BODMAS Order of Operations
BODMAS fixes the sequence for any simplification: B - Brackets (solve innermost first: (), {}, []), O - Of / Order (powers, roots, 'of' means multiply), D - Division, M - Multiplication, A - Addition, S - Subtraction. Division and multiplication rank equally — work left to right; same for addition and subtraction. The word 'of' is treated as multiplication but is performed before normal division (e.g., 1/2 of 8 / 4 = 4/4 = 1). Memory aid: 'Brackets Order DM AS.' A single misstep in operation order is the most common reason candidates lose marks in the simplification section — always rewrite the expression bracket-by-bracket.
VBODMAS & Fraction Simplification Tips
Some boards use VBODMAS where V = Vinculum (bar/line), solved first — e.g., in 12 - (8 - bar over 3-1), simplify the bar 3-1=2 first. For mixed fractions, convert to improper fractions before applying BODMAS. Cancel common factors early to avoid large numbers. For chained 'of' and division: 'of' binds tighter, so 24 / 4 of 3 = 24 / 12 = 2 (do the 'of' multiplication first). When you see surds or squares, evaluate Order before Division. Shortcut: replace repeated decimals like 0.333... with fractions (1/3) to keep arithmetic exact rather than approximate.
Worked Example — Nested Brackets
Simplify: 36 - [18 - {14 - (15 - 6 / 3 x 2)}]. Step 1 innermost: 6/3 = 2, then 2 x 2 = 4, so (15 - 4) = 11. Step 2 next bracket: {14 - 11} = 3. Step 3: [18 - 3] = 15. Step 4: 36 - 15 = 21. Answer = 21. Note how division and multiplication inside the parentheses were done left to right BEFORE the subtraction. Working strictly from the innermost bracket outward prevents sign errors — a frequent trap in RPF SI multi-bracket simplification problems.
Simplification & BODMAS — Flashcards
Cover the answer, recall, then check. 12 cards on BODMAS and speed simplification for RPF SI.
Q1. Expand BODMAS.
A1. Brackets → Orders (powers/roots) → Division → Multiplication → Addition → Subtraction.
Q2. Order of solving brackets?
A2. Innermost first: ( ) then { } then [ ].
Q3. Evaluate 12 + 6 ÷ 2 × 3.
A3. Division and multiplication left-to-right: 6÷2=3, 3×3=9, then 12+9 = 21.
Q4. "of" in an expression — how is it treated?
A4. As multiplication, but done at the "O" stage (before division). E.g. 1/2 of 8 ÷ 2 = 4 ÷ 2 = 2.
Q5. 25% of 480 quickly?
A5. 480 ÷ 4 = 120.
Q6. 87 × 99 using distribution?
A6. 87×(100−1) = 8700 − 87 = 8613.
Q7. (a+b)² identity?
A7. a² + 2ab + b². Useful: 103² = 100² + 2·100·3 + 9 = 10609.
Q8. a² − b² identity for 53²−47²?
A8. (a+b)(a−b) = 100×6 = 600.
Q9. 15% of 15% of 2000?
A9. 0.15×0.15×2000 = 0.0225×2000 = 45.
Q10. Value of √(0.0064)?
A10. 0.08 (since 0.08² = 0.0064).
Q11. 3⁴ ÷ 3² × 3?
A11. 3^(4−2+1) = 3³ = 27.
Q12. 999 × 999 shortcut?
A12. (1000−1)² = 1000000 − 2000 + 1 = 998001.
Simplification & BODMAS — Summary
Simplification is the highest-frequency, lowest-risk scoring area in RPF SI Quant — expect 3–5 direct questions plus its use inside every other topic. Because SI aspirants face a higher cutoff, clearing these in under 30 seconds each is what separates selection from the waitlist. The whole game is a fixed order of operations plus a handful of algebraic identities used as speed tricks.
Why it matters
Every messy expression has exactly one correct order. Get BODMAS right and the arithmetic is trivial; get it wrong and a confident wrong answer awaits in the options.
The BODMAS order
| Step | Meaning | Note |
|---|---|---|
| B | Brackets | Innermost first: ( ) → { } → [ ] |
| O | Orders | Powers and roots |
| D | Division | Left to right with M |
| M | Multiplication | Left to right with D |
| A | Addition | |
| S | Subtraction |
"of" acts as multiplication but is resolved at the Orders stage (before ÷).
Speed identities (memorise cold)
- (a+b)² = a² + 2ab + b²; (a−b)² = a² − 2ab + b²
- a² − b² = (a+b)(a−b)
- (a+b)³ = a³ + b³ + 3ab(a+b)
- a×99 = a×100 − a; a×101 = a×100 + a
- x% of y = y% of x (24% of 50 = 50% of 24 = 12)
Worked flow
12 + 6 ÷ 2 × 3 → do ÷ and × left-to-right → 6÷2=3, 3×3=9 → 12+9 = 21.
Exam Tricks & Tips
- 🎯 Never add before finishing all ÷ and × — that single slip is the most common trap distractor.
- 🎯 Use x% of y = y% of x to flip an ugly percentage into an easy one.
- 🎯 Split near-round multipliers: ×99 = ×100 − once; ×102 = ×100 + twice.
- 🎯 Recognise a²−b² patterns (53²−47²) and factor instead of squaring.
- 🎯 For nested fractions, simplify from the innermost bracket outward — don't cross-multiply early.
- ❌ Common mistake: doing division and multiplication in fixed D-then-M order instead of strictly left-to-right — 8÷4×2 is 4, not 1.
Expected exam pattern
Straight "find the value of (?)" expressions mixing brackets, decimals, powers, roots and percentages; plus 1–2 "approximate value" items where options are spread wide enough to round aggressively.
Quick recap
Follow BODMAS exactly, resolve division/multiplication left-to-right, and lean on (a±b)², a²−b² and the x%-of-y flip to turn heavy arithmetic into mental math.