12 divided by 1 1/2

Steps to Solve

1. Convert the mixed number to an improper fraction

To divide by $1 \frac{1}{2}$, we first convert it to an improper fraction.

The mixed number $1 \frac{1}{2}$ can be converted as follows:

$$ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} $$

2. Set up the division problem

We can express the problem of dividing by an improper fraction as follows:

$$ 12 \div (1 \frac{1}{2}) = 12 \div \left( \frac{3}{2} \right) $$

3. Change division to multiplication

When dividing by a fraction, we can multiply by its reciprocal. The reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$. Therefore:

$$ 12 \div \left( \frac{3}{2} \right) = 12 \times \left( \frac{2}{3} \right) $$

4. Multiply the fractions

Now we can perform the multiplication:

$$ 12 \times \left( \frac{2}{3} \right) = \frac{12 \times 2}{3} = \frac{24}{3} $$

5. Simplify the fraction

Finally, simplify $\frac{24}{3}$:

$$ \frac{24}{3} = 8 $$