Percentage Change
Compare new and old values relative to the old value.
Key idea
Compare new and old values relative to the old value.
In depth
Percentage change = (new − old) ÷ old × 100. It measures growth or loss relative to the starting value. Always divide by the original amount.
Worked example
A price rises from 40 to 50: (50−40)/40 = 0.25, a 25% increase. Falling back from 50 to 40 is only a 20% decrease.
Formula
Real-world uses
- Measuring inflation, price rises, weight loss and growth in sales or population figures
Common mistake
Dividing by the new value. The base is always the starting value.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Percentage Change?
Compare new and old values relative to the old value. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Percentage Change?
The key formula is (new − old)/old × 100%.
Where is Percentage Change used in real life?
Real-world examples: Measuring inflation, price rises, weight loss and growth in sales or population figures.
What should I learn before Percentage Change?
Make sure you are comfortable with Percentage of a Quantity, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Percentage Change?
Dividing by the new value. The base is always the starting value.
How can I practise Percentage Change?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Percentage Change?
Move on to Discounts and Sales Tax next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.