Simplification & Fractions

Syllabus Unit: Quantitative Aptitude

Why it matters

Chapter overview

Simplification is the foundation chapter of SSC CGL Quantitative Aptitude — nearly every other chapter (algebra, mensuration, DI) eventually reduces to a BODMAS expression, a fraction comparison, or a surd/index law. This topic builds the order-of-operations discipline, fraction-decimal fluency, approximation speed and index laws needed to solve calculator-free arithmetic in under 30 seconds per question.

Tier-I Examination Syllabus Quantitative Aptitude 25% weightage

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Resolve vinculum & brackets

Resolve 'of'

Division & multiplication, left to right

Addition & subtraction, left to right

1BODMAS & Simplification

BODMAS fixes the exact order to resolve a mixed expression — get the order wrong and every later step is wrong too.

Learning Objectives

State the BODMAS/VBODMAS order and apply it to multi-operator expressions without a calculator.
Correctly resolve 'of' before division and multiplication, as SSC's VBODMAS convention requires.
Resolve nested brackets in the correct innermost-to-outermost order: vinculum, (), {}, [].
Identify and avoid the common trap of doing addition/subtraction before finishing multiplication/division.

Key Terms

BODMASBrackets, Of, Division, Multiplication, Addition, Subtraction — the standard order for evaluating a mixed expression.

VBODMASSSC's variant that places the Vinculum (bar/line grouping) above even ordinary brackets in resolution priority.

VinculumA horizontal bar drawn over a group of terms (e.g. line over a − b + c) that must be resolved before any bracket.

Nested BracketsMultiple bracket types in one expression, always resolved in the order (), then {}, then [], innermost first.

Simplification questions test one thing: whether you resolve operations in the fixed order **VBODMAS** — Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction. Any deviation gives a different, wrong, answer.

The correct resolution order

Vinculum (bar over terms) — resolved first, even before brackets.
Brackets — innermost to outermost: ( ) → { } → [ ].
Of — treated as multiplication but resolved before plain division/multiplication.
Division and Multiplication — left to right, same priority level.
Addition and Subtraction — left to right, same priority level, resolved last.

Exam Tip'Of' is not the same priority as '×' — in 1/2 of 40 ÷ 4, resolve 'of' first: 1/2 of 40 = 20, then 20 ÷ 4 = 5.

Worked example

8 + 12 ÷ 4 × 2 − 3 = 8 + (3 × 2) − 3 = 8 + 6 − 3 = 11

Common MistakeCommon trap: solving left-to-right across all operators (8+12=20, 20÷4=5...) ignores priority and gives a wrong answer. Multiplication/division must be fully resolved before any addition/subtraction.