How do you calculate a percentage increase or a percentage decrease?

Method 1

The simple way to increase or decrease a quantity by a percentage is to find the percentage of the quantity that you want to increase or decrease it by and add it on or take it off.   To do this is easy; the best way to do it is it break it down step by step.  

To solve the question: 

Increase £50 by 15% 

All you have to do is this, 

 

1) Work out 10% of £50, move the decimal point once to the left, which gives you £5.

 

2) Then work out 5%, 5% is half of 10% so half £5 to get £2.50. 

 

3) Add the two figures together to get £7.50 which equals 15% and

 

4) Then add it onto the original value of £50 which gives you £57.50

If you are asked to decrease a value by a given percentage then follow the same steps but instead of adding the end value on take it off. 

Note: The best way to work out difficult percentages such as 17.5% is to break it down into sections, so work out 10%, 5%, 2.5% and then add all of those values together. 

 

Examples:

Decrease £30 by 60%

50% = £15

10% = £3

60% = £18

 

£30-£18 = £12 

 

Increase £43 by 32%

10% = £4.30 x 3 

        = £12.90

1% = £0.43 x 2

      = £0.86

 

32% = £13.76

£43 + £13.76 = £56.76

 

Method 2

Another method of calculating percentages is by using this equation, Percentage = Percentage x Cost ÷ 100.

So, for increasing £50 by 15%:

(15x50) ÷ 100 = 7.5

Then you add the £7.5 onto the £50, giving you £57.50. 

  • The Percentage and Cost in the equation change depending on the exmaple, but those numbers are always divided by 100. 
  • When using this formula always do the first part, multiply the percentage by the cost, before you divide by 100. 

 

Calculator Method

If you are allowed to do it on your calculator then it makes it extremely easy as a percentage can easily be turned into a decimal:

15% = 0.15, 5% = 0.05, etc.

Just remember though that if you are looking to increase a number by a certain percentage then you will need to ensure you multiply it by 1.?? on your calculator. Also if you are decreasing by a percentage then you need to remember to take this percentage away from 1. Alternatively if you find it easier you can just find what the percentage of that number equals and then add/subtract it from your original answer.

Examples:

Increase 40 by 6%  = 40 x 1.06 = 42.4

Decrease 50 by 8% = 50 x 0.92 = 46

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Follow the links below to see how this topic has appeared in past exam papers

 

AQA Unit 2 March 2011 (H)  - Page 3, Question 4

AQA Unit 2 March 2011 (H) - Page 7, Question 11

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