Mathematics (4024)
Fraction → Decimal: Divide top by bottom (¾ = 3÷4 = 0.75) Decimal → Percentage: Multiply by 100 (0.75 × 100 = 75%) Percentage → Fraction: Put over 100 and simplify (75% = 75/100 = ¾)
Increase: New value = Original × (1 + rate/100) Decrease: New value = Original × (1 - rate/100) % Change = (Change / Original) × 100
Profit % = (Profit / Cost Price) × 100 Loss % = (Loss / Cost Price) × 100
Simple: I = PRT/100 (same interest each year) Compound: A = P(1 + R/100)ⁿ (interest on interest!)
Topic 2 of 5Cambridge O Levels
Fractions, Decimals & Percentages
Converting between them and using them in real life
Fractions, decimals, and percentages are three ways to represent the same thing!
Converting Between Them:
Common Conversions to Memorize:
½ = 0.5 = 50% | ¼ = 0.25 = 25% | ¾ = 0.75 = 75%
⅓ ≈ 0.333 ≈ 33.3% | ⅕ = 0.2 = 20% | ⅛ = 0.125 = 12.5%
Percentage Increase/Decrease:
Profit & Loss:
Simple & Compound Interest:
Key Points to Remember
- 1Fraction → Decimal: divide. Decimal → %: multiply by 100
- 2% increase: multiply by (1 + rate/100)
- 3Profit% = (Profit/Cost Price) × 100
- 4Compound interest: A = P(1 + R/100)ⁿ
Pakistan Example
Eid Sale Discounts
Khaadi announces a 30% Eid sale. A kurta originally costs Rs 5,000. Discount = 30% of 5000 = Rs 1,500. Sale price = Rs 3,500. But wait — they also have 'Buy 2 Get Extra 10% off'! If you buy 2 kurtas: 2 × 3,500 = Rs 7,000. Extra 10% off: 7,000 × 0.90 = Rs 6,300. Total saving = Rs 10,000 - Rs 6,300 = Rs 3,700 (37% total discount!). Understanding percentages helps you spot real deals vs marketing tricks.