Topics / Maths
Percentages, fractions and decimals
Converting between fractions, decimals and percentages, and using them in problems, is core Stage 1 and Stage 2 content. The most demanding type is usually 'reverse percentages', where you are given the price AFTER a change and must find the original.
What is tested
- Converting between fractions, decimals and percentages
- Percentage of an amount, increase and decrease
- Reverse percentages (finding the original amount)
- Comparing and ordering mixed forms
Worked example
A jacket costing £80 is reduced by 15%. What is the sale price?
- 10% of £80 = £8, and 5% = £4, so 15% = £12.
- Sale price = £80 − £12 = £68.
- Check with a multiplier: 85% of £80 = 0.85 × 80 = £68.
Answer: £68
Exam-day checklist
- Decide first: are you finding a percentage of something, or working backwards from a changed value?
- For reverse percentages, write the multiplier (e.g. a 20% increase is ×1.2) and divide by it.
- Build awkward percentages from 10% and 1% blocks.
- Sense-check: a decrease must give a smaller number.
Common mistakes
- For a reverse percentage, taking the percentage off the new price instead of dividing by the multiplier.
- Adding and subtracting percentages of different amounts as if they were the same base.
- Forgetting to convert 7/40 style fractions properly (7 ÷ 40 = 0.175 = 17.5%).
Try it yourself
1. After a 25% decrease, a bike costs £60. What was the original price?
Show answer
£80
A 25% decrease means the new price is 75% of the original: 0.75 × original = 60, so original = 60 ÷ 0.75 = £80.
2. Write 7/40 as a percentage.
Show answer
17.5%
7 ÷ 40 = 0.175, and 0.175 × 100 = 17.5%.
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