BODMAS is not a formula — it is a traffic signal for arithmetic. When multiple operations crowd a single expression, BODMAS tells you which one has the right of way.
The acronym expands to:
Think of it like assembling furniture. You always attach the inner frame before bolting the outer panels. If you bolt the outer shell first, the whole thing collapses. An expression like 12 + 48 ÷ 2 − 20 + 6 × 2 has the same problem — touch the wrong operation first and your answer is dead on arrival.
In Indian classrooms you will also see PEMDAS (American) and VBODMAS (where V stands for Vinculum, the bar bracket). For UP Police Constable, BODMAS is the standard. If the paper prints "VBODMAS", the only addition is that you resolve the vinculum (overline bar) before all other brackets.
A useful analogy: Imagine a foreman giving tasks to workers. Division and Multiplication workers are senior-level — they get to finish their tasks before Addition and Subtraction workers even start. Brackets are the site manager who overrides everyone: whatever is inside brackets must be resolved before the foreman (D, M, A, S) is consulted.
One critical nuance that costs marks: Division and Multiplication have equal priority — you work them left to right, not D always before M. Same applies to Addition and Subtraction — equal priority, left to right. This left-to-right rule for equal-priority operations is where most wrong answers come from.
| Priority | Operations | Rule |
|---|---|---|
| 1 (highest) | Brackets: ( ) then { } then [ ] | Innermost first |
| 2 | Of / Order (powers, roots) | Right to left for stacked powers |
| 3 | Division ÷ and Multiplication × | Left to right |
| 4 (lowest) | Addition + and Subtraction − | Left to right |
When brackets are nested, the rule is simple: peel from inside out.
Standard nesting in Indian textbooks: ( ) innermost → { } middle → [ ] outermost.
Example: 40 − {17 − 12 ÷ (5 + 9 × 2 − 17)}
Step 1 — Resolve ( ):
Inside the round bracket: 5 + 9 × 2 − 17
Multiplication first: 9 × 2 = 18
Now: 5 + 18 − 17 = 6
Step 2 — Replace and resolve division:
{17 − 12 ÷ 6}
Division: 12 ÷ 6 = 2
{17 − 2} = 15
Step 3 — Final subtraction:
40 − 15 = 25
This is exactly how the PYQ from 2026 expects you to work. If you had subtracted before dividing inside the curly bracket, you would have gotten a wrong answer.
Look at 24 ÷ 4 × 3.
Wrong approach (D always before M): 24 ÷ 4 = 6, then 6 × 3 = 18. This happens to be correct here.
But for 24 × 4 ÷ 3:
Wrong approach (D before M regardless of position): 4 ÷ 3 first, giving a messy fraction.
Correct approach (left to right): 24 × 4 = 96, then 96 ÷ 3 = 32.
The rule is not "D then M" — it is "D and M together, left to right."
"Of" appears in fraction problems: "find 1/4 of 360" means 1/4 × 360 = 90. It ranks with powers, above D and M. In simplification questions with fractions, handle "of" before you divide or multiply standalone terms.
When the question gives you LHS = RHS and asks for a missing value K, do not panic — it is just simplification in two steps:
K = simplified_known_side − simplified_rest.Example: 13450 + 12846 − 1230 − K = 23670 + 987
LHS without K: 13450 + 12846 − 1230 = 25066
RHS: 23670 + 987 = 24657
25066 − K = 24657 → K = 25066 − 24657 = 409
When you see a² − b² hiding in an expression, do not multiply it out. Use the identity:
a² − b² = (a + b)(a − b)
This converts a two-multiplication problem into one multiplication with smaller, friendlier numbers. The PYQ 545² − 125² becomes (545 + 125)(545 − 125) = 670 × 420 = 281,400 — far faster than squaring 545 directly.
For expressions like 4/12 × 3/2 ÷ 4/8 − 12 + 4, the fraction chain 4/12 × 3/2 ÷ 4/8 must be fully resolved before touching the −12 + 4.
Division of a fraction = multiply by its reciprocal:
÷ 4/8 = × 8/4 = × 2
Chain: (4/12) × (3/2) × 2 = (1/3) × (3/2) × 2 = 1
Then: 1 − 12 + 4 = −7
Left to right for the final addition/subtraction: (1 − 12) + 4 = −11 + 4 = −7.
Mnemonic: Brackets → Of → Division → Multiplication → Addition → Subtraction. Phrase: "Big Mouth Eats Dinner After School." The key memory peg is "Eats Dinner" — D and M are a pair at the same table, served left to right. Applying this, 8 ÷ 4 × 2 = (8÷4)×2 = 4 in 5 seconds vs. the wrong 8÷8=1 if you freeze and go right to left. Step count: correct path = 2 steps vs. wrong path = same 2 steps but wrong answer. Saves zero time but saves the mark.
Whenever you see A² − B² in a simplification question, immediately write (A+B)(A−B). For 545² − 125²: standard method requires computing 545² = 297025 and 125² = 15625, then subtracting — roughly 60 seconds. Shortcut: (670)(420) = 670 × 400 + 670 × 20 = 268000 + 13400 = 281400 — about 15 seconds. Standard method: ~60s vs. shortcut: ~15s. Look for this pattern whenever two perfect or near-perfect squares are subtracted.
For "find K" questions: lump all known numbers on each side into one number first, then find K. Do not rearrange term by term — that invites sign errors. In 13450 + 12846 − 1230 − K = 23670 + 987: compute LHS-without-K = 25066, RHS = 24657, K = 409. This two-lump approach takes 3 additions vs. moving terms one by one (5–6 steps). Step count: 3 vs. 6. The fewer the rearrangement steps, the fewer the sign-flip errors.
