How to divide fractions

I would love to help you master dividing fractions! It is a super useful skill, and once you get the hang of a few simple steps, it becomes second nature.

Before we dive in, I have a quick question to help me tailor our session perfectly for you:

To help me tailor our session, could you let me know how comfortable you currently feel with fractions in general, and what specific types of problems (e.g., just simple fractions, or also mixed numbers) you are looking to master?

I feel good with basic fractions and just want to master the division rules.

It is great to have you here! Since you are already comfortable with basic fractions, we can jump right into making sense of how division works with them. Before we look at any rules or shortcuts, let's build some quick intuition about what dividing a fraction actually means.

When we divide whole numbers, like

10 \div 2

, we are simply asking: "How many times does

2

fit inside

10

?" The logic is exactly the same for fractions. If we write

3 \div \frac{1}{2}

, we are asking: "How many fit inside

3

whole things?"

Three whole circles shown split into six equal halves, each numbered sequentially to demonstrate that six halves fit into three wholes.

As you can see, if you have $3$ whole pizzas and you cut every single one of them in half, you end up with $6$ slices. So, $3 \div \frac{1}{2} = 6$ .

Does this visual way of thinking about dividing by a fraction make sense to you?

Can we try one more visual example?

You bet! Let's look at another classic visual example: $2 \div \frac{2}{3}$ .

Instead of cutting things in half, we are dividing our wholes into thirds. This means we want to find out how many groups of two-thirds can fit into $2$ whole things. Let's start with $2$ whole blocks, cut each of them into three equal pieces so we have six thirds in total, and see how many groups of $\frac{2}{3}$ we can make.

An absolute visual showing two whole horizontal bars subdivided into six equal thirds, color-coded and grouped into pairs of thirds.

When you group those six individual thirds into pairs of two, you end up with exactly $3$ complete groups. So, $2 \div \frac{2}{3} = 3$ .

Now that you have a solid visual grasp of what's actually happening when we divide fractions, let's look at the simple three-step trick to get this exact same answer every time without drawing it out: the Keep, Change, Flip method.

Continue to Keep, Change, Flip

Let's dive into the Keep, Change, Flip method. It's a simple, foolproof strategy that turns any fraction division problem into a straightforward multiplication problem. To see how it works, let's look at this problem:

\frac{3}{4} \div \frac{2}{5}

We solve this by following three simple steps:

Keep the first fraction exactly as it is: $\frac{3}{4}$ .
Change the division sign ( $\div$ ) to a multiplication sign ( $\times$ ).
Flip the second fraction upside down to its : $\frac{2}{5}$ becomes $\frac{5}{2}$ .

\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}

By flipping the second fraction, we are using the mathematical rule that dividing by a number is the exact same thing as multiplying by its reciprocal.

Would you like to try one yourself to test it out, or would you prefer to see another worked example first?

Let me try one myself

Awesome! Trying it yourself is the best way to make the steps stick. Let's practice with this problem:

\frac{2}{3} \div \frac{4}{5}

Take your time to write down the new multiplication problem and solve it. What answer do you get?