Ratio is a level 4/5 topic and, depending on where they decide to throw it in, can easily be a level 6 to 9 topic too.

Ratio can come up in both the foundation and higher gcse maths exam.

Its worth spending time to learn what ratio is and the different kinds of questions that can come up.

The questions on ratio in the foundation paper are usually quite straight forward.

This topic is not too bad, most of it is simple - it does get hard when dealing with vectors, but that will be covered in a different post.

So what is ratio?

You’ve actually been doing ratios since primary school.

When you start mixing paint or play-doh to get a specific colour and shade, you are doing ratios.

Also if you are into baking or cooking, you’ll notice that the ingredients are in a specific ratio.

What does this mean?

If you are mixing red and blue paint to make purple, you might notice that 2 pots of red mixed with one pot of blue gives you the colour that you want. That’s a ratio of 2 red: 1 blue or 2 : 1 (we say 2 to 1).

Ratios are similar to fractions.

You can simplify them, multiply them up/down and use them to work out amounts of stuff.

They are used to compare one thing to another.

For example, if you’re making home made strawberry ice cream, you’ll want to make sure you have enough strawberries compared to the amount of milk and cream.

You might say: I’ll add in 2 strawberries for every 100ml of milk.

That’s a ratio of 2 : 100

(You can also simplify this down to 1 : 50).

So if you are making 1 litre of milk - 1000ml - you will need to multiply both sides of the ratio by 10.

So the number of strawberries, to the amount of milk you need will be:

20 : 1000

To simplify ratios or to multiply them up, you must divide or multiply each side by the same number.

e.g. 1 : 5. can be: 2 : 10, or 3 : 15 or 4 : 20 and so on.

35 : 50 can be simplified down by dividing each side by 5 -> 7 : 10

Simplifying Ratios Practice

Practice Simplifying Ratios

Ratios in the form 1 : n

This is one of those things in gcse maths that looks more confusing than it actually is.

If a question asks you to rewrite a ration in the format 1 : n or n : 1, you need to divide one side to give 1 and then divide the other side by the same number.

E.g. Rewrite: 5 : 6 in the form 1 : n

We need a 1 on the left hand side.

So divide 5 by 5 to get 1.

As we discussed earlier, you have to divide both sides of a ratio by the same number. Since we divided the left side by 5, we also now divide the right side by 5. 6 divided by 5 is: 1.2.

So the ratio 5 : 6 is written as 1 : 1.2 in the form 1 : n.

(It is common and perfectly fine to have decimals in these kinds of questions).

Practice Changing Ratios to the Form 1:n

Ratios and Fractions

You need to know how to change a ratio into a fraction.

For example, if I have blue sweets to red sweets in the ratio 5 : 7

What fraction of my sweets are blue?

You can work out the total sweets by adding the numbers in the ratio, 5 + 7 is 12.

So there are 5/12 blue sweets.

Ratio and Proportion - Strawberries to Ice Cream