Common Percentage Mistakes and How to Avoid Them
Common Percentage Mistakes and How to Avoid Them
GCSE Maths | percentages.co.uk
These are the ten errors that appear most frequently in GCSE percentage questions. For each mistake, you will see an example of what goes wrong and a clear explanation of the correct method.
Mistake 1: Adding percentage changes directly
Incorrect
A price increases by 20%, then decreases by 20%. Change = +20 - 20 = 0%, so the price is unchanged.
Correct
Multiply the multipliers together: × 1.20 × 0.80 = × 0.96. The combined multiplier is 0.96, which means the final price is 96% of the original. This is an overall 4% decrease, not 0%.
Each percentage change is calculated on a different base value. The 20% increase is applied to the original price, but the 20% decrease is then applied to the higher (increased) price. The two changes do not cancel out.
Mistake 2: Using the new value as the base for percentage change
Incorrect
A price rises from £80 to £100. Percentage change = (20 ÷ 100) × 100 = 20%.
Correct
Percentage change = (change ÷ original) × 100 = (20 ÷ 80) × 100 = 25%.
Percentage change must always use the original value as the base. The change (£20) is expressed as a fraction of where you started (£80), not where you ended up (£100).
Mistake 3: Subtracting the percentage from the new value to find the original
Incorrect
After a 20% increase, a price is £240. To find the original: 240 - 20% of 240 = 240 - 48 = £192.
Correct
Divide by the multiplier. The multiplier for a 20% increase is 1.20, so: original = 240 ÷ 1.20 = £200.
When you subtract 20% of the new value, you are taking 20% of £240. But the 20% increase was applied to the original (smaller) value, not to £240. Dividing by the multiplier correctly reverses the operation.
Mistake 4: Rounding too early in compound interest calculations
Incorrect
£1,000 at 5% for 3 years compound interest: Year 1 = £1,050. Year 2 = £1,103 (rounded to nearest £). Year 3 = £1,158 (rounded to nearest £). Answer: £1,158.
Correct
Use the formula and only round at the very end. A = 1000 × 1.053 = 1000 × 1.157625 = £1,157.63. Answer: £1,157.63.
Rounding intermediate values introduces an error that grows with each subsequent calculation. Always carry full decimal precision through every step and only round your final answer.
Mistake 5: Confusing the percentage increase with the new value
Incorrect
A salary increases by 15%. The new salary is 15% of the original salary.
Correct
The new salary is 115% of the original salary (the original 100% plus the 15% increase). Multiply by the decimal 1.15, not 0.15.
A 15% increase does not give you 15% of the original. It gives you 100% + 15% = 115% of the original. If you multiply by 0.15, you find only the increase itself, not the new total.
Mistake 6: Not fully simplifying a fraction when converting from a percentage
Incorrect
Convert 24% to a fraction: 24/100. Divide top and bottom by 2 to get 12/50. Stop there.
Correct
The highest common factor (HCF) of 24 and 100 is 4. Divide both by 4: 24/100 = 6/25. This is the fully simplified form. (12/50 can be simplified further to 6/25.)
Always divide by the highest common factor in one step, or keep simplifying until the numerator and denominator share no common factor other than 1. Stopping early gives a fraction that is not in its simplest form.
Mistake 7: Using the selling price instead of the cost price for percentage profit
Incorrect
An item costs £40 and sells for £50. Percentage profit = (10 ÷ 50) × 100 = 20%.
Correct
Percentage profit = (profit ÷ cost price) × 100 = (10 ÷ 40) × 100 = 25%.
Percentage profit is always measured against the original cost price, not the selling price. Think of it this way: the profit is a fraction of what you originally paid, not a fraction of what you received.
Mistake 8: Forgetting to convert the percentage to a decimal in the multiplier
Incorrect
Increase £60 by 15%: 60 × 15 = £900.
Correct
Multiplier = 1 + (15 ÷ 100) = 1.15. New value = 60 × 1.15 = £69.
The multiplier for a 15% increase is 1.15, not 15. Always divide the percentage by 100 before building the multiplier. Multiplying by 15 instead of 1.15 gives a result 1,000 times too large.
Mistake 9: Dividing the wrong way when expressing A as a percentage of B
Incorrect
Express 20 as a percentage of 5: (5 ÷ 20) × 100 = 25%.
Correct
"A as a percentage of B" means (A ÷ B) × 100. So: (20 ÷ 5) × 100 = 400%.
The phrase "express A as a percentage of B" tells you: A goes on top, B goes on the bottom. Reversing the division gives a completely different (and wrong) answer. In this case, 20 is four times larger than 5, so the answer must be greater than 100%.
Mistake 10: Applying the simple interest formula when compound interest is required
Incorrect
£800 invested at 4% for 3 years compound interest. Using simple interest formula: Interest = 800 × 4 × 3 ÷ 100 = £96. Total = £896.
Correct
Use the compound interest formula: A = P(1 + r/100)n = 800 × 1.043 = 800 × 1.124864 = £899.89 (to the nearest penny).
Simple interest applies the same percentage to the original principal each year, giving a fixed interest payment every year. Compound interest applies the percentage to the growing total (principal plus accumulated interest), so each year's interest is slightly larger than the last. Always read the question carefully to identify which type is required.