Multiply 3 × 1½: Mixed Number Calculation Step-by-Step

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

• Step 1: Convert the mixed number into an improper fraction.
• Step 2: Multiply the whole number by the improper fraction.
• Step 3: Convert the result back to a mixed number if needed and simplify.

Now, let's work through each step:

Step 1: Convert the mixed number.
The mixed number given is $1\frac{1}{2}$.
To convert $1\frac{1}{2}$ into an improper fraction, multiply the whole number part (1) by the denominator (2) and add the numerator (1):
$1 \times 2 + 1 = 3$.
So, $1\frac{1}{2}$ converts to $\frac{3}{2}$.

Step 2: Multiply the whole number by the improper fraction.
Now we multiply the whole number 3 by the improper fraction $\frac{3}{2}$:
$3 \times \frac{3}{2} = \frac{3 \times 3}{2} = \frac{9}{2}$.

Step 3: Convert the result to a mixed number.
The improper fraction $\frac{9}{2}$ can be converted into a mixed number by performing the division $9 \div 2$.
9 divided by 2 equals 4 with a remainder of 1, so $\frac{9}{2}$ is the same as $4\frac{1}{2}$.

Therefore, the solution to the problem is $4\frac{1}{2}$.