Dividing fractions with whole numbers

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.

When you come across dividing a fraction by a whole number, the steps to doing this is pretty simple.

First, multiply the bottom number of the fraction part of the question with the whole number.

So for example, if we've got:

\(\frac{1}{2} \div 2\), take the 2 from the bottom of \(\frac{1}{2}\) and multiply it with the 2 that's on the right. We're actually changing 2 into \(\frac{1}{2}\) in order to move it to the bottom so the sign becomes a multiplication sign instead of a division one: \(\frac{1}{2}\) * \(\frac{1}{2}\). This will give you \(\frac{1}{4}\).

Secondly, simplify the questions if needed. In this case, \(\frac{1}{4}\) is already the most simplified form of the answer, so there's no need to further mess with it. Your final answer will be \(\frac{1}{4}\).

These two steps will help you solve any questions involving dividing fractions with whole numbers.

Let's put what we just learned to use. We'll even look at a number line to clearly understand what we're doing when we divide whole numbers by a fraction.

Question 1:

Use number lines to find the following quotient:

\(\frac{1}{3} \div 4\)

Solution:

Let's first start by creating a number line with 0 on one end and 1 on the other. Note that 3/3 is also equalled to 1.

The question asks us to divide \(\frac{1}{3}\) by 4. So we'll take a closer at the number line, zooming in to specifically the area between 0 and \(\frac{1}{3}\).

So let's divide this section into 4 sections.

The shaded part is what the question is asking for.

To look for the exact number, here is the trick. Look at the number line from 0 to 1, there are three \(\frac{1}{3}\) parts. We divide each of them by 4. We've got 12 smaller parts in total.

We are only looking for 1 part out the 12 smaller parts (a quarter of \(\frac{1}{3}\) ). So the final answer is \(\frac{1}{12}\).

Question 2:

It takes 3/5 cup of sugar to make four cupcakes. How much sugar is needed for three cupcakes?

Solution:

First, look for the sugar to cupcake ratio. We need \(\frac{3}{5}\) cups of sugar for every 4 cupcakes. If we divide \(\frac{3}{5}\) by 4, we'll find out how much sugar is needed per cupcake.

\(\frac{3}{5} \div 4\)

\(\frac{3}{5} \div \frac{4}{1}\)

\(\frac{3}{5} \times \frac{1}{4}=\frac{1}{20}\) sugar/cupcake

We want to know how much sugar is needed for three cupcakes. So simply take the answer we've got from above via fraction division, which tells how much sugar is needed per cupcake, and multiply it by 3.

\(\frac{3}{20}\) sugar/cupcake \(\times 3 = \frac{9}{20}\)

There's your final answer!

If you're ever unsure about your answer in questions involving dividing a whole number by a fraction, use this calculator to help you double check your work.

To review concepts to help you with solidifying your understanding of this lesson, take a look at how to determine common factors and multiplying a fraction and whole numbers. You'll have to take these concepts with you when you eventually learn how to solve two step linear equations.