Why this topic matters · 6 min read
BODMAS questions appear in almost every RRB Group D paper under the Arithmetic or Simplification section. Typically 2-4 questions per paper test your ability to simplify expressions with mixed operations. These are easy marks if you follow the correct order. Most aspirants lose marks here due to left-to-right habit instead of following the correct hierarchy.
What is BODMAS?
BODMAS is the rule that tells you which operation to perform first when an expression has multiple operations. Without this rule, the same expression can give different answers depending on who solves it. BODMAS makes math universal.
Think of it like a queue at a railway ticket counter — everyone has a fixed priority. Brackets always go first, then Orders (powers/roots), then Division and Multiplication (left to right), and finally Addition and Subtraction (left to right).
- B — Brackets: solve innermost bracket first. Order: () then {} then []
- O — Orders: powers (squares, cubes) and roots (square root, cube root)
- D — Division: solve before addition/subtraction
- M — Multiplication: same priority as Division, go left to right
- A — Addition: same priority as Subtraction, go left to right
- S — Subtraction: last in the chain
Key formulas
Bracket priority order
( ) first, then { }, then [ ]
When: When nested brackets appear — solve the innermost round bracket first
D and M same level
Division and Multiplication — solve left to right, whichever comes first
When: When both divide and multiply appear in same expression without brackets
A and S same level
Addition and Subtraction — solve left to right, whichever comes first
When: When both add and subtract appear at the end after higher operations are done
Worked examples
Example 1: Simplify 18 + 12 / 4 x 2 - 3
Step 1 (D): 12 / 4 = 3. Expression becomes 18 + 3 x 2 - 3
Step 2 (M): 3 x 2 = 6. Expression becomes 18 + 6 - 3
Step 3 (A then S, left to right): 18 + 6 = 24, then 24 - 3 = 21. Answer: 21
Example 2: Simplify [3 + {5 x (2 + 1)}] - 4
Step 1 (innermost bracket): (2 + 1) = 3
Step 2 (curly bracket): {5 x 3} = 15
Step 3 (square bracket): [3 + 15] = 18
Step 4: 18 - 4 = 14. Answer: 14
Handling Powers and Roots (the O in BODMAS)
The O step (Orders) is often forgotten or placed wrong. Powers and roots are solved right after brackets and before any division, multiplication, addition, or subtraction. This is a common trap in RRB papers.
For example, in the expression 2 + 3 squared x 4, you must first calculate 3 squared = 9, giving 2 + 9 x 4. Then multiply: 9 x 4 = 36. Then add: 2 + 36 = 38. Many aspirants do 2 + 3 = 5 first, which is wrong.
- Always calculate squares, cubes, and square roots immediately after solving brackets
- Root of a number is also an Order — treat it the same as a power
- Do NOT jump to addition or multiplication before handling powers
- If a power is inside a bracket, solve the bracket first, then apply the power outside
Worked example
Example: Simplify 5 + 2 cubed / 4 - 1
Step 1 (O): 2 cubed = 8. Expression: 5 + 8 / 4 - 1
Step 2 (D): 8 / 4 = 2. Expression: 5 + 2 - 1
Step 3 (A then S): 5 + 2 = 7, then 7 - 1 = 6. Answer: 6
Left-to-Right Rule for D-M and A-S
Division and Multiplication have equal priority — neither is more important than the other. Same for Addition and Subtraction. When two equal-priority operations appear together, simply go left to right — whichever comes first, do it first.
This is the most commonly misunderstood part. Many aspirants think Multiplication always beats Division. That is wrong. 8 / 2 x 4 means do 8 / 2 first (= 4), then 4 x 4 = 16. If you do 2 x 4 first (= 8) then 8 / 8 = 1, you get the wrong answer.
- Division does NOT always come before Multiplication — left to right decides
- Addition does NOT always come before Subtraction — left to right decides
- Scan from left to right for D and M together, pick the leftmost one first
- Same scan rule applies for A and S at the final step
Worked example
Example: 20 / 5 x 2
Left to right: 20 / 5 = 4, then 4 x 2 = 8. Answer: 8
Wrong approach (M first): 5 x 2 = 10, 20 / 10 = 2. This is WRONG.
⚠ Common mistakes to avoid
- Solving left to right without any priority — treating all operations as equal. Always check for brackets and powers first.
- Thinking Multiplication always beats Division. They are equal — go left to right.
- Forgetting the O (Orders) step entirely and jumping to Division after Brackets.
- Solving outer brackets before inner brackets. Always start with the innermost bracket.
- In expressions with only Addition and Subtraction at the end, doing Addition first instead of going left to right. Example: 10 - 3 + 2 should be 7 + 2 = 9, not 10 - 5 = 5.
🧠 Memory aids
- Mnemonic: Big Orange Dogs Must Always Sit — B(rackets) O(rders) D(ivision) M(ultiplication) A(ddition) S(ubtraction)
- Bracket priority visual: Think of nesting dolls — smallest doll (round bracket) opens first, then medium (curly), then big (square).
- For D and M confusion: think of a race — both start together, whoever is on the LEFT wins.
- Analogy: BODMAS is like a VIP queue at a station — Brackets are VVIPs, Orders are VIPs, D-M are regular reserved, A-S are general ticket holders.
🎯 RRB GROUP D exam tips
- RRB Group D typically gives 2-3 BODMAS simplification questions per paper. They are straightforward if you follow the rule — these are score-securing questions, do not skip.
- Recent papers include expressions with nested brackets and at least one power — practice problems with all three bracket types together.
- Time target: Each BODMAS question should take under 60 seconds. If it is taking longer, you are likely redoing steps — practice the sequence until it is automatic.
- Watch for trick questions where Division and Multiplication appear together without brackets — this tests the left-to-right rule specifically.
- Negative numbers inside brackets appear occasionally. Remember: minus outside a bracket flips signs of everything inside when you remove the bracket.
Q1 · medium · AI-verified
Solve: 8 + 4 × 3 - 16 ÷ 4
- 16
- 18
- 20
- 12
Q2 · medium · AI-verified
Calculate: 7 × 4 - 16 + 12 ÷ 3
- 16
- 20
- 12
- 14
Q3 · medium · AI-verified
Evaluate: 50 - 2 × (15 - 9) + 6
- 50
- 44
- 42
- 38
Q4 · medium · AI-verified
Solve: 4 × (9 - 3) + 20 ÷ 5 - 6
- 22
- 24
- 26
- 28
Q5 · medium · AI-verified
Evaluate: 18 + 6 × 3 - 12 ÷ 4
- 39
- 27
- 21
- 33