Simplification is the process of reducing a mathematical expression to its most basic numerical value. For IBPS Clerk, this means you're handed a jumbled mix of addition, subtraction, multiplication, division, brackets, powers, and roots — and your job is to evaluate it correctly and quickly.
The foundation is BODMAS (also written as BODMAS/PEMDAS in global textbooks, but the Indian classroom version is BODMAS):
() before {} before [])², ³, √)Here's the critical nuance most students miss: Division and Multiplication have equal priority — you resolve them left to right, not Division always before Multiplication. Same logic applies to Addition and Subtraction. This is where wrong answers get generated in the exam hall.
Think of it like traffic lanes. BODMAS tells you which lane has right of way. Brackets are ambulances — they always go first. Of/Orders are police cars — second in line. Division and Multiplication share the same lane and whoever appears first (left to right) goes first. Addition and Subtraction share the last lane the same way.
Approximation is the cousin of simplification. Instead of computing exact values, you round numbers to the nearest convenient figure and then operate. The trick is knowing how much rounding is acceptable — for IBPS Clerk, rounding to the nearest integer or nearest 5 is usually safe enough to eliminate 3 of the 4 options, leaving one obvious answer.
These two skills together — exact simplification via BODMAS and smart approximation via rounding — cover a significant chunk of the Numerical Ability section. They also show up inside Data Interpretation (DI) questions disguised as multi-step calculations. Getting fast here creates a compounding time advantage across the paper.
Work through this order without exception:
Step 1 — Brackets. Resolve the innermost bracket first. Within a bracket, apply BODMAS recursively. Only remove the bracket once the interior is a single number.
Step 2 — Orders (Powers and Roots). Evaluate 3² = 9, 2³ = 8, √25 = 5 before doing anything else outside brackets.
Step 3 — Division and Multiplication (left to right). Scan the expression left to right. Whichever of ÷ or × you encounter first, execute it. Do not jump ahead to multiply just because multiplication "feels more important."
Step 4 — Addition and Subtraction (left to right). Same rule. Scan left to right, execute in order.
When adding or subtracting fractions, the LCM of denominators is your common denominator. Don't reach for cross-multiplication for addition — it inflates numbers unnecessarily.
For a/b + c/d, find LCM(b, d), convert each fraction, then add numerators.
For multiplication: (a/b) × (c/d) = ac/bd. Cross-cancel common factors before multiplying — this keeps numbers small.
For division: (a/b) ÷ (c/d) = (a/b) × (d/c). Flip the second fraction, then multiply.
The most common error in decimal questions is misplacing the decimal point. Here is a reliable two-step approach:
For example: 0.25 × 4. Treat as 25 × 4 = 100. Decimal places in 0.25 = 2, in 4 = 0. Total = 2. So the answer is 1.00 = 1.0.
Memorising key percentage-to-fraction equivalents removes an entire calculation step:
| Percentage | Fraction | |------------|----------| | 10% | 1/10 | | 20% | 1/5 | | 25% | 1/4 | | 33.33% | 1/3 | | 50% | 1/2 | | 75% | 3/4 |
So "30% of 120" becomes (3/10) × 120 = 36 — no need to write out 30/100 and then cancel.
You do not need deep surds theory for IBPS Clerk. You need these four identities cold:
aᵐ × aⁿ = aᵐ⁺ⁿaᵐ ÷ aⁿ = aᵐ⁻ⁿ(aᵐ)ⁿ = aᵐⁿa⁰ = 1 (for any non-zero a)For surds: √(a × b) = √a × √b and √(a/b) = √a / √b. Use these to simplify expressions like √(48) = √(16 × 3) = 4√3.
When the question says "approximately" or gives non-round numbers like 398, 1203, 0.487:
398 ≈ 400, 1203 ≈ 1200, 0.487 ≈ 0.5.Never approximate when the question asks for an exact value. The word "approximately" or "~" in the question stem is your trigger.
When you have a ÷ b × c, students instinctively multiply b × c first — wrong. The pattern fix: after identifying all × and ÷ operators in a row, underline them left to right and number them 1, 2, 3... Execute in that numbered order. Example: 48 ÷ 8 × 3 — underline ÷ (first), then × (second). So 48 ÷ 8 = 6, then 6 × 3 = 18. Jumping to 8 × 3 = 24 first gives 48 ÷ 24 = 2 — dead wrong. Standard ad-hoc approach: 3 steps, risk of error. Left-right scan: 2 mechanical steps, error eliminated.
Replace any percentage with its fraction equivalent before calculating. "30% of 120" — substitute 30% = 3/10. Now (3/10) × 120 = 3 × 12 = 36. No long division, no 30/100 cancellation chain. Compare: standard method writes (30 × 120)/100 = 3600/100 = 36 — 4 written steps. Fraction substitution: 2 mental steps. Time saved on a 5-question simplification block: ~40 seconds cumulative.
For decimal multiplication, strip decimals, multiply integers, reattach. 0.75 + 0.25 × 4 — 0.5: BODMAS first — multiply 0.25 × 4. Strip: 25 × 4 = 100, two decimal places in 0.25, zero in 4, reattach: 1.00 = 1. Now 0.75 + 1 - 0.5 = 1.25. The strip-reattach step takes 5 seconds vs. aligning decimals manually which takes 15 seconds and introduces alignment errors.
