Simplification and Approximation
Syllabus Unit: Quantitative Aptitude
Why it matters
Chapter overview
Simplification and Approximation questions open the SBI PO Quant paper as quick, calculator-free scoring opportunities — typically 5 marks that reward knowing BODMAS, smart rounding, and surd/index rules cold, since the whole point is solving each one in under 20-25 seconds.
Preliminary Examination Syllabus Quantitative Aptitude 35% weightage
Live Animation1 / 4
Vinculum/Brackets (inner to outer)
Orders (powers & roots)
Division & Multiplication (left to right)
Addition & Subtraction (left to right)
1BODMAS & Simplification
One order of operations, applied consistently, turns a scary-looking expression into arithmetic a child could do.
Learning Objectives
- State the full order of operations: Vinculum, Brackets, Orders, Division/Multiplication, Addition/Subtraction.
- Simplify nested brackets from the innermost pair outward.
- Apply the left-to-right rule correctly when division and multiplication (or addition and subtraction) appear together.
- Recognize when simplification is disguised inside a fraction or a mix of operations spanning a full line.
Key Terms
BODMASBrackets, Orders (powers/roots), Division/Multiplication (left to right), Addition/Subtraction (left to right) — the fixed order for evaluating an expression.
VinculumA bar or line grouping terms (like a long fraction bar or overline) that must be resolved before brackets are opened.
Nested BracketsBrackets within brackets — solved from the innermost pair ( ) outward through [ ] and finally { }.
Left-to-Right RuleWhen only ×/÷ (or only +/−) remain in an expression, operate strictly left to right — 'multiplication before division' is a common myth, not a rule.
Every simplification question, however long, reduces to applying one fixed order of operations without skipping a step. The exam's difficulty comes entirely from length and disguised operations, never from a new rule.
The full order, in sequence
- Vinculum — resolve any overline/bar grouping first.
- Brackets — solve innermost ( ) first, then [ ], then { }.
- Orders — powers and roots.
- Division & Multiplication — strictly left to right, whichever comes first in the expression.
- Addition & Subtraction — strictly left to right, whichever comes first in the expression.
15 + 6 ÷ 3 × 2 − 4 → 15 + 2 × 2 − 4 → 15 + 4 − 4 → 15
Common MistakeMyth to unlearn: multiplication is NOT always done before division, and addition is NOT always done before subtraction — when both appear together, work strictly left to right.
Exam TipWrite the expression on your rough sheet and rewrite it after each single step (not each operation type) — this catches the sign errors that mental-math shortcuts often miss.