Percentages — Deep Dive Learning
Understand and calculate percentages in real life
What is a percentage?
- A percentage is a number out of 100.
- The word "percent" means "per hundred".
- We use the symbol %.
- Example: 50% means 50 out of every 100.
- Percentages appear in shops, banks, food labels and test scores.
Finding 50%
- 50% means half.
- To find 50% of any number, divide it by 2.
- 50% of £20 = £20 ÷ 2 = £10
- 50% of 80 = 80 ÷ 2 = 40
- If a price is "50% off", you pay half the original price.
Finding 25%
- 25% means one quarter.
- To find 25%, divide the number by 4.
- 25% of £40 = £40 ÷ 4 = £10
- 25% of 60 = 60 ÷ 4 = 15
- Think: 25% is half of 50%.
Finding 10%
- 10% means one tenth.
- To find 10%, divide the number by 10.
- 10% of £50 = £50 ÷ 10 = £5
- 10% of 200 = 200 ÷ 10 = 20
- Once you know 10%, you can build other percentages from it.
Worked Examples
Example 1: 50% off a £30 jacket
- Original price: £30
- 50% of £30 = £30 ÷ 2
- = £15
- You save £15 and pay £15.
Example 2: 10% tip on a £40 meal
- Meal cost: £40
- 10% of £40 = £40 ÷ 10
- = £4
- A 10% tip is £4.
Practice Problems
- What is 50% of £60?
Hint: Divide £60 by 2.
Answer: £30 - What is 10% of £90?
Hint: Divide £90 by 10.
Answer: £9 - A coat costs £80. It is 25% off. How much do you save?
Hint: Find 25% by dividing by 4.
Answer: £20
Challenge Question
A jacket costs £120. It is reduced by 30%. Then there is an extra 10% off the sale price. What do you pay?
Hint: First find 30% of £120. Then find 10% of the new price.
Answer: £75.60
30% of £120 = £36, so sale price = £84. Then 10% of £84 = £8.40. Final price = £84 - £8.40 = £75.60.
Common Mistakes to Avoid
- Mistake: Thinking 50% of £30 is £60
Correction: 50% means half, so 50% of £30 = £15
Why: Percent means divide, not multiply. 50% = divide by 2. - Mistake: Adding 10% by adding 10
Correction: 10% of £70 is £7, not £70 + 10 = £80
Why: 10% means divide by 10. It depends on the amount. - Mistake: Thinking 30% off = paying 30%
Correction: 30% off £100 means you pay £70 (not £30)
Why: The discount is what you save. You pay 100% minus the discount.