Mathematics (Core)Exam code: 0580
Percentages
Number
Building blocks without a calculator
- A few percentages are quick to find directly, and the rest are assembled from them
| Percentage | How to find it |
|---|---|
| 50% | Halve the amount |
| 25% | Halve it twice |
| 10% | Divide by 10 |
| 5% | Halve the 10% |
| 1% | Divide by 100 |
- Combine these to reach any figure the question asks for
- 35% is three lots of 10% plus one lot of 5%
- Above 100%, the original amount is the 100%, so add the extra on
Using the multiplier
- Multiply the amount by the decimal equivalent
- 18% of 450 is 0.18 × 450 = 81
Worked example
A percentage of an amount, without a calculator
Work out 35% of 480.
Solution:
- Build the percentage from blocks that are easy to find
- 10% of 480 is 480 ÷ 10 = 48
- 30% is three lots of that: 3 × 48 = 144
- 5% is half of 10%: 48 ÷ 2 = 24
- 35% = 30% + 5% = 144 + 24 = 168
- Check with the multiplier: 0.35 × 480 = 168
Comparing two quantities
- Express the first quantity as a fraction of the second, then scale by 100
- Whichever quantity the question treats as the whole becomes the denominator
Worked example
One quantity as a percentage of another
(a) Ravi scores 39 out of 60 in a test. Work out his percentage score without a calculator.
(b) A bag holds 14 red, 21 blue and 35 green counters. Find the percentage of the counters that are blue.
Solution:
- (a) The test total, 60, is the whole, so it is the denominator: 39/60
- Simplify, then scale to a denominator of 100: 39/60 = 13/20 = 65/100, which is 65%
- (b) First find the whole: 14 + 21 + 35 = 70 counters
- Blue as a fraction of the whole: 21/70 = 3/10 = 0.3
- 0.3 × 100 = 30%