What happens when we divide fractions?

Before we talk about dividing fractions, let's review dividing whole numbers. Here, we will divide 12 by 4.

We can look at this problem on the number line.

This bar represents the unit 4. The unit 4 is a single unit.

Now we break the number 12 up into units of 4.

This model shows us that the unit 4 divides into 12 one time…

…two times…

…three times.

12 divided by 4 equals 3.

Now, let's look at what happens when we divide a whole number by a fraction. Let's look at the problem 5 divided by one half. We can write the problem this way…

…or this way.

We can also look at this problem on the number line.

This bar represents one half. This is our unit.

We divide 5 into units of one half.

This model helps us see that 5 is divided into ten units of one half…

…so 5 divided by one half equals 10.

We can also use a number line to help us understand what is happening when we divide fractions. Here we have three fourths divided by one fourth, written two ways.

This number line is divided into fourths between 0 and 1.

This bar represents the unit one fourth.

We divide three fourths into units of one fourth.

This model shows us that there are 3 units of one fourth in three fourths…

…so three fourths divided by one fourth equals 3.

Let’s compare what happens when we divide whole number to what happens when we divide fractions.

When we divide whole numbers, the quotient…

…is smaller than the dividend.

In fractions, the quotient…

…is larger than the dividend.

It’s important to remember that when we divide one fraction by another, the quotient is often larger than the dividend.

What is the shortcut for dividing fractions?

Just like multiplying fractions, there is a shortcut for dividing fractions. Let’s look at the problem four eighths divided by one fourth.

When we divide, we can invert, or flip over, the second fraction…

…and multiply.

Four eighths times four over one…

…equals sixteen eighths.

WE use good number sense to simplify the answer. Sixteen eighths…

…equal two over one, or two.

The number line helps us see why this shortcut works.

We know that the fraction four eighths is the same as one half…

…so we break up one half using a unit of four.

It breaks up the fraction exactly two times.s

Let’s look at another problem, two fourths divided by six eighths.

We invert the second fraction…

…and multiply.

The product is sixteen twenty-fourths…

…which simplifies to two thirds.