GCSE Maths: How To Calculate Percentages Easily
Introduction
Knowing how to calculate percentages is very important as they occur in everyday life in a variety of areas from price increases or decreases, the cost of loans as well as the interest on savings. Percentages are generally used to describe these so it is important that you are able to work with them.
Quite often you are also asked to determine a percentage increase or decrease and this can be worked out using the following formula which you should memorise:
\text { Percentage Increase or Decrease }=\frac{\text { Difference }}{\text { Original }} \times 100 \%You need to remember that a percentage means out of 100.
How To Calculate Percentages - An Example
Example
Take a look at the following question:
The first thing to do in this question is to determine what 17 \frac{1}{2} \% \text { is of } f 7.60. Now suppose that the block below is £7.60 and because this is the full amount this will be 100%.
Suppose the entire block is divided into 10 red blocks. You can see that one block is shown and this is going to represent 10% of the total amount.
What would this be in monetary terms?
Well 100 ÷10 = 10, so £7.60 ÷ 10 = £0.76.
You need to remember that when you are finding 10% of any amount you are dividing by 10, and this illustration with the blocks has hopefully helped you to visualise that.
But you don’t need 10% you need to find 1712%. How can the value for 10% be used?
10% 🡺 £0.76
You can obtain 17 \frac{1}{2} \% \text { from } 10 \%+5 \%+1 \%+1 \%+\frac{1}{2} \%
So to find 5% you can simply halve the value for 10% to give £0.38. In order to find 1% you can divide the value of 5% by 5 to give £0.076 and to find the value of \frac{1}{2} \% you can simply halve the value for 1% to give £0.038.
So 17 \frac{1}{2} \% = £0.76 + £0.38 + £0.076 + £0.076 + £0.038 = £1.33. This is the VAT and needs to be added back on to the price of the book. So the total price of the book is £7.60 + £1.33 = £8.93.
So if 1650 books are sold then the amount received will be £8.93 x 1650 = £14,734.50
One part of percentages that students do find tricky is reverse percentages which we will be covered in another blog post. But for now it is important that you have a strong understanding of being able to calculate percentages and to be able to do this without the aid of a calculator. If you need any additional support then you use an experienced online GCSE maths tutor who can provide additional weekly homework from what you get at school, for you to further consolidate your understanding and knowledge.
How To Calculate Percentages - Another Example
Consider the following question:
To answer this question you need to make use of the formula that was mentioned at the beginning.
\text { Percentage Increase or Decrease }=\frac{\text { Difference }}{\text { Original }} \times 100 \%The difference can be calculated as 91 – 85 = 6.
But what is the original?
You need to look at what comes first. Clearly the month of April is before the month of May, so the amount of 85 is the original.
So the percentage increase = \frac{6}{85} \times 100 \%=7.06 \%
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 £29.44.
There are actually two ways in terms of how to calculate percentages in this question and both methods will lead to the same result.
Method 1 – finding the value of 20%
You can find the value of 20% and then subtract this from the normal price of the dress. It is a subtraction because of the word “reduction” that has been used in the question.
20% = 2 x 10%.
Remember in order to find 10% of anything you simply need to divide by 10.
So £36.80 ÷ 10 = £3.68 🡸 this is the value of 10% so this value can be doubled in order to have the value for 20% so £7.36.
The amount of £7.36 is the reduction and it is this amount that needs to be subtracted from the normal price.
So sale price = £36.80 – £7.36 = £29.44
Method 2 – finding what 80% is worth
An alternative method is to find the value of 80%. Because the normal price is 100% and the price is reduced by 20% this means that the price paid represents 80%.
It was shown that 10% = £3.68 so 80% = £3.68 x 8 = £29.44.
Both methods produce the same result but you need to find a method that you’re happy with.
You have hopefully understood the various solutions that have been presented to you, so hopefully you have much greater confidence in how to calculate percentages. But if you haven’t then you should try the questions again on your own. If you are looking for guidance on GCSE maths exam preparation then one of our half term revision courses would be more than suitable for you.
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