Percentages
A percentage expresses a part of a whole as a fraction of 100, where the symbol % represents 'per hundred'. Converting percentages to decimals involves dividing by 100: 35% becomes 0.35. The Year 10 National Curriculum focuses on calculating percentages of amounts and understanding percentage increases and decreases.
Why it matters
Percentages appear throughout daily life in the UK, from calculating VAT at 20% on purchases to understanding mortgage rates at 4.5% annually. In retail, discounts of 30% off £80 trainers save £24, whilst restaurant tips of 12.5% on a £45 meal add £5.63. Financial literacy depends on percentage calculations: a 3% annual interest rate on £1,000 generates £30 yearly. GCSE mathematics extensively uses percentages in probability, statistics, and compound interest problems. Scientific contexts employ percentages for concentration solutions, where a 15% salt solution contains 15g salt per 100ml. Understanding percentage increase and decrease proves essential for analysing data trends, population growth at 2% annually, and price inflation affecting household budgets across Britain.
How to solve percentages
Percentages — how to
- Convert the percent to a decimal by dividing by 100.
- Multiply the decimal by the base number.
- For discounts: subtract the discount from the original.
Example: 20% of 80 → 0.20 × 80 = 16.
Worked examples
You have 40 candies and give away 10%. How many do you give away?
Answer: 4
- Convert percent to fraction → 10% = 110 — 10% is a common fraction — memorise these.
- Apply to the base → 40 × 10100 = 4 — Take a tenth of 40.
- Verify → 4 × 100 ÷ 40 = 10% ✓ — Check backwards.
True or false: 75% of 60 = 50
Answer: False
- Convert percent to decimal → 75% = 0.75 — 75% means 75 per hundred, so divide by 100.
- Multiply by the base → 0.75 × 60 = 45 — Multiplying the decimal by the base gives the percentage amount.
- Verify → 45 ÷ 60 × 100 = 75% ✓ — Working backwards confirms the percent.
What is 50% of 200?
Answer: 100
- Convert to decimal → 50% = 0.5 — Divide the percent by 100.
- Multiply → 0.5 × 200 = 100 — Multiply the decimal by the base.
- Verify → 100 ÷ 200 × 100 = 50% ✓ — Check in reverse.
Common mistakes
- A common error involves adding percentages directly rather than converting to decimals first, calculating 20% + 30% of 50 as 25 instead of the correct 25
- Another mistake treats the percentage symbol as multiplication, writing 15% × 60 = 900 instead of converting to 0.15 × 60 = 9
- Many incorrectly calculate percentage decrease by subtracting the percentage from 100%, finding 25% off £40 as £75 rather than £30