Simplification — Study Notes for SSC MTS (Paper 1)
Overview
Simplification questions test your ability to perform arithmetic operations in the correct order and handle fractions, surds, and exponents accurately. In SSC MTS, expect 2–4 direct questions worth 8–16 marks. These are scoring questions if you follow rules systematically and avoid calculation errors.
The key skill is applying **BODMAS** (Brackets, Orders, Division/Multiplication, Addition/Subtraction) correctly while handling mixed operations involving whole numbers, fractions, decimals, surds (roots), and exponents (powers). Most errors happen from rushing through steps or misapplying operator priority. Master this topic early — it's the foundation for almost every other quantitative topic in the exam.
Success in simplification means: (1) knowing operation hierarchy cold, (2) quick fraction arithmetic, (3) confidence with basic surd rules and exponent laws, and (4) disciplined step-by-step calculation without mental shortcuts that introduce errors.
Key Concepts
- **BODMAS/BODMAS rule**: Operations must be performed in strict order — Brackets first, then Orders (exponents/roots), then Division and Multiplication (left to right), finally Addition and Subtraction (left to right). Ignoring this order guarantees wrong answers.
- **Brackets hierarchy**: Solve innermost brackets first. The nesting order is: ( ) inner parentheses, { } curly braces, [ ] square brackets. Work from inside out.
- **Fractions**: To add/subtract fractions, find the LCM of denominators and convert to equivalent fractions. For multiplication, multiply numerators and denominators directly. For division, multiply by the reciprocal of the divisor.
- **Surds (roots)**: √a × √b = √(ab); √a / √b = √(a/b); √a ± √b cannot be simplified unless a = b. Rationalization means removing surds from denominators by multiplying numerator and denominator by the conjugate or the surd itself.
- **Exponents (powers)**: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ / aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 (a ≠ 0); a⁻ⁿ = 1/aⁿ; (ab)ⁿ = aⁿbⁿ. These laws apply universally and must be memorized cold.
- **Order of operations with mixed types**: When an expression has fractions, decimals, surds and exponents together, apply BODMAS strictly while respecting each number type's arithmetic rules. Convert everything to the same form (all fractions or all decimals) if it simplifies calculation.
- **Simplification strategy**: Break complex expressions into smaller chunks, solve brackets step by step, reduce fractions at every stage, and recheck your final answer by rough approximation.