Multiplying fractions and whole numbers

What is a whole number

You've encountered lots of whole numbers before now. Whole numbers are numbers that aren't fractions—they are integers. For example, $2, 12$, and $50$ would all be whole numbers.

On the other hand, numbers that aren't whole numbers would look something like $1.25$ or $\frac{4}{5}$. Although a fraction is a rational number, it is not a whole number. Knowing the difference will be important in this lesson

How to multiply fractions with whole numbers

When you're given a question that requires you to deal with multiplying fractions with whole numbers, there's $4$ main steps you'll have to carry out.

Firstly, rewrite the question so that the whole number is turned into a fraction. As you probably already know, when you have a whole number, turning it into a fraction just requires you to put it over $1$. So for example, if you wanted to convert $8$ into a fraction, it'll be rewritten as $\frac{8}{1}$.

Secondly, multiply the two numerators in the two respective fractions. This just means taking the two numbers on top of each of the fractions and then multiplying them with one another.

For the third step, do the same as step two but now you're using the two numbers in the denominators in the fractions. You'll end up with a new fraction after doing steps two and three!

Lastly, you'll just have to simplify the fraction you've gotten after solving the problem. You have to show your answer in the lowest terms possible, or you may get marks deducted for not having completely finished the question. Let's take a look at some examples and put the four steps into use to help you with multiplying fractions and whole numbers.

Practice problems

Question 1:

Calculate

$2 \times \frac{1}{5}$

Solution:

First, we can express $2$ as a fraction:

$\frac{2}{1}$

Our question will then be converted to something that looks like this:

$\frac{2}{1} \times \frac{1}{5}$

We multiply these fractions, first tackling the top numbers ($2 \times 1$) and then doing the bottom ones ($1 \times 5$). Then we'll get our final number, which is a new fraction.

$\frac{2}{1} \times \frac{1}{5} = \frac{2}{5}$

Since $\frac{2}{5}$ is already the most simplified form of the fraction, this will be your final answer.

Question 2:

A pizza had $12$ slices, and $\frac{3}{4}$ of it was eaten in a party. How many slices of pizza were eaten during the party?

Solution:

There were $12$ slices and $\frac{3}{4}$ were eaten. So we multiply $12$ and $\frac{3}{4}$ to get the answer. Let's express $12$ as a fraction.

$\frac{12}{1} \times \frac{3}{4}$

Before doing multiplication, we can simplify the question first and get this:

$\frac{3}{1} \times \frac{3}{1}$

Now, do the multiplication. We've got $9$ as the final answer

$\frac{3}{1} \times \frac{3}{1} = \frac{9}{1} = 9$

If you're ever unsure about your answer in questions involving the multiplication of whole numbers and fractions, use this calculator to help you double check your work.

Good lessons to review and move forward with to help you understand this lesson better includes finding common factors, comparing rational numbers, and solving problems with rational numbers in fraction form. These will eventually lead you into the more advanced problems of solving two-step linear equations.