📐 BODMAS — The Foundation of Simplification
Master the strict order of operations that governs every simplification question in banking exams
BODMAS — The Foundation of Simplification
Every simplification question in banking exams (IBPS PO, SBI PO, RRB, FCI, NABARD) follows one universal rule: BODMAS. Violating BODMAS is the #1 cause of wrong answers. Master this, and you eliminate careless errors forever.
What is BODMAS?
BODMAS defines the strict order in which operations must be performed:
| Order | Letter | Operation | Symbol |
|---|---|---|---|
| 1st | B | Brackets — solve innermost first | ( ), [ ], { } |
| 2nd | O | Of (powers, roots, "of") | x², √x, x³, "of" |
| 3rd | D | Division | ÷ |
| 4th | M | Multiplication | × |
| 5th | A | Addition | + |
| 6th | S | Subtraction | − |
Critical detail: Division and Multiplication have equal priority — solve left to right. Same for Addition and Subtraction — left to right.
Bracket Priority
When multiple types of brackets appear, always solve innermost first:
{ [ ( ) ] } → solve ( ) first, then [ ], then { }
Example:
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BODMAS — The Foundation of Simplification
Every simplification question in banking exams (IBPS PO, SBI PO, RRB, FCI, NABARD) follows one universal rule: BODMAS. Violating BODMAS is the #1 cause of wrong answers. Master this, and you eliminate careless errors forever.
What is BODMAS?
BODMAS defines the strict order in which operations must be performed:
| Order | Letter | Operation | Symbol |
|---|---|---|---|
| 1st | B | Brackets — solve innermost first | ( ), [ ], { } |
| 2nd | O | Of (powers, roots, "of") | x², √x, x³, "of" |
| 3rd | D | Division | ÷ |
| 4th | M | Multiplication | × |
| 5th | A | Addition | + |
| 6th | S | Subtraction | − |
Critical detail: Division and Multiplication have equal priority — solve left to right. Same for Addition and Subtraction — left to right.
Bracket Priority
When multiple types of brackets appear, always solve innermost first:
{ [ ( ) ] } → solve ( ) first, then [ ], then { }
Example:
{ 4 × [3 + (12 ÷ 4 − 1)] } + 2³
Step 1 — Innermost ( ): 12 ÷ 4 = 3; 3 − 1 = 2
Step 2 — Square [ ]: 3 + 2 = 5
Step 3 — Curly { }: 4 × 5 = 20
Step 4 — Powers: 2³ = 8
Step 5 — Addition: 20 + 8 = 28
The "Of" Trap
The word "of" means multiplication, but it comes BEFORE division and multiplication in BODMAS.
1/3 of 270 + 50
= (1/3) × 270 + 50 ["of" = multiply, done before + ]
= 90 + 50
= 140
Common mistake: Students treat "of" as regular multiplication and lose order priority. In BODMAS, "Of" is at position 2 — it comes right after brackets.
Worked Examples
Example 1 — Basic BODMAS:
18 + 4 × (12 ÷ 3) − 2²
= 18 + 4 × 4 − 4 [Brackets first, then Of/powers]
= 18 + 16 − 4 [Multiplication]
= 30 [Left to right: +, then −]
Example 2 — The Trap Question:
70 + 20 × 3 − 40
WRONG: (70 + 20) × 3 − 40 = 230 ← adding before multiplying!
RIGHT: 70 + (20 × 3) − 40 = 70 + 60 − 40 = 90
This is a classic exam trap. Students instinctively add 70+20 first because they read left-to-right. But multiplication comes before addition in BODMAS.
Example 3 — Division before Multiplication:
48 ÷ 8 × 3
WRONG: 48 ÷ (8 × 3) = 48 ÷ 24 = 2
RIGHT: (48 ÷ 8) × 3 = 6 × 3 = 18
When D and M have equal priority, go LEFT to RIGHT.
Example 4 — Negative number handling:
150 − ? − 40 = −60
150 − 40 = 110
110 − ? = −60
? = 110 + 60 = 170
When the RHS is negative, students often get the sign wrong. Think: "110 minus WHAT gives −60?" The answer must be MORE than 110.
Speed Strategy for Exams
- Scan for brackets first — solve all brackets mentally before touching anything else
- Look for powers/roots — compute √ and ² immediately after brackets
- Scan left-to-right for × and ÷ — do these next
- Finally, + and − left-to-right — this is always the last step
- Never write intermediate steps — in exam conditions, do steps 1-2 mentally, then scan for 3, then 4
Target time: Pure BODMAS questions should take 8–12 seconds maximum.
Master Guide: Quant Question Type Recognition
In the exam, the first 3 seconds should be: "What type is this?" → pick the right method → solve.
| If the question looks like... | Topic | Go-to Method | Target Time |
|---|---|---|---|
| 23.7 × 14.9 + 187.3 ÷ 9.1 = ? | Simplification | BODMAS + approximation | 8-12 sec |
| √? + 17² = 345 | Missing number (simplification) | Isolate ?, reverse operations | 10-15 sec |
| 2, 5, 11, 23, 47, ? | Number series | Check differences → double-differences → ×2±1 patterns | 15-40 sec |
| A is 20% more than B... | Percentage | Convert to fraction: 20% more = ×6/5 | 15-20 sec |
| CP = 800, SP = 1000, find profit% | Profit & Loss | Profit% = (SP−CP)/CP × 100 = fraction method | 10-15 sec |
| A:B = 3:4, B:C = 5:7, find A:C | Ratio | Make B common (LCM), read A:C | 10-15 sec |
| x² − 11x + 30 = 0, y² − 9y + 20 = 0 | Quadratic comparison | 4-step: multiply-split-flip-divide → compare roots | 15-25 sec |
| 5 years ago, A was twice B... | Ages | Timeline method or ratio method | 20-30 sec |
| 20L milk, 5L removed + water, repeat... | Mixture/Replacement | Formula: T×(1−r/T)ⁿ or perfect-power pattern | 15-25 sec |
| Bar/line/pie chart + 5 questions | DI | Read Q1 first → extract only needed data → fraction shortcuts | 60-90 sec per Q |
Time allocation in exam (35 questions, 20 minutes):
- Simplification (10 Qs): 2 min total (12 sec each)
- DI (2 sets × 5 Qs): 8 min total (48 sec each)
- Arithmetic (10-15 Qs): 8-10 min total (40-60 sec each)
- Series (5 Qs): 2-3 min total (30 sec each)
Do simplification FIRST (fastest, guaranteed marks). Then DI (highest weightage). Then arithmetic. Series last (can be time-sinks).