GCSE Maths Proportion Recipes
Introduction
Suppose that you buy a pack of 10 pens for £1. How much would you expect to pay for 4 pens?
Now, here you are going to assume that all pens have the same cost. In other words, no matter how many pens you purchase, the cost of one pen will always be the same.
So if 10 pens cost £1, then 1 pen will cost just 10 pence. This has been found by converting £1 into pence i.e. 100p and then dividing by 10.
This then means that the cost of 4 pens would cost 40p. And you will notice that the cost of one pen is 10p.
Because the cost of one pen is always 10p, it is said that the cost of the pens are in proportion.
This principle can be applied to weight, length and so on and proportion questions are regularly featured within questions that relate to GCSE Maths proportion recipes.
GCSE Maths Proportion Recipes - An Example
Consider the following GCSE Maths proportion recipes question:
ou are given the ingredients required for 10 flapjacks and you are asked to determine the number of ingredients for 15 flapjacks.
There are two main ways in which this can be done.
Method 1 – finding what is required for 1 flapjack
10 flapjacks require 80g of oats. What would be the calculation required to determine the number of grams needed for 1 flapjack?
If you are not sure, try to draw a simple diagram such as the one shown.
The diagram shows the 10 flapjacks, and because all 10 are equivalent to 80 grams, the calculation to determine what 1 flapjack is equivalent to is done by division. So 80 ÷ 10 = 8 grams
This means that 1 flapjack needs 8 grams of oats, so to find the amount of oats needed for 15 flapjacks; this is found by 15 x 8 = 120 grams.
This process can then be repeated for each of the other ingredients and the calculations are shown in the table below:
Looking at the table above we have the following:
In column 2 we have the original ingredients required for 10 flapjacks.
In column 3 we have shown how to obtain the ingredients needed for just 1 flapjack which has been done by performing a division.
In column 4 we have obtained the ingredients needed for 15 flapjacks which have been done by multiplication.
Method 2 – looking for a pattern
The following GCSE Maths proportion recipes question gives you the information that is needed for 10 flapjacks and you are required to find the ingredients for 15 flapjacks.
Well an alternative method is to halve the ingredients given, which would then give the ingredients needed for 5 flapjacks, and then adding this to the ingredients needed for 10 flapjacks, so giving the total ingredients needed for 15 flapjacks.
You may find this method to be quicker than the first one, but you need to pick a method that you are comfortable with as both work.
The table below shows the calculations for the alternative method:
Looking at the table above we have the following:
In column 2 we have the original ingredients required for 10 flapjacks
In column 3 we have found the ingredients needed for just 5 flapjacks and this has been done by halving the numbers in column 2
In column 4 we have the ingredients needed for 15 flapjacks which has been obtained by adding the numbers in columns 2 and 3
There is no set technique to doing proportion questions, it is always a case of finding a technique that works for you. As you have seen above, two methods have been discussed. If you think you still need any help with proportion questions try the above examples once again on your own. We have a range of professional online tutors for GCSE maths who are experts in making maths so much easier.
Question Practice
Try the following GCSE Maths proportion recipes 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 flour, almonds and sugar.
You should notice here that the question is asking for which ingredients are needed, not necessarily the amounts. But the methods shown still need to be used.
The ingredients for 4 people are given, but the ingredients for 10 people are needed. Because 4 is not a factor of 10, this makes this calculation a little trickier.
Now 4 x 2 = 8, so this gives the ingredients needed for 8 people, so to get the ingredients needed for 10 people, it is important to know what ingredients are needed for 2 people.
Ingredients | 4 people | 8 people | 2 people | 10 people |
Flour | 80g | 80 x 2 = 160g | 80 ÷2 = 40g | 160 + 40 = 200g |
Almonds | 60g | 60 x 2 = 120g | 60 ÷2 = 30g | 120 + 30 = 150g |
Sugar | 90g | 90 x 2 = 180g | 90 ÷2 = 45g | 180 + 45 = 225g |
Butter | 60g | 60 x 2 = 120g | 60 ÷2 = 30g | 120 + 30 = 150g |
Pears | 4 | 4 x 2 = 8 | 4 ÷2 = 2 | 8 + 2 = 10 |
From the above table in column 2 we have the original ingredients. In column 3 we have obtained the ingredients needed for 8 people by doubling the numbers in column 2.
In column 3 the numbers from column 2 have been halved to give the ingredients for 2 people.
Finally the numbers in the final column have been obtained by adding the numbers from columns 2 and 3 to give the ingredients needed for 10 people.
Of course you could have also obtained the ingredients for 2 people and then multiplied by 5. Again this highlights the point that these questions do not have a set method.
So in order to answer the question you need to look at the ingredients that Jessica already has.
Jessica has:
And comparing this with the last column of the table you can see that flour is needed, so are almonds, sugar is needed, there is enough butter and there are enough pairs also.
Proportion questions are generally quite accessible but you do need to make sure you are reading the questions carefully in determining what the questions are actually asking for.
Whether you are doing foundation or higher gcse maths you are more than likely going to see a question related to proportion. These questions are not very complicated and so obtaining full marks is more than doable. Keep trying the questions shown as well as trying other questions from your school book.