12 divided by 1 1/2
Understand the Problem
The question is asking to perform the division of 12 by 1 and a half (1 1/2). This involves converting the mixed number into an improper fraction to carry out the division.
Answer
$8$
Answer for screen readers
The final answer is $8$.
Steps to Solve
- 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:
$$ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} $$
- Set up the division problem
We can express the problem of dividing by an improper fraction as follows:
$$ 12 \div (1 \frac{1}{2}) = 12 \div \left( \frac{3}{2} \right) $$
- 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:
$$ 12 \div \left( \frac{3}{2} \right) = 12 \times \left( \frac{2}{3} \right) $$
- Multiply the fractions
Now we can perform the multiplication:
$$ 12 \times \left( \frac{2}{3} \right) = \frac{12 \times 2}{3} = \frac{24}{3} $$
- Simplify the fraction
Finally, simplify $\frac{24}{3}$:
$$ \frac{24}{3} = 8 $$
The final answer is $8$.
More Information
The process of dividing by a mixed number involves converting it into an improper fraction, which allows us to rearrange the division into a multiplication problem. This method can be applied to other mixed numbers as well.
Tips
- Mixing up addition and multiplication when converting mixed numbers.
- Forgetting to convert the division into multiplication by using the reciprocal of the fraction.