## What you need to know

Things to remember:

• Ratios are concerned with multiplying and dividing, so we have to multiply or divide to find equivalent ratios.
• 3:5 and 5:3 mean different things. The order of your ratio matters.

Ratios are used to compare amounts of things. For example, look at the following counters.

We can see that there are 6 red counters and 18 blue counters. As a ratio, we would write this as:

6 : 18

Note: The order of a ratio matters, if we had written 18 : 6, that would mean 18 red counters and 6 blue counters.

These counters don’t look very neat though, so let’s line them up a little.

This definitely looks a lot neater, and much easier to see the ratio of 6 : 18. But, is this our only way of laying them out?

If we lay them out like this, it is telling us that every time we have 3 red counters there are 9 blue counters, or, as a ratio, 3 : 9. But, can we do this in ANOTHER way?

If we lay them out like this, it is telling us that every time we have 2 red counters there are 6 blue counters, or, as a ratio, 2 : 6. So which is the right ratio? Well, they all are! They are called “equivalent ratios”.

Let’s have a look at our 3 ratios:

6 : 18

3 : 9

2 : 6

How can we compare these? How can we get from one ratio to another? Let’s look at the first two.

6 : 18

3 : 9

So, it looks like the 6 has turned into a 3, and the 18 has turned into a 9, but how? Let’s try doing some subtraction to turn the 6 into 3.

6-3 : 18 – 3

3 : 15

Hmmmm, this isn’t what we wanted. Let’s try some division.

$$6\div2:18\div2$$

3 : 9

So, division seemed to work here, will it work again for 2 : 6?

$$6\div3:18\div3$$

2 : 6

It worked again! So, to find equivalent ratios, we can divided OR multiply.

Find some equivalent ratios to 24:36

24 : 36

Divide by 2               12 : 18

Divide by 4               3  :  4.5

Divide by 6               4 : 6

Divide by 12               2 : 3

Multiply by 2               48 : 72

Multiply by 3               72 : 108

Multiply by 4               96 : 144

We need to be careful with what we divide by. For example, look at the ratio in bold. We don’t like to have decimal values in ratios, so we wouldn’t use this one.

## Example Questions

#### Question 1: Are 14 : 12 and 7 : 6 equivalent ratios?

Yes, they are equivalent ratios, we can divide them both by 2.

$$14\div2:12\div2$$

7 : 6

#### Question 2: Are 24 : 15 and 4 : 3 equivalent ratios?

$$24\div6:15\div6$$