A worked lesson · Learn and practise
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Compare two price changes, then try a small puzzle. You can do it all without typing.
Same amount. Same percentage?
80 → 100 → 80
An increase of 25%
- Starting amount
- 80
- Change in amount
- 20
20 ÷ 80 = 0.25 = 25%
The price increases by 20. We compare that increase with the starting price, 80. Twenty is one quarter of 80.
The change is 25% of the starting amount.
The whole bar represents the starting amount for the selected change. The shaded part shows the size of the change as a share of that amount.
The starting amount changed. That is why equal changes in amount need not be equal changes in percentage.
Authored example. No AI service, no grading.
Try before revealing
A price goes from 50 to 60, then returns to 50. What are the percentage increase and decrease?
Work it out in your head or on paper. Ask for a hint whenever you like. Optional notes stay on this page and are never checked automatically.
Optional: jot down a guess
The worked answer
- Increase: 10 ÷ 50 = 0.20 = 20%.
- Decrease: 10 ÷ 60 ≈ 0.1667, or approximately 16.7%.
The decrease is one sixth of 60. Its percentage has been rounded to one decimal place. Compare the starting amount in each calculation with the one you used.
Optional: explain it in your own words
Why does the same change of 10 give two different percentages? Try an explanation before opening the example.
An authored explanation to compare with yours
“The same ten-unit change is a different share of 50 than of 60.”
Does your explanation name the starting amount for each change? You do not need the same wording. Read the two explanations side by side and decide what you would clarify.
Take the learning method with you
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- Ask for a concrete example, then a question you can attempt yourself.
- Use a hint when you need one. Ask for a different example if the explanation is not helping.
- Explain the idea back in your own words, then compare it with the explanation you were given.
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About this lesson
The examples, hints and explanations were written for this lesson. The prices are fictional; the percentage calculations use the change divided by the starting amount. No AI service runs here, and the page does not assess your understanding.
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