BODMAS is the rulebook that tells you which operation to perform first when an expression has multiple operations mixed together. Without it, the same expression can give five different answers depending on how you read it — and the exam will use that ambiguity against you.
The acronym expands as:
3² + 2 or ½ of 20)Here is the analogy that sticks: think of a construction site. Before you can paint the walls (Addition, Subtraction — finishing touches), you need to lay the bricks (Multiplication, Division — structural work), and before that you must build within each room separately (Brackets — isolated zones). "Of" is the foundation work before even the structure.
The reason RRB Group D loves this topic is that it costs you nothing if you know the rule, but it costs you 1-2 marks if you apply operations left-to-right blindly the way a calculator without parentheses would. Most wrong answers in the option list are designed for the "left-to-right" trap — and if you see your calculated value sitting right there in the options, do not relax. Always verify the BODMAS sequence.
One more thing worth naming: Division and Multiplication have equal priority. So do Addition and Subtraction. When two operations share a priority level, you resolve them left to right. This is where 80% of mistakes happen in Group D questions. 24 ÷ 8 × 2 is not 24 ÷ 16. It is 3 × 2 = 6, because division comes first only because it is on the left — not because it outranks multiplication.
Keep that rule in your head like a reflex and you will not drop marks here.
Write this once on your rough sheet before any simplification question:
() then {} then [] (curly inside square, if nested)Look at this expression: 15 + 24 ÷ 8 × 2 - 5
Wrong approach (treating D always before M regardless of position):
24 ÷ 8 = 3, then 3 × 2 = 6 — this is actually correct here, but students misapply it as "always divide first, everywhere."The rule is not "D before M always." The rule is: scan left to right, and whenever you hit a D or M, resolve it immediately before moving right. In this case, ÷ 8 appears before × 2, so yes — divide first, then multiply. But if the expression were 24 × 2 ÷ 8, you would multiply first: 48 ÷ 8 = 6, not 24 × 0.25 = 6 (same answer here, but the process matters when numbers are not symmetric).
Result: 15 + 6 - 5 = 16.
If you see [2 × {3 + (4 - 1)}], work from the innermost bracket outward:
(4 - 1) = 3{3 + 3} = 6[2 × 6] = 12In Group D questions, you rarely see triple-nested brackets. Most questions have one pair of simple parentheses. Solve inside, then treat the result as a single number and proceed with D-M-A-S.
"Of" in simplification typically means multiplication applied to fractions or percentages. ½ of 40 = ½ × 40 = 20. It comes after brackets and exponents but before division. In Group D, it appears less frequently, but do not treat it as addition when you see it.
For any simplification question, apply this exact sequence:
÷ or ×, resolve that operation immediately with the number immediately before and after it, replace those three elements with the result, and continue scanning.+ and -. Scan left to right and resolve.This template is mechanical. Apply it the same way every time — no intuition, no re-ordering by feel.
The exam writers know that left-to-right reading is the natural instinct. Consider 8 + 4 × 3 - 16 ÷ 4:
8 + 4 = 12, 12 × 3 = 36, 36 - 16 = 20, 20 ÷ 4 = 5. Answer: 5.20 (stop one step early) or 12 (skip the division).4 × 3 = 12, 16 ÷ 4 = 4, then 8 + 12 - 4 = 16.The wrong options in these questions are reverse-engineered from specific mistakes. If you see an option that matches your answer but feel uncertain about your process, redo it — don't trust the answer, trust the method.
After resolving brackets, underline every × and ÷ in the expression. Then resolve them one by one from left to right, crossing each out as you go. This physical act prevents the "divide all, then multiply all" error. Standard mistake: 2 wrong operations. With underlining: 0. Saves re-checking time (~15s per question).
When you see a × (bracket result), do not expand the bracket and distribute. Solve the bracket first, get a single number, then multiply. For example, 5 × (8 + 4): solve (8 + 4) = 12 first, then 5 × 12 = 60. Distributing would mean 5 × 8 + 5 × 4 = 40 + 20 = 60 — same answer but 2 extra steps. Standard method: 4 steps. Substitution: 2 steps.
Before solving, check if the final answer must be odd or even. In 4 × (9 - 3) + 20 ÷ 5 - 6: even + even - even = even. Options with odd values (23, 25, 27) are immediately eliminated. This narrows 4 choices to 2 in under 3 seconds, before you even compute.
Before full computation, do a rough magnitude check. In 6 + 18 ÷ 3 × 2 - 4, the 18 ÷ 3 × 2 portion gives about 12, plus 6 minus 4 is roughly 14. If your final answer is wildly different (say, 30 or 4), you made a process error — go back. This sanity check takes 5 seconds and catches gross errors before you mark the answer.
