Percentages Simply Explained
"Percent" literally means "out of 100." So 25% means 25 out of every 100. Once you know a few tricks, percentages become some of the easiest marks in the test.
The Building Blocks
If you can find 10% of something, you can find almost any percentage. Here is the cheat sheet:
- 50% — divide by 2 (half)
- 10% — divide by 10
- 5% — find 10%, then halve it
- 1% — divide by 100
- 25% — divide by 4 (quarter)
Now combine them! Want 35%? That is 10% + 10% + 10% + 5%. Want 15%? That is 10% + 5%. Easy.
Key Formulas
- Percentage of amount = (percentage ÷ 100) × amount
- 10% of anything = move the decimal point one place left
- Discount price = original price − discount amount
- Percentage as a fraction: 25% = 25/100 = 1/4
Worked Examples
Example 1 — Find 30% of £120
- 10% of £120 = £120 ÷ 10 = £12
- 30% = 10% × 3 = £12 × 3 = £36
Answer: £36
Example 2 — A jacket costs £60. There is a 15% discount. How much do you pay?
- 10% of £60 = £6
- 5% = half of 10% = £6 ÷ 2 = £3
- 15% = 10% + 5% = £6 + £3 = £9 discount
- Sale price = £60 − £9 = £51
Answer: £51
Tip: always check — is my answer less than the original? ✓
Example 3 — There are 200 pupils. 45% are boys. How many girls?
- If 45% are boys, then 100% − 45% = 55% are girls
- 10% of 200 = 20
- 50% of 200 = 100
- 5% of 200 = 10
- 55% = 50% + 5% = 100 + 10 = 110
Answer: 110 girls
Percentages in Real Life
Percentages are everywhere — shop sales, test scores, battery levels, even how much of your homework you have finished! When you see "20% off" in a shop, you now know exactly how to work out the new price. That makes you a smart shopper.
Practice Questions
- Find 20% of 150
- Find 35% of £80
- A game costs £40 with 25% off. What is the sale price?
- There are 300 sweets. 60% are red. How many are not red?
- What is 1% of 5,000?
Answers: 1) 30 2) £28 3) £30 4) 120 5) 50