Percentage Reasoning Worksheet
Free to print and use in your classroom. No sign-up required.
Percentage Reasoning Worksheet
Show your working and write your reasoning clearly. These questions require you to explain, justify and prove.
1. Is 30% of 80 the same as 80% of 30? Show your working and explain why.
2. Sophie says “50% of 50 is 25.” Ben says “50% of 50 is 50.” Who is correct? Explain your answer.
3. A price rises by 50%, then falls by 50%. Tom says the price is back to the original. Is Tom correct? Prove it using an example.
4. Explain why you cannot find the original price by subtracting 20% from a sale price when the item was discounted by 20%. Use an example to demonstrate.
5. Jack says “20% of 60 is 12, and 60% of 20 is also 12.” Is he correct? Explain why or why not.
6. A school reports that attendance improved from 90% to 95%. Is this a 5% increase? Explain the difference between a 5 percentage point increase and a 5% increase.
7. Show that increasing by 10% twice is not the same as increasing by 20%. Use £500 as your starting amount.
8. A value is reduced by 40%. What percentage increase is needed to return to the original value? Show your working.
9. Two students calculate 15% of 240 differently. Alice finds 10%, then adds half of 10% to get 15%. Ben multiplies 240 by 0.15. Show that both methods give the same answer.
10. A shop offers “25% off, then a further 10% off the sale price.” A customer claims this is the same as 35% off. Is the customer correct? Explain and show your working.
11. Is 1% of £100 the same as £1? Is 1% of £1,000 also £1? Explain your answer.
12. Sam says “If you increase a number by 25% and then decrease it by 25%, you always end up with the original number.” Show he is wrong using an example.
13. Arrange these values in order from smallest to largest without a calculator: 3/7, 42%, 0.43. Explain your method.
14. A number increases by 50%. What single multiplier represents this increase? What multiplier would reverse the change and return to the original value?
15. Prove that percentage change depends only on the ratio of the new value to the original, not on the original value itself. Use two examples with the same ratio to illustrate.
16. A teacher says “If you know 10% of a number, you can find any percentage.” Explain how, and give an example finding 17% of 350.
17. Is it possible for a percentage increase to be greater than 100%? Give an example where a value more than doubles.
18. A class has 24 girls and 16 boys. What percentage are girls? A new boy joins. Do both percentages change? Recalculate and explain.
19. Two towns each grow by 10% per year. Town A has 50,000 people. Town B has 80,000 people. After 2 years, what is the difference in population? Explain which town gains more people in absolute terms and why.
20. A student writes: “25% of 80 = 80 ÷ 4 = 20.” Write three different correct methods for finding 25% of a number and explain why they all work.
Free to print and use in your classroom. No sign-up required. percentages.co.uk