Number
Fractions, decimals, and standard form
Fractions: Add/subtract: common denominator. Multiply: numerators × numerators, denominators × denominators. Divide: **KFC** — Keep, Flip, Change.
Conversions: Fraction → Decimal: divide. Decimal → %: ×100. % → Fraction: over 100, simplify.
Standard form: A × 10ⁿ where 1 ≤ A < 10. Example: 45,000 = 4.5 × 10⁴. 0.0032 = 3.2 × 10⁻³.
Indices rules: aᵐ × aⁿ = aᵐ⁺ⁿ. aᵐ ÷ aⁿ = aᵐ⁻ⁿ. (aᵐ)ⁿ = aᵐⁿ. a⁰ = 1. a⁻ⁿ = 1/aⁿ.
Surds: Simplify by finding square factors. √12 = 2√3. **Rationalise denominator:** 1/√5 = √5/5.
Key Points to Remember
- 1Four operations with fractions
- 2Converting between fractions, decimals, percentages
- 3Standard form
- 4Surds and indices
Pakistan Example
Mobile Data Plans — Jazz vs Telenor Maths
Jazz offers 10 GB for Rs. 350 vs Telenor 15 GB for Rs. 490. Jazz costs Rs. 35/GB vs Telenor Rs. 32.67/GB — Telenor wins by ~6.7%. Real fraction and percentage calculations with Pakistan context.
Quick Revision Infographic
Mathematics — Quick Revision
Number
Key Concepts
Mobile Data Plans — Jazz vs Telenor Maths
Jazz offers 10 GB for Rs. 350 vs Telenor 15 GB for Rs. 490. Jazz costs Rs. 35/GB vs Telenor Rs. 32.67/GB — Telenor wins by ~6.7%. Real fraction and percentage calculations with Pakistan context.