Percentages (%)

% Means out of 100.

So 20% is the same as;20 parts out of 100,or 20p in the £

Sometimes we are asked to convert, for example, 18 marks out of 40 into a percentage.

To do this we use the following procedure:

18 ÷ 40 = 0.45 Then multiply the answer by 100 = 45%We use this method every time we have

to convert one number out of another into a percentage (%).

Now try this one:

What is 54 out of 80 as a percentage?

This is where you first divide 54 by 80 and multiply the answer by 100.

54 ÷ 80 x 100

=

= 67.5 %

10080

54

Knowing about percentages (%) is very important in life.

How can you work out the discount on purchases or know if you are paying the correct amount of VAT, etc?

A question may ask you to work out a percentage of an amount.

For example: Work out 15% 0f £25

To do this we use the following technique:-

15 ÷ 100 then multiply the answer by 25 (£3.75)You may know another method……If it works don’t change !!!!

We will now look at % Discounts

For a % discount, we need to work out how much the discount is in value and then SUBTRACT it from the original price.

Example: A TV has a discount of 25% off the original price of £296. What is the new sale price?

Method 1

£296.00 x 25 ÷ 100 = £74.00

£296.00 - £74.00 = £222.00

Method 2This method involves knowing how your calculator operates!!!

On my calculator I key in:

296 x 25% –

When I press the % button, the calculator reads ‘74’ the discount value.

When I press the – button I get ‘222’, the new sale price.

Note: I do not need to press the “ = “

College calculator…. 296 – 25 % (NO = sign!!)

If you want to save time and effort and have less risk of wrong answers, I STRONGLY suggest you make sure you know how your calculator operates!!!

And now % Increases

Harry’s pay of £184 is to be increased by 5%. What is his new pay?

The method is virtually identical to the above system, the difference being that this time we ADD the new value to the original pay.

Method 1£184.00 x 5 ÷ 100 = £9.20£184.00 + £9.20 = £193.20

Method 2

I key in: 184 x 5 % +

When the % button is pressed I get 9.2

When the + button is pressed I get 193.2

Again I do not need to press the “ = “ sign

College calculators….184 + 5 %

Again, no need to press the “ = “ sign

Calculating other % increases or VAT on a bill is the same as this, you just change the value 5% to the new % value or the VAT %.

I will now show you how to work out 17.5% WITHOUT a calculator on the board.

This is often called “Fag Packet” maths since it was originally done by traders on cigarette packets.

Inverse %(Working backwards)

This is a little more difficult, but providing you remember the rules it becomes a little easier!!

A radio on sale at £85 has been discounted by 20%. What was the original price?

Rule 1 If the discount was 20%, this means that

the sale price is 80% of the original price. (100% - discount % !!!)

Rule 2Work out what 1% of the price is (in this case, divide 85 by 80) then multiply by 100

In the above case £85 is 80%

So 1% is £85 ÷ 80 = £1.0625 (leave in ALL the decimal places!!)

£1.0625 x 100 = £106.25

A meal at a restaurant was £30.55 including VAT at 17.5%. What was the cost of the meal BEFORE VAT was added?

If the VAT is 17.5% AND it was added on to the original cost:

Then the £30.55 is 100% + 17.5% =117.5%

So £30.55 ÷ 117.5 = £0.26

£0.26 x 100 = £26.00