 \times 5 = 5$.
- Add the numerator: $5 + 4 = 9$.
- The improper fraction is $\frac{9}{5}$.

For the number $1\frac{1}{2}$:
- Multiply the whole number by the denominator: $1 \times 2 = 2$.
- Add the numerator: $2 + 1 = 3$.
- The improper fraction is $\frac{3}{2}$.

Step 2: Multiply the Improper Fractions
Multiply $\frac{9}{5}$ by $\frac{3}{2}$:
$\frac{9}{5} \times \frac{3}{2} = \frac{9 \times 3}{5 \times 2} = \frac{27}{10}$.

Step 3: Simplify and Convert Back to Mixed Number
- The fraction $\frac{27}{10}$ is already in simplest form.
- Convert it to a mixed number: Divide 27 by 10, which is 2 with a remainder of 7.
- Therefore, $\frac{27}{10} = 2\frac{7}{10}$.

Thus, the product of $1\frac{4}{5}$ and $1\frac{1}{2}$ is $2\frac{7}{10}$.