 # Dividing unit fractions by whole numbers

Lesson

## Dividing unit fractions by whole numbers

We've seen how to divide whole numbers by unit fractions, but what if we work in the other direction? This time we'll start with a unit fraction, and then think about sharing it out. Our whole number tells us how many we need to share it among.

### Picturing it

We can use number lines, fraction bars, area models, and even time to help us share unit fractions out. Let's take a look at how we might approach this. If you only want to watch one method, you might like to jump to these times, for your preferred approach:

• using time 0:00
• using number lines 1:48
• using fraction bars 2:25

The rule for dividing a unit fraction by a whole number is important, once you understand what the number problem means, so be sure to check that out, at 4:26 in the video.

Remember!

Dividing means sharing into pieces, so the pieces get smaller. When our piece is a fraction to start with, it gets even smaller, so the denominator gets bigger. That's a good way to check your answer is reasonable, by making sure the denominator is larger.

#### Worked Examples

##### Question 1

Let's use the image below to help us find the value of $\frac{1}{3}\div2$13÷​2. This number line shows the number $1$1 split into $3$3 divisions of size $\frac{1}{3}$13.

1. Which image shows that each third has been divided into $2$2 parts?

A

B

C
2. What is the size of the piece created when $\frac{1}{3}$13 is divided by $2$2?

##### Question 2

Let's use the image below to help us find the value of $\frac{1}{3}\div3$13÷​3. This image shows the $1$1 whole split into $3$3 divisions of size $\frac{1}{3}$13.

1. Which image shows that each third has been divided into $3$3 parts?

A

B

C
2. What is the size of the piece created when $\frac{1}{3}$13 is divided by $3$3?

### The rule

Now you're ready to have a go using the rule for dividing a fraction by a whole number. If you need a refresher, this is at 4:26 in the chapter video.

##### Question 3

Calculate the following divisions:

1. What is $\frac{1}{4}\div2$14÷​2?

2. What is $\frac{1}{4}\div4$14÷​4?