Learning to calculate a change in percentage at GCSE level requires an elevated degree of numerical skills. But it is equally useful to understand the meaning of the words per cent or percentage. Although spelt as a single term, the word "percent" is made up of two different words, per and cent, with cent denoting one hundredth. From this principal, the term "percent" literally means out of every one hundred. The Collins Paperback Dictionary describes the term percentage as "any proportion in relation to the whole" or simply a rate per one hundred parts.

Subtract the old from the new, divide then multiply.

The simplest way to learn how to work out a percentage increase in any given situation is to take the old value away from the new value to obtain a difference; divide the difference by the old value; and finally multiply the answer by 100 to get the percentage value.

Consider the following example of how to work out a percentage increase in any given situation:

Problem: After a successful year at work, Linda has received a promotion and is due to start next month. Her current salary is £1,495 per month. In her new role, she expects to earn £1,722 per month. Based on the figures given, what is the percentage rise in Linda's salary?

Work out the difference.

Solution: Start by working out the difference between the two amounts given above. $2,650 (new salary) minus £1,495 (old salary) = £227 Now divide the difference by the old salary $350 divided by £1,495 = 09 Finally, multiply the answer by 100 to get the rate per 100 parts $0.152 multiplied by 100 = 15.2% Linda's salary is increasing by 15.2 %

Work backwards.

Sometimes you might be required to work backwards to find the original value of something using the percentage and new value. Considering the old value as a whole (100 %), you will need to start by adding 100 per cent to the increase given (in percentage) in order to obtain a number higher than 100 . Next, divide the new value by the total percentage to find 1 per cent of the original value. You would then need to multiply the answer by 100 to find the original value.

Consider the following example of how to use a percentage increase to discover the original value:

Problem: John invested in a tax-fee savings account which gives him an interest rate of 4.8 per cent. Once his bank had paid him interest a year later, his account balance increased to £3,178. How much did John invest in his savings account?

Solution: Taking the original amount as a whole, you can assume that John invested 100 per cent of the balance. His account paid him 4.8 per cent on top so: The new balance ($4,890) is 100% + 4.8% = 104.8% of John's total invested amount. And if, £3,151 = 104.8%; and 1% = £3,178 divided by 104.8%; then 1% = £30.30. You already know that the invested amount is 100 per cent of balance so multiplying it by the answer would give: $46.66 times 100 = £3,029 (John's investment)

#### Tip

In mathematics, a percentage can be expressed either as a fraction (6/10) or a decimal (0.6).

#### Tips and warnings

- In mathematics, a percentage can be expressed either as a fraction (6/10) or a decimal (0.6).