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 ÷ 80 x 100 = = 67.5 %

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 £ x 25 ÷ 100 = £74.00 £ £74.00 = £222.00

Method 2 This 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 £ x 5 ÷ 100 = £9.20 £ £9.20 = £193.20

Method 2 I k ey in: 184 x 5 % + When the % button is pressed I get 9.2 When the + button is pressed I get Again I do not need to press the “ = “ sign College calculators… % 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 2 Work 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 = £ (leave in ALL the decimal places!!) £ 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% % =117.5% So £30.55 ÷ = £0.26 £0.26 x 100 = £26.00