Division using a number line

What is division?

When you divide, you share or group an amount into a number of equal parts.

Division is normally represented by the symbol ‘÷’.

Division is the opposite of multiplication.

Quiz: Using number lines for division

Why not see how much you know about this topic already? Then work through the page and see if you can beat your score.

Division by grouping

Let’s look at a question.

What is 15 ÷ 5?

Counting groups is a good way of understanding division.

Here are 15 beads.

How many groups of 5 can you make with these beads?

When you divide 15 into groups of 5, you make 3 groups.

Therefore:

15 ÷ 5 = 3

Using a number line to divide

A number line can help you to divide.

You count on in steps of the number you want to divide by.

Then, count how many steps there are and that is the answer to the division.

Let's look at another example.

What is 30 divided by 5?

30 ÷ 5

Here is a number line from 0 to 30 with intervals of 5.

Count on in steps of 5. How many steps of 5 are needed to reach 30?

Look at the number line and count the steps, following the arrow jumps:

0 to 5 → 5 to 10 → 10 to 15 → 15 to 20 → 20 to 25 →> 25 to 30

Can you see that there are 6 jumps of 5?

So there are 6 fives in 30.

30 ÷ 5 = 6

Can you see that the steps are the same as 6 groups of 5?

You are counting the number of groups of 5 to make 30.

Division as repeated subtraction

You can also use repeated subtraction to divide.

Let's try this one.

12 ÷ 2

Remember that this means 12 put into groups of 2.

Take away each group of 2 until you reach zero, then count the groups.

You can use counters to help you keep track.

How many groups of 2 are in 12?

There are 6 groups of 2.

You can look at the same things on a number line.

Count back from 12 in steps of 2.

Now count the steps.

There are 6 steps. So:

12 ÷ 2 = 6