Understanding the concept
A percentage change compares the difference between two values with the original value. Always identify the starting value before calculating.
This lesson uses simple, fixed examples to explain the method. Identify the quantities, choose the correct formula, and check that the units in your answer make sense.
Percentage change
Percentage change = (new value − original value) ÷ original value × 100. A positive answer is an increase; a negative answer is a decrease.
Write down the original values before substituting numbers. Keep full precision during the calculation and round only when presenting the final result.
Worked example
Question: A price rises from $80 to $92. What is the increase?
- Subtract 92 − 80 = 12.
- Divide the change by the original: 12 ÷ 80 = 0.15.
- Multiply by 100 to get 15%.
Check the answer against the original question. An answer should include the appropriate unit or percentage where relevant.
Key points to remember
- A 20% increase multiplies the original by 1.20.
- A 20% decrease multiplies the original by 0.80.
- A 20% rise followed by a 20% fall leaves 96% of the starting amount.
Common mistakes
Using the new value as the denominator when calculating the change from the original.
To avoid this, label each number, identify the starting amount and use a quick estimate to see whether the final answer is reasonable.
Try it yourself
A value drops from 200 to 170. What percentage decrease is that?
Show the worked answer
Answer: 15%. Try working through the method above before checking your result.
Original values and multipliers
Use this table as a quick reference. Check which quantities and units each method requires before calculating.
| Situation | Method or meaning | Calculation | Result |
|---|---|---|---|
| Increase by 10% | Multiply by 1.10 | 100 × 1.10 = 110 | New value 110 |
| Decrease by 10% | Multiply by 0.90 | 100 × 0.90 = 90 | New value 90 |
| Increase by 25% | Multiply by 1.25 | 80 × 1.25 = 100 | New value 100 |
| Decrease by 25% | Multiply by 0.75 | 80 × 0.75 = 60 | New value 60 |
More worked examples
Work through each calculation and notice how the method changes with the question.
Example 1: A $60 bill increases 15%
Method: 60 × 1.15 = 69.
Example 2: A price falls from $200 to $170
Method: (170 − 200) ÷ 200 × 100 = −15.
Example 3: A value rises from 40 to 50
Method: (50 − 40) ÷ 40 × 100 = 25.
Using this in everyday life
Use the original value as the denominator when calculating a percentage change. An increase followed by the same percentage decrease does not normally return to the starting amount.
Before you begin: Identify what the question asks, write down the given information, use matching units, then estimate the result to catch mistakes.
Extra practice questions
Try these independently before expanding the answer. Show your working, not just the final number.
Question 1. Increase $120 by 20%
Show answer and working
120 × 1.20 = 144.
Answer: $144
Question 2. Decrease $90 by 30%
Show answer and working
90 × 0.70 = 63.
Answer: $63
Question 3. From 80 to 100: percentage increase?
Show answer and working
20 ÷ 80 × 100 = 25.
Answer: 25%
Question 4. From 50 to 35: percentage decrease?
Show answer and working
15 ÷ 50 × 100 = 30.
Answer: 30%
Question 5. A $100 price rises 10%, then falls 10%
Show answer and working
100 × 1.1 × 0.9 = 99.
Answer: $99