Percentage Change
(KS3, Year 7)

A percentage change is the change from one value to another value, expressed as a percentage.

A Real Example of a Percentage Change

Imagine that a company sells 100 calculators in a week. The next week the company sells 120 calculators. The percentage change from 100 to 120 is 20%.

How to Find a Percentage Change

100 to 120 is a percentage change of 20%. How do we know it is 20%?

• The change from 100 to 120 is the difference between the numbers.
  120 − 100 = 20
  The change is 20.
• The percentage change expresses the change (20) as a percentage of the original number (100).
  20 = 20% of 100
  The percentage change is 20%.

how to find a percentage change

Other Questions with a Percentage Change

In the example above, we found the percentage change from an old number to a new number. You need to use percentage changes in other ways:

• You need to be able to find the new number if you are told the old number and the percentage change. For example, if a £10 an hour wage increased by 20%, you would have to work out that the new wage would be £12 an hour.
  
  
• You need to be able to find the old number if you are told the new number and the percentage change. For example, if there are 33 students in a class after a 10% increase, you would have to work out that there were originally 30 students in the class.
  
  

Why Is a Percentage Change Useful?

You will see percentage changes used all the time if you read the news. The economy grew by 3%. Crime has fallen by 1%. Profits are up 2%. Why do we use percentage changes? We often need to describe the change from one number to another number. We could just write the difference between the numbers. Imagine 2 companies selling cars: Company A and Company B.

• Company A sold 10 cars last week and 20 cars this week.
• Company B sold 100 cars last week and 110 cars this week.

Both companies sold an extra 10 cars this week. But this doesn't do justice to the difference between the companies' performances. Instead, let's compare how many extra cars they sold compared to the number of cars they sold last week.

• Company A doubled the number of cars it sold from 10 to 20. This is a very impressive 100% increase (because the 10 extra cars are 100% of the 10 cars sold last week).
• Company A did a lot better than Company B because it improved much more in a week. Only the percentage change shows this.

Percentage changes are more useful than the simple change in numbers because it tells you how big the change is relative to the original number.

Percentage Increase, Percentage Decrease

In this lesson, we found that the percentage change from 100 to 120 is 20%. This is a percentage increase because the number has increased: 120 is larger than 100. The percentage change is positive. If a number decreases (for example, from 100 to 80) then there would be a percentage decrease. The percentage change would be negative.