**Ratios** are used in maths to **compare** two (or more) quantities which have something in common.

For example, if I had 3 red balls and 9 blue balls in a bag, the ratio of red to blue balls would be 3:9.

One thing that is absolutely vital when working with ratios is to remember that the **order in which the numbers are placed **is very important, as it determines what is being compared to what.

**Cancelling a Ratio**

When we are trying to cancel a ratio, the rules are the same as if we were trying to cancel a fraction.

Just like with fractions, we want to ensure our ratios are expressed in their **simplest possible forms**, so that they can be applied as easily as possible in simple calculations.

To simplify a ratio, we need to find the **Highest Common Factor (HCF) **and then **divide** all elements by this number to find an **equivalent**.

Let's look at this process in action.

**e.g. Cancel the ratio 9:3 into its simplest form.**

We need to ask ourselves: *"What is the Highest Common Factor between 9 and 3?"*

Remember, the Highest Common Factor (HCF) of two (or more) numbers is simply the **highest number which all values can be divided by**, which does not leave any remainders or decimals.

The HCF of 9 and 3 is 3, as 3 × 3 = 9 and 3 × 1 = 3.

So we need to divide both sides by 3:

9:3 ÷ 3 --> **3:1**

**e.g. Simplify the ratio 25:85 as far as possible.**

The HCF of 25 and 85 is **5**, so we need to divide both sides by 5:

25:85 ÷ 5 --> **5:17**

**e.g. Write a ratio which compares £2 to 30 p in its simplest possible form. **

The key thing to notice here is that the units which our amounts are expressed in <b>are not</b> the same, so we have to convert these into the same units before we start.

There is 100 p in £1, so **£2 = 200 p**.

Remember that the order for our ratio must be the same as in the question:

**200 p:30 p**

As both our units are now the same, we can remove them:

**200:30 **

Now we can cancel this ratio down by finding the HCF.

The HCF of 200 and 30 is **10**, so we need divide both sides by 10:

200:30 ÷ 10 --> **20:3**

In this activity, we will cancel ratios down into their simplest possible forms using the method shown above of converting amounts into the same units then finding the Highest Common Factor.