Module 4
Fractions & percentages
Quick-reference revision notes for parents.
4.1 Fractions reminder
- Equivalent fractions: multiply or divide top and bottom by the same number. 2/3 = 4/6 = 6/9.
- Simplify: divide top and bottom by their highest common factor.
- Adding/subtracting: needs a common denominator first.
4.2 Multiplying fractions
Top × top, bottom × bottom. No common denominator needed. Simplify before or after.
2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15
Look for a number that divides into a top and a bottom diagonally — cancel before multiplying. 3/8 × 4/9: 4 and 8 share 4, 3 and 9 share 3 → 1/2 × 1/3 = 1/6.
For mixed numbers (e.g. 2 1/3): convert to top-heavy first: 2 1/3 = 7/3.
4.3 Dividing fractions
Keep, change, flip (KCF). Keep the first fraction; change ÷ to ×; flip the second.
3/4 ÷ 2/5
= 3/4 × 5/2
= 15/8 = 1 7/8
4.4 Percentages reminder
"Per cent" means "per 100". 50% = 1/2 = 0.5.
To find a percentage of a number, multiply by the decimal:
15% of 80 = 0.15 × 80 = 12
Common conversions worth knowing
| % | Decimal | Fraction |
|---|---|---|
| 10% | 0.1 | 1/10 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
4.5 Percentage increase and decrease
Multiplier method is fastest:
- Increase by 15% → × 1.15
- Decrease by 15% → × 0.85
- Increase by 8% → × 1.08
- Decrease by 30% → × 0.70
80 × 1.12 = £89.60
200 × 0.65 = £130
4.6 Percentage change
Going the other way — given an original and new value, find the % change:
% change = (change ÷ original) × 100
A jacket cost £50, now sells for £62.50. Percentage increase?
change = 62.50 − 50 = 12.50
% = (12.50 ÷ 50) × 100 = 25%
Always divide by the original, not the new value.
Quick reference
- Multiply fractions: top × top, bottom × bottom
- Divide fractions: keep, change, flip
- x% of N = (x/100) × N
- Increase by x% → × (1 + x/100). Decrease → × (1 − x/100)
- % change = change ÷ original × 100