Percentage increase and decrease is confusing for many students.

If you’re panicking when you see a question like this:

Increase 54 by 12%

It’s ok, you are allowed to panic.

However, it would be best to save that panic for something else (like biscuits running out whilst you’re revising) and master this topic of percentage increase and decrease.

What exactly is a percentage increase?

Most things in our lives increase or decrease in amount or value. For example, the device you are reading this on might be a phone, tablet or laptop etc. and depending on how old your device is, there is a good chance that it’s value or price, if you were to resell it, is going to be less than what you paid for it.

If you are drinking tea or coffee whilst reading this, the amount of your drink has decreased or will do eventually.

Hopefully, by the end of this article and after doing some practice questions, your knowledge of maths and possibly your confidence will increase.

In some situations we like to or need to measure that increase or decrease as a percentage.

Percentages help us to understand the change better.

For example a sale sign that says 50% off this jumper compared to a sign that says £7 off this jumper is much clearer and is faster for us to see if we are getting a good deal or not.

So a percentage increase or decrease is the amount that something has increase or decreased by, worked out and presented as a percentage rather than a number or fraction.

Let’s start with working out a percentage increase:

Let’s increase the number 10 by 10%.

First find 10% of 10 – you can divide by 100 and multiply by 10, or you can simply divide by 10 (please see my previous posts on calculating percentages if you are unsure about this.)

10% of 10 is 1.

So to increase 10 by 10%, add 1 to 10, which gives us 11.

10, increased by 10% is 11.

Similarly, if you want to decrease 10 by 10%, simply subtract 1, which gives you 9.

Here are some more examples:

100 increased by 25% is 125. 25% of 100 is 25, so you add 25 to 100 to increase it by 25%

50 increased by 10% is 55. 10% of 50 is 5, so you add 5 on to 50 to increase it by 10%.

30 increased by 50% is 45. 50% is half of 30, which is 15, so you add 15 onto 30, which gives 45.

NB Knowing your common fractions, decimals and percentages is a massive help for this topic.

Let’s look at some harder examples:

- Increase 40 by 17%.

Calculate 17% of 40. Without a calculator you can work out 10%, 5% and 2% and add them up.

With a calculator you do 40/100 =0.4 and multiply by 17 giving: 6.8.

40 + 6.8 = 46.8.

2. Decrease 234 by 23%

Find 23% of 234: 234/100 = 2.34 multiplied by 23 gives: 53.82

3. A coat in a shop costs £135, the shop owner wants to offer a sale on this coat with a discount of 25%. What will be the new price of this coat?

Work out 25% of £135: 135/100 = 1.35, multiplied by 25 is £33.75.

25% is the same as 1/4, so you could also do 135/4 = £33.75

Be careful now, the new price is NOT £33.75!!

£33.75 is the amount of discount, the amount off of the original price.

So £135 – £33.75 = £101.25

£101.25 is the new price of the coat.

Hope that helps, please ask or comment if you need more examples or help.

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