Once all brackets and DM are resolved, you have a simple a + b - c string. Add all positive terms together, add all negative terms together, then subtract. For 8 + 12 - 4: positives sum = 20, negatives sum = 4, result = 16. Fewer running totals means fewer arithmetic slips. Saves 1-2 mental steps versus sequential left-to-right addition/subtraction.
In the exam hall, this is your decision tree. Apply it without pausing:
Step 1 — Brackets present? Yes → Solve the innermost bracket first. Replace with result. Repeat until no brackets remain. No → Go to Step 2.
Step 2 — Any "Of" or exponents? Rare in Group D. If present, resolve now.
Step 3 — Any × or ÷ in the expression?
Yes → Scan left to right. Resolve the first × or ÷ you see. Replace those three tokens with the result. Rescan from the left again.
No → Go to Step 4.
Step 4 — Only + and - remain.
Add all positive terms, subtract all negative terms. Write the answer.
Sanity check: Does the answer match an option? Does the rough magnitude make sense? If yes, mark and move on. If no, re-examine Step 3 — the left-to-right DM rule is the most common failure point.
Total time budget per question: 30-45 seconds.
Why this question: This is a pure DM-priority test with no brackets. It targets students who do 42 ÷ 7 + 3 × 4 - 2 × 3 left to right.
Solving path: Identify the DM operations: 42 ÷ 7, 3 × 4, 2 × 3. Resolve all three: 6, 12, 6. Now the expression is 6 + 12 - 6 = 12. The left-to-right trap would give (42 ÷ 7 + 3) × 4 = 36 style errors — none of which appear in the options, but 14 and 16 are planted for partial-computation errors.
Why this question: Tests D-before-M in a left-to-right scan. The ÷ 3 × 2 sequence is a classic trap.
Solving path: No brackets. DM scan: 18 ÷ 3 = 6, then 6 × 2 = 12 (left to right, not 3 × 2 = 6 then 18 ÷ 6 = 3). Expression becomes 6 + 12 - 4 = 14. Option 16 is the trap for students who compute 18 ÷ 3 = 6, then skip left-to-right and do 6 + 6 × 2.
Why this question: Multiple DM operations in one expression — requires resolving all before touching A/S.
Solving path: DM operations: 4 × 3 = 12, 16 ÷ 4 = 4. Replace: 8 + 12 - 4. Positives: 8 + 12 = 20. Negatives: 4. Result: 16. Option 20 is the trap — it is what you get if you forget to subtract the division result.
Why this question: Introduces a bracket, forcing students to handle B before DM. The question tests whether students respect bracket priority over the nearby ×.
Solving path: Bracket first: (8 + 4) = 12. Expression becomes 5 × 12 ÷ 6 - 2. Now DM left to right: 5 × 12 = 60, 60 ÷ 6 = 10. Then 10 - 2 = 8. Trap: doing 5 × 8 = 40 before solving the bracket gives 40 + 4 ÷ 6 - 2 — a mess that leads to option 10 or 12.
Why this question: Two-step bracket plus multiple DM operations. Tests complete BODMAS sequencing from start to finish.
Solving path: Bracket: (9 - 3) = 6. Expression: 4 × 6 + 20 ÷ 5 - 6. DM: 4 × 6 = 24, 20 ÷ 5 = 4. A/S: 24 + 4 - 6 = 22. The number 28 (option D) appears if you add 6 instead of subtracting — sign error in the final step.
Dividing and multiplying in strict D-then-M order regardless of position. The rule is left-to-right within the DM tier. 24 × 2 ÷ 8 is 48 ÷ 8 = 6, not 24 × 0.25 = 6 (happens to be the same here, but the process is wrong and will fail you on asymmetric numbers).
Solving addition before division when reading left to right. In 6 + 18 ÷ 3 × 2, the 6 + at the start is not the first thing to do. Skip it, resolve the DM chain 18 ÷ 3 × 2 = 12, then come back and add 6.
Not replacing the bracket with its value before proceeding. Students solve (8 + 4) = 12 mentally but then write 5 × 8 + 4 on paper because they forgot to substitute. Always physically write the post-bracket expression.
Sign errors in the final A/S step. 24 + 4 - 6 is 22, not 28. The -6 is the result of a subtraction in the original expression, and students flip its sign after all the DM processing. Use the "sum positives, sum negatives, subtract" pattern to avoid this.
Treating "of" as addition. ½ of 20 is ½ × 20 = 10, not ½ + 20 = 20.5. If "of" appears in a Group D question, multiply — and do it before D/M in the priority order.
Stopping one operation too early and matching a trap option. The exam deliberately places the "one step short" answer in the options. Finishing 4 × 6 = 24 and marking 24 when the expression still has + 4 - 6 remaining is how option D gets picked by rushed candidates. Always check that no operation remains before marking.