# Understanding percentages

Percentages are everywhere, from invoices and payslips to shop receipts and restaurant bills, so it’s vital to get to grips with the basics.

Per cent means ‘per hundred’, so a percentage is a fraction of 100. Eg 100% is the whole of 100. 75% is 75 parts of 100. As a fraction this would be 75/100 and as a decimal it would be 0.75.

You will come across percentages in many aspects of your life but in accounts, they are most commonly used for calculating discounts and VAT payments.

# Calculating a percentage of a quantity

This is when you need to work out what a percentage of an amount is worth in real terms. To do this you must turn the percentage into a fraction and multiply it by the full quantity.

EG 5% of 300

= 5 /  100 x 300

= 5 ÷ 100 x 300

= 15

Alternatively you can turn the percentage into a decimal: 0.05 x 300 = 15

# Calculating one quantity as a percentage of another

First of all you have to display the quantity as a fraction and then multiply it by 100.

EG 36 as a percentage of 90 = 36/90 x 100

It may be easier to turn the fraction into a decimal by diving 36 by 90: 36 ÷ 90 = 0.4, so 0.4 x 100 = 40%

# Increasing an amount by a percentage

If you are adding VAT, for example, you will have to add 20% of the amount to the original figure.

EG £300 + VAT

First calculate 20% of £300

20/100 x £300 = 0.2 x 300 = £60.00

£60.00 + £300 = £360.00

An alternative method is to the add percentage to 100% (ie 20 +100), which is the whole amount, to give you the new percentage, divide it by 100 and then multiply it by the original figure.

EG 100 = 20% x £300

= 120% x £300

= 120/100 x £300

= 1.20 x £300

= £360.00

# Decreasing an amount by a percentage

This is the opposite of the above calculation. It is used when working out discounts, ie an amount is taken off.

Eg. 20% discount of £300 = 20/100 x £300

Which reduces to 0.2 x 300 = £60

So, £300 – £60 = £240

# Calculating VAT when it is in the price

If a price includes VAT, you may want to work out the actual cost of the product. To do this you treat the price as 20% which includes the value of the product – 100% and the 20% VAT.

EG £80 excludes VAT, how much is the VAT?

20/100 x £80 = £16

EG £80 includes VAT, how much would it be without VAT? 100/120 x £80 = £66.67

Practice makes perfect so keep practicing until it becomes second nature!

AAT Comment offers news and opinion on the world of business and finance from the Association of Accounting Technicians.