 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

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

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?

Outcomes

NA5-3

Understand operations on fractions, decimals, percentages, and integers