For a/b + c/d where b and d share a common factor, do not default to b × d as denominator. Find the actual LCM. Example: 2/5 + 3/10. LCM(5, 10) = 10, not 50. Working with denominator 10: 4/10 + 3/10 = 7/10. Working with denominator 50: 20/50 + 15/50 = 35/50 = 7/10 — correct but requires a final cancellation step. LCM approach: 3 steps. Cross-multiply approach: 5 steps including final reduction.
Before doing anything else in a simplification, circle every power and root in the expression. Evaluate all of them immediately after resolving brackets. Why: if you skip a power and start adding, you'll reach the power mid-calculation and lose track of partial totals. Circling first costs 2 seconds. Getting lost mid-calculation and restarting costs 30+ seconds. On 3² + 4² - 2³: circle 3², 4², 2³ — evaluate to 9, 16, 8 — replace in expression — then do 9 + 16 - 8 = 17. Three mechanical substitutions, no path errors.
When you see a simplification question in the exam hall, run this decision tree:
Step 1 — Spot the keyword. Does the question say "approximately" or "~"? If yes, go to approximation mode: round aggressively, eliminate options. If no, go to exact mode.
Step 2 — Exact mode scan. Identify: any brackets? Any powers/roots? Mark them. Resolve brackets first (innermost out), then powers/roots.
Step 3 — Left-to-right sweep. Scan for × and ÷. Execute in left-to-right order. Write the intermediate result.
Step 4 — Final +/- sweep. Resolve remaining additions and subtractions left to right.
Step 5 — Sanity check. Does your answer match one of the options exactly? If yes, mark and move. If not, check whether you applied left-to-right on D/M and A/S — that's where 80% of errors live.
For fraction questions: identify LCM of denominators first, before touching the numerators.
For percentage questions: swap to fraction form immediately, before any arithmetic.
Target: under 45 seconds per straightforward simplification, under 75 seconds for multi-bracket compound expressions.
Why this question: Tests pure BODMAS on a three-operation expression — the most common simplification format in IBPS Clerk.
Solving path: Identify the × first: 12 × 2 = 24. Expression becomes 25 + 18 - 24. Left to right: 25 + 18 = 43, then 43 - 24 = 19. Answer: 19. No brackets, no powers — pure D/M before A/S.
Why this question: Tests fraction addition and subtraction with different denominators — a staple in IBPS Clerk simplification.
Solving path: LCM(5, 10, 2) = 10. Convert: 2/5 = 4/10, 3/10 = 3/10, 1/2 = 5/10. Now (4 + 3 - 5)/10 = 2/10 = 1/5. Answer: 1/5.
Why this question: Tests mixed multiplication-division sequence — the exact trap where left-to-right rule catches people out.
Solving path: Identify all × and ÷: 5 × 6 = 30, 48 ÷ 8 = 6, 3 × 4 = 12 (all at same BODMAS level, resolve left to right). Expression becomes 30 + 6 - 12. Left to right: 30 + 6 = 36, 36 - 12 = 24. Answer: 24.
Why this question: Tests brackets combined with division — two BODMAS layers in one expression.
Solving path: Brackets first: 12 × 5 = 60 and 15 - 5 = 10. Expression: 60 ÷ 10 + 8. Division: 60 ÷ 10 = 6. Addition: 6 + 8 = 14. Answer: 14.
Why this question: Tests powers (Orders) — the O in BODMAS — which many students forget sits above Division and Multiplication.
Solving path: Evaluate orders first: 3² = 9, 4² = 16, 2³ = 8. Expression becomes 9 + 16 - 8. Left to right: 9 + 16 = 25, 25 - 8 = 17. Answer: 17.
Ignoring left-to-right for Division/Multiplication. Writing 48 ÷ 8 × 3 as 48 ÷ 24 = 2 instead of 6 × 3 = 18 is the single most common error in this topic. Drill left-to-right until it is automatic.
Skipping the LCM step for fractions. Using b × d as the default denominator instead of LCM(b, d) creates unnecessarily large numbers that increase the chance of arithmetic mistakes. Always find the actual LCM first.
Treating "Of" as an afterthought. In an expression like 2/5 of 50 + 10, "of" means multiplication and it comes after brackets but before regular × and ÷ in the BODMAS sequence. Treating it as addition or ignoring it changes the answer completely.
Misplacing the decimal point. After stripping decimals and multiplying integers, students lose track of how many decimal places to reattach. Count total decimal places in all factors before you begin, write that number down, and reattach at the end.
Approximating when the question demands an exact answer. If the question does not explicitly say "approximately" or use the "~" symbol, do not round. Rounding 12 × 5 to 12 × 5 ≈ 60 is fine only when approximation is asked; doing it in an exact question gives a coincidentally close but potentially wrong answer.
Not resolving powers before multiplication. In 3² × 4, computing 3 × 4 = 12 then squaring to get 144 instead of 9 × 4 = 36 is a classic trap. Powers belong to the Orders step — handle them before × or ÷.