Finding a Percentage

Finding a Percentage

A percentage is a number out of 100. When you write out a percentage you use the symbol %. Fractions, decimals and percentages are all just different ways of writing a number. You can concert between them using the following rules

To change a fraction into a decimal we divide the numerator by the denominator. To change a decimal into a percentage we multiply by one hundred. To change a percentage into a decimal we divide by 100 as multiplication and division are opposite functions.

To change a decimal into a fraction we make use of our knowledge of tenths, hundredths and thousandths.


In your exam you might be asked to work out the percentage of an amount.

For example, what is 60% of 70g?

First of all, write the 60% as a fraction: 60/100 = 6/10 = 3/5

You can then multiply the 70g by this fraction:

70 x 3/5 = 42g

(Don’t forget to add the measurement where necessary).

You might be questions regarding income tax or VAT:

      • – Income tax is paid by people when they earn money (or their income).
      • – VAT is short for Value Added Tax. This is added to most goods before you buy them.


Percentage increases and decreases

mathsYou might get a question which looks at how much an amount decreases or increases. In order to work this out you need to make a fraction from both amounts and then multiply your answer by 100

For example, simple interest: with simple interest how much you borrow stays the same.

So, if you were to borrow £600 from a bank for 4 years with an interest rate of 6% per annum (pa) then:

Interest from a year = 6% of £600

= (6/100) x 600

= £36

The interest is for a 4 year period so: £36 x 4 = £144

The formula you can use to work out questions involving simple interest is:

Amount to pay back = P x R x T

P stands for principal which is the amount borrowed.

R is the rate of interest charged each year.

T is the time it’s borrowed in years.

Another kind of question deals with profit and loss. For instance, if you wanted to sell your second hand bicycle over the Internet then if it’s in a good condition and you put a price more than what you originally paid for it then you make a profit. However, if it has a few stratches and you need to sell it for less than you brought it for you make a loss.

For example, let’s say you brought your bicycle originally for £250 and you want to sell it on for £175. What is the percentage decrease?

Decrease = 250 – 175 = 75

75 250 x 100 = 30%

You decide to do up another old bike. You brought it for £40 and now want to sell it for £60. What’s the percentage increase?

60 – 40 = 20

20 40 x 100 = 50%