Whether you’re studying for your end-of-year/term exams or preparing for GCSE Maths, a spot of percentages revision never goes amiss!
To help you on your way to becoming 100% confident in the topic (or close to!), here’s a slice of magic taken from our expert-made resources at Beyond Maths.
The tips, methods and worked examples given below should help you boost your percentages revision and increase the effectiveness of your self-study for KS3 Maths.
Included in these notes are the subtopics ‘Percentage Increase and Decrease’, ‘Finding the Percentage of an Amount’, and ‘Original Value Problems’. You can also find a huge number of complementary worksheets and resources in our dedicated Percentages section.
But, for now, we hope this post on percentages revision will help you multiply your confidence!
Percentages Revision Part 1 – Percentage Increase and Decrease
Percentage Multipliers
Percentage multipliers can be used to find percentages of an amount.
For example: Find 7% of 30.
- 7% as a decimal is 7 ÷ 100 = 0.07
This is the multiplier we use to find 7% of 30.
- 0.07 × 30 = 2.1
Percentage Increase and Decrease
To increase or decrease by a percentage, begin by either adding or subtracting the relevant percentage from 100%, then find the multiplier.
Example 1
Increase 50 by 20%.
Since we are increasing, we want to add 20% to 100%.
- 100 + 20 = 120%
We need to find 120% of 50.
- 120 ÷ 100 = 1.2
This is the multiplier we use to find 120% of 50.
- 1.2 × 50 = 60.
Example 2
A video game usually costs £40. Its price is reduced by 6% in the sale. Work out the sale price of the game.
This time, we are decreasing the amount so we want to subtract 6% from 100%.
- 100 – 6 = 94%
We need to find 94% of £40.
- 94 ÷ 100 = 0.94
This is the multiplier we use to find 94% of 40.
- 0.94 × 40 = £37.60
Note that, when we are working with money, we give our answers correct to 2 decimal places.
If you’d like a deeper dive into Percentage Increase and Decrease – perhaps as part of your percentages revision programme, then the following resource provides the full walkthrough complete with plentiful examples to work through!
Percentage Increase and Decrease
Part 2 – Finding the Percentage of an Amount
It is useful to remember that percent comes from the words per- (meaning out of) and -cent (meaning 100). A percentage is measured out of 100.
You should know how to find the percentage of an amount, without using a calculator. You can calculate any percentage by finding either 10% or 1%.
| To find: | |
| 10% – Divide by 10 1% – Divide by 100 | |
| Other useful percentages: | Alternative methods: |
| 5% – Half of 10% (Divide by 10, then divide by 2) 2.5% – Half of 5% (Divide by 10, then divide by 4) 0.5% – Half or 1% (Divide by 100, then divide by 2) | 50% – Divide by 2 25% – Divide by 4 75% – Divide by 4, then multiply by 3 |
Example 1
Work out 10% of 128.
To find 10% of 128, simply divide 128 by 10.
- 10%: 128 ÷ 10 = 12.8
- 10% of 128 = 12.8
Example 2
Work out 30% of 155.
If we know how to find 10% of a number, then we can easily find 30% of it too. First, find 10%:
- 10%: 155 ÷ 10 = 15.5.
We can add three lots of 10% together to find 30%:
- 30%: 15.5 + 15.5 + 15.5 = 46.5
Or, we could multiply the 10% by 3 to find 30%.
- 30%: 15.5 × 3 = 46.5
- 30% of 155 = 46.5
Example 3
Calculate 14% of 200.
Start by finding 10%:
- 10%: 200 ÷ 10 = 20
Next, find 1% of 200. To do this, simply divide 200 by 100:
- 1%: 200 ÷ 100 = 2
To make 14%, we need 10% and 4%.
We have 10% already and if we know 1%, we can easily find 4%:
- 4%: 2 + 2 + 2 + 2 = 8
- Or 4%: 2 × 4 = 8
Finally, add 10% and 4% to find 14%:
- 14%: 20 + 8 = 28
- 14% of 200 is 28.
Example 4
Calculate 7.5% of 50.
Start by finding 10%:
- 10%: 50 ÷ 10 = 5
We can use this to find 5%. 5% is half of 10% so, to find 5%, we halve 5:
- 5%: 5 ÷ 2 = 2.5
We could also find this value in one calculation:
- 5%: 50 ÷ 10 ÷ 2 = 2.5
2.5% is half of 5% so that means we can also halve the 5% value.
- 2.5%: 2.5 ÷ 2 = 1.25
We have a couple of choices on how to make 7.5%. We could take 2.5% from 10%:
- 7.5%: 5 – 1.25 = 3.75
Or add 5% to 2.5%:
- 7.5%: 2.5 + 1.25 = 3.75
We could also have added together seven lots of 1% and a 0.5%. There are lots of ways of making a percentage. If you do them correctly, they will all give the same answer.
If you’ve found your rhythm as well as your percentages and would like to carry on, this link below will provide you with the unfiltered 100% experience!
Finding the Percentage of an Amount
Part 3 – Original Value Problems
We can use multipliers to help us find the original amount after a percentage increase or decrease.
Example 1:
A number is increased by 12%. The new number is 44.8. What was the original number?
To increase by 12%, begin by adding 12% to 100%.
- 100 + 12 = 112%
The percentage multiplier is 112 ÷ 100 = 1.12
To find the original number, *we divide 44.8 by 1.12.
- 44.8 ÷ 1.12 = 40
*How about a recap? – when we know the original number and are finding the new number, we multiply. So in reverse, to find the original number, we must divide the new number by the ‘multiplier’.
Example 2:
A number is decreased by 35%. The new number is 39. What was the original number?
To decrease by 35%, begin by subtracting 35% from 100%.
- 100 – 35= 65%
The percentage multiplier is 65 ÷ 100 = 0.65
To find the original number, we divide 39 by 0.65.
- 39 ÷ 0.65 = 60
If you’ve found value in these percentages revision tips, then you can find the full resource in the link below.
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