(KS3, Year 7)
The LessonA percentage change is the change from one value to another value, expressed as a percentage.
A Real Example of a Percentage ChangeImagine 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 Change100 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 = 20The change is 20.
The percentage change expresses the change (20) as a percentage of the original number (100).
20 = 20% of 100The percentage change is 20%.
Read more about how to find a percentage change
Other Questions with a Percentage ChangeIn 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.
Lesson SlidesThe slider below gives more examples of percentage changes. Open the slider in a new tab
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.
- 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 Increase, Percentage DecreaseIn 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.
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