3 1/2 times 2

Steps to Solve

1. Convert Mixed Number to Improper Fraction

To begin, we first convert the mixed number $3 \frac{1}{2}$ to an improper fraction. We do this by multiplying the whole number (3) by the denominator (2) and then adding the numerator (1).

The formula for this is: $$ \text{Improper fraction} = (3 \times 2) + 1 = 6 + 1 = 7 $$

So, $3 \frac{1}{2} = \frac{7}{2}$.

2. Setup Multiplication with the Whole Number

Next, we set up the multiplication of the improper fraction $\frac{7}{2}$ by the whole number 2.

This can be written as: $$ \frac{7}{2} \times 2 $$

3. Multiply the Numerators and Denominators

Now, we multiply the fractions. Since the whole number can be expressed as a fraction (e.g., $\frac{2}{1}$), we can multiply straight across:

$$ \frac{7 \times 2}{2 \times 1} = \frac{14}{2} $$

4. Simplify the Resulting Fraction

The next step is to simplify the fraction $\frac{14}{2}$.

We can do this by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$$ \frac{14 \div 2}{2 \div 2} = \frac{7}{1} = 7 $$

So, the result is 7.