Use known benchmark percentages
25% means one quarter, so 25% of 60 is 60 divided by 4.
halve the amount
quarter the amount
divide by 10
Convert to a familiar fraction when it makes the calculation easier.
Year 8
Percentages of amounts without a calculator
Find percentages of amounts efficiently, connect fractions, decimals and percentages, and compare values in simple best-buy contexts.
Lesson overview
Number - percentages and proportional thinking
A percentage means out of 100. Many percentage questions can be solved mentally by using benchmark fractions and percentages such as 50%, 25%, 10%, 5% and 1%. Strong percentage work comes from choosing an efficient route, not from one fixed method every time.
Build percentages from 10% and 1%
To find 23% of 80, work out 20% and 3%, then combine them.
Breaking a percentage into simpler parts often avoids unnecessary long methods.
Percentages support best-buy comparisons
A 20% discount on 50 pounds reduces the price by 10 pounds.
| Original price | Discount | Amount off | New price |
|---|---|---|---|
| 50 pounds | 20% | 10 pounds | 40 pounds |
Find the amount off first, then subtract from the original price.
Worked example
Find 35% of 240.
| 10% | 30% | 5% | 35% |
|---|---|---|---|
| 24 | 72 | 12 | 84 |
- Find 10% of 240 by dividing by 10 to get 24.
- Multiply by 3 to find 30%, which is 72.
- Find 5% by halving 10%, which is 12.
- Add 72 and 12 to get 84.
Try it
Choose the most efficient benchmark percentage or percentage split before you calculate.
Question 1
What is 25% of 80?
Question 2
What is 15% of 60?
| 10% | 5% | 15% |
|---|---|---|
| 6 | 3 | 9 |
Question 3
A jumper costs 40 pounds and is reduced by 25%. What is the sale price?
Question 4
What is 35% of 200?
Question 5
Which statement is correct?
divide by 10
half of 10%
quarter the amount
Common mistakes
Watch for these when working through the lesson.
- Dividing by the percentage instead of using 10%, 5% or 1% benchmarks.
- Finding the percentage amount correctly but forgetting to add or subtract in a discount question.
- Mixing up 5% with one fifth.
Related topics
These ideas fit closely with this lesson.
- Ratio scaling, simplifying and sharing in a ratio.
- Rounding to significant figures.
- Solve two-step linear equations.