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Simplification

About 6 min · Numerical and Mathematical Ability · English

Time worked out from the lesson's 435 words at 150 words a minute, plus a minute for each question.

Simplification questions test your ability to perform arithmetic operations in the correct order and handle fractions, surds, and exponents accurately. These are scoring questions if you follow rules systematically and avoid calculation errors.

Key ideas

• 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 combined unless both reduce to like surds (e.g. √8 + √2 = 2√2 + √2 = 3√2). 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.

Watch out for

• Mistake: Adding/subtracting before multiplying/dividing when no brackets present. Fix: Always complete all multiplication and division first (left to right), then do addition and subtraction (left to right). Write out intermediate steps to avoid this error.
• Mistake: Solving brackets in wrong order (outer before inner). Fix: Always start with the innermost bracket and work outward. Mark each bracket type clearly as you solve.
• Mistake: Applying exponent laws incorrectly: writing 2³ × 3² = 6⁵. Fix: Exponent addition rule (aᵐ × aⁿ = aᵐ⁺ⁿ) applies only when bases are identical. Here, bases differ (2 and 3), so compute each power separately: 8 × 9 = 72.

Quick reference

• BODMAS order: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right)
• Fraction addition: Find LCM of denominators first; for multiplication, no LCM needed — just multiply straight across
• Exponent rules: Same base → add/subtract powers; power of power → multiply exponents; a⁰ = 1; a⁻ⁿ = 1/aⁿ
• Surd multiplication: √a × √b = √(ab); cannot add √a + √b unless they reduce to like surds (√8 + √2 = 3√2)
• Rationalization: Multiply by the surd (or conjugate) to clear the denominator

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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