GCSE Maths Ratio: How to Calculate Ratio Amounts
Introduction
A ratio is simply a way of comparing one thing to another.
For instance looking at the diagram below:
You can see that from the four blocks in total, three are shaded blue and one is shaded yellow. So, there are 3 blue squares for 1 yellow square.
This can be written as 3 to 1 or more traditionally as 3:1.
You should think of these numbers as “parts”.
One of the most common areas that students find difficult is solving GCSE Maths ratio questions.
GCSE Maths Ratio: An Example
Consider the following question:
Solution
In this question there are 3 numbers in the ratio. It does not matter how many numbers are given; it could have been 2, 4 or more. The method is generally the same and it is quite useful to use the aid of a diagram to help you solve such questions.
Suppose the following block represents 36 sweets.
Now one person receives 2 parts, another 3 parts and another 4 parts.
You will see that these parts have been shaded in and if you count all the parts together there are 2 + 3 + 4 = 9 parts in total.
Remember that the whole block is 36 sweets and there are 9 parts in total. So what is the value of 1 part going to be?
This can be found by division so 36 ÷ 9 = 4. This means that 1 part is going to equal 4 sweets.
The whole aim of ratio questions is to find the value of 1 part.
Then 2 parts are going to be worth 8 sweets.
3 parts are going to be worth 12 sweets and 4 parts are going to be worth 16 sweets.
As a final check you check that the number of sweets obtained does indeed total 36: 8 + 12 + 16 = 36, so you can be confident that the amounts received are correct.
There are a range of ratio questions whether it is simplifying ratios, sharing a ratio amount or finding one part when given that a particular ratio has a certain value such as in the last example. If you are doing the GCSE Maths Higher Paper then you can get some ratio questions that involve algebra. There will be an article that will cover such questions. If you are looking for an online maths tutor based in the UK then we are able to help you.
Example
Consider the following question:
Solution
Now this GCSE Maths ratio question is a little different in that you are told that 5 parts is 70 grams of dough.
So by drawing a block of 5 parts you will have the following:
Now the above 5 parts are 70 grams. What is 1 part? This can be found by division so 70 ÷ 5 = 14. This means that every 1 part must be worth 14 grams.
The amount of cheese, which is 2 parts, will be 2 x 14 = 28 grams.
And the amount topping, which is 3 parts, will be 3 x 14 = 42 grams.
Question Practice
Try the following GCSE Maths ratio question on your own before looking at the solution.
Question Practice Solution
So how did you get on? Hopefully you found the answer to be £30.
Now showing this as blocks:
Pat receives 2 parts.
Julie receives 5 parts.
What is tricky here is that you are told that Julie gets £45 more.
So, you can say that Julie gets 3 more parts than Pat. So these 3 parts must be worth £45. Which in turn will mean that 1 part can be found by: £45 3 = £15.
And from this you can then calculate that Pat receives £15 x 2 = £30
Question Practice
Try the following question on your own before looking at the solution.
Question Practice Solution
So how did you get on? Hopefully you found the answer to be 1:3.
The wording of the question actually makes this appear to be more difficult than it actually is.
The best thing to do with questions like this is to take each sentence one at a time.
The question is asking for the ratio of the total value of 5p coins and 10p coins.
Well from the ratio given, there are two 5p coins and three 10p coins. So the value is 10p and 30p.
Writing 10p and 30p as a ratio is 10:30 or in its simplest form; 1: 3
Ratio as a topic is part of your number work and you need to ensure that you are strong in this area. Whether you are doing the foundation or the higher paper, a part of your gcse maths revision needs to focus on this topic area. If you are doing the higher paper then you could see a ratio question that involves algebra but there will be an article covering that in due course.