In a fraction chain a/b × c/d ÷ e/f, the moment you see ÷ e/f, write × f/e before doing anything else. This converts the entire chain into a single multiplication, which you can then cancel across numerators and denominators before multiplying. For 4/12 × 3/2 ÷ 4/8: flip to get 4/12 × 3/2 × 8/4. Cancel: 4/12 = 1/3, 8/4 = 2. Chain = 1/3 × 3/2 × 2 = 1. Without early flipping, you might compute partial decimals and lose precision. Time saved: ~20s vs. decimal intermediate steps.
When brackets are 2–3 levels deep, place a small dot under the innermost bracket before starting. This stops you from accidentally opening the outer bracket first. For 40 − {17 − 12 ÷ (5 + 9 × 2 − 17)}, dot under (...). Resolve dotted bracket → erase dot → dot the next level. This visual queue eliminates the most common error in nested-bracket questions. Exam data shows nested-bracket questions are answered wrongly 40–60% of the time in mock tests — the dot method reduces re-checking steps from 3 to 1.
In the exam hall, use this decision sequence every time:
See brackets? Count the nesting levels. Start at the innermost ( ), work outward to { }, then [ ].
Inside each bracket, apply BODMAS again — O first, then D/M left to right, then A/S left to right.
No brackets? Scan for "Of" or powers. Resolve those.
Then scan for × and ÷ — mark them, resolve left to right in one sweep.
Finally, + and − — left to right. Watch signs carefully when a subtraction comes before an addition: −20 + 12 = −8, not +8.
See A² − B²? Stop. Factor it. Always faster.
See K or unknown? Simplify both sides fully, then isolate K in one step.
Fraction chain? Flip divisors immediately, cancel before multiplying.
If you are stuck, eliminate obviously wrong options. In most UP Police Quant questions, two options are far too large or too small — cross them out and work the remaining two carefully.
Why this question: The most tested BODMAS format — nested brackets with all four operations crammed inside. This exact structure appeared in 2026.
Solving path:
Start at the innermost ( ): apply BODMAS inside — multiplication first (9 × 2 = 18), then addition and subtraction left to right (5 + 18 − 17 = 6). Move to { }: division first (12 ÷ 6 = 2), then subtraction (17 − 2 = 15). Final subtraction: 40 − 15 = 25. Never touch the outer expression until all inner brackets are resolved to single numbers.
Why this question: The "find K" equation type is a staple of UP Police Quant — it tests whether you can simplify both sides independently before isolating the unknown.
Solving path:
LHS without K: 13450 + 12846 = 26296, then 26296 − 1230 = 25066. RHS: 23670 + 987 = 24657. Equation: 25066 − K = 24657. Therefore K = 25066 − 24657 = 409. No algebra needed beyond this one subtraction.
Why this question: Difference of squares appears in simplification questions disguised as large multiplications. Recognising the pattern is the entire skill.
Solving path:
Recognise 545² − 125² as (a+b)(a−b) where a = 545, b = 125. Compute a + b = 670, a − b = 420. Multiply: 670 × 420 = 670 × 400 + 670 × 20 = 268000 + 13400 = 281400. Mark answer C (281400) without touching a single square.
Why this question: A clean, single-line BODMAS question — exactly the type that appears as a warm-up item. Getting this wrong (usually by adding before dividing) drops easy marks.
Solving path:
D/M sweep first: 360 ÷ 12 = 30, 4 × 3 = 12. Expression becomes 30 + 12 = 42. Two arithmetic steps. The trap is doing 12 + 4 = 16 first (left to right ignoring priority), then 360 ÷ 16 = 22.5 — wrong. Always do division and multiplication before addition.
Why this question: Fraction simplification with a negative result tests both BODMAS and sign handling — two skills in one question.
Solving path:
Resolve the fraction chain first (it is a multiplication/division group): 4/12 × 3/2 ÷ 4/8. Flip the divisor: ÷ 4/8 = × 8/4. Chain becomes (4/12) × (3/2) × (8/4). Cancel before multiplying: 4/12 = 1/3, 8/4 = 2. So (1/3) × (3/2) × 2 = (3/6) × 2 = (1/2) × 2 = 1. Now the expression is 1 − 12 + 4. Left to right: (1 − 12) = −11, then −11 + 4 = −7. Answer: −7.
Treating D/M as strictly D before M regardless of position. The rule is left to right. 6 × 10 ÷ 2 should give 60 ÷ 2 = 30, not 6 × 5 = 30 (accidentally correct here) — but 6 ÷ 2 × 10 must give 3 × 10 = 30, not 6 ÷ 20 = 0.3.
Jumping into the outer bracket before fully resolving the inner one. If (5 + 9 × 2 − 17) is not first reduced to 6, everything downstream is corrupted. The dot-marking technique described in Memory Tricks prevents this.
Ignoring the sign in front of a bracket. −{17 − 2} means you subtract the entire result 15 from 40, not subtract 17 then add 2. The sign outside applies to the whole bracket value.
Left-to-right A/S error with negative numbers. 1 − 12 + 4 is not 1 − 16 = −15. You must go left to right: (1 − 12) + 4 = −11 + 4 = −7. Grouping the addition terms and subtracting their sum is a classic trap.
Not recognising a² − b² and computing squares manually. This wastes 45+ seconds on a question that has a 10-second path. Train yourself to spot the subtraction of two squared terms before you reach for pencil-column multiplication.
Skipping simplification of fractions before multiplying in a chain. Computing 4/12 × 3/2 as 12/24 = 1/2 and then continuing is correct but slow. Cancelling across the chain (4 with 4, 3 with 3) before multiplying is faster and reduces error risk.