Simplification questions in SSC CGL are deceptively simple — the rule is fixed, but the traps are sneaky. Every simplification question tests one thing: do you know the exact order in which operations must be performed?
The framework is BODMAS (or VBODMAS — the V stands for Vinculum, a bar written over grouped terms):
(), then curly {}, then square [])Think of BODMAS as a priority queue. Anything inside brackets gets resolved before you touch anything outside them. Within the same level of priority — say, division and multiplication — you work left to right.
Here's an analogy that sticks: imagine you're peeling an onion. The innermost layer (the vinculum or the deepest bracket) comes out first, then the next layer, and so on. You never skip a layer. If you try to peel from the outside, you get mush.
The practical challenge in SSC CGL is not that students don't know BODMAS — most do. The challenge is:
That last point kills more marks than any other. When you have −{a − b + c}, it becomes −a + b − c. Students often flip the first term correctly and forget the rest.
This topic is a guaranteed 2–4 question cluster in every SSC CGL Tier-I attempt. Getting them right is about process discipline, not raw intelligence. Nail the process, and these become free marks.
Always resolve in this order: () inside {} inside []. If a vinculum appears, it is resolved before any bracket.
Example of vinculum: $\overline{3+4}$ inside an expression means evaluate 3+4=7 first, then proceed.
For nested brackets, work from the inside out:
Step 1 — Round brackets: (2−1) = 1
Step 2 — Expression becomes: 13 − [7 − {4 + 1}]
Step 3 — Curly brackets: {4 + 1} = 5
Step 4 — Expression becomes: 13 − [7 − 5]
Step 5 — Square brackets: [7 − 5] = 2
Step 6 — Final: 13 − 2 = 11
When a negative sign precedes a bracket, every term inside changes sign upon removal.
−(a + b − c) becomes −a − b + c
−{p − q + r} becomes −p + q − r
This is the single most common error source in bracket-heavy questions. Before removing any bracket preceded by a minus, mentally tag every term inside with its new sign first, then write it out.
The second major skill is fluent conversion between forms.
Mixed fraction to improper fraction:
$2\frac\{5\}\{8\} = \frac{(2 \times 8) + 5}\{8\} = \frac\{21\}\{8\}$
Decimal to fraction:
$3.375 = \frac\{3375\}\{1000\}$ — then find GCD. Since 3375 = 27 \times 125 and 1000 = 8 \times 125, cancel 125 to get $\frac\{27\}\{8\}$.
Fraction to decimal: Division, or use known benchmarks.
$\frac\{1\}\{8\} = 0.125$, $\frac\{1\}\{16\} = 0.0625$ — memorize these. You will see them.
| Fraction | Decimal |
|----------|---------|
| 1/4 | 0.25 |
| 1/8 | 0.125 |
| 1/16 | 0.0625 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
| 1/3 | 0.333... |
| 2/3 | 0.666... |
These eight values cover 80% of the decimal-to-fraction conversions you'll encounter.
Surds (√ and ∛ terms) appear at the start of multi-step simplification questions. Evaluate them first — they are effectively just numbers once you recognize the perfect square or perfect cube.
Perfect squares up to 400: know them cold. Perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
$\sqrt\{144\} = 12$, $\sqrt[3]\{27\} = 3$ — these are not computation, they are recall. If you're actually computing √144 during an exam, you're burning time you don't have.
"Of" means multiplication and ranks between brackets and division. $\frac\{1\}\{2\}$ of 20 = 10 is evaluated before any standalone division or multiplication outside brackets. Students often treat "of" as just a word and miss this.
$12 \div 3 \times 2$ is NOT 12 \div 6 = 2. It is (12 \div 3) \times 2 = 4 \times 2 = 8. When D and M appear at the same level, resolve left to right.
When you see nested brackets [], {}, (), always start from the innermost layer and work outward — like peeling an onion. Before writing a single number, scan the entire expression and circle the deepest bracket. Resolve that, rewrite, then find the next deepest. This prevents the "skipped a layer" error that students make under time pressure.
Micro-example: 13 − [7 − {4 + (2−1)}]
Wrong approach (outside-in): Students try to handle [...] first and get confused.
Correct approach (inside-out): (2−1)=1 → {4+1}=5 → [7−5]=2 → 13−2=11 — done in 3 lines.
Standard method (guessing/confusion): 60s. Onion rule (systematic inside-out): 20s.
Before removing any bracket preceded by a minus sign, write the sign that each term will carry after removal, directly above the term. Do not remove the bracket until all signs are tagged.
−{3 − 5 + 2}: tag → −3, +5, −2. Then write −3 + 5 − 2.
This adds one second of tagging but eliminates the sign errors that cost 2–4 marks per paper. Students who skip tagging and "do it mentally" drop marks consistently on 5+ mocks before they catch the pattern.
Step count without tagging: 2 steps, ~30% error rate under pressure.
Step count with tagging: 3 steps, near-zero error rate.
Memorize these seven anchors: 1/8 = 0.125, 1/16 = 0.0625, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, 1/3 ≈ 0.333, 2/3 ≈ 0.667. Any fraction with denominator 8 or 16 is a multiple of 0.0625.
Micro-example: 1/8 + 1/16 — don't find LCM 16, don't do long division. Recall: 0.125 + 0.0625 = 0.1875. Done.
Standard LCM method: 5 steps, ~25s. Anchor recall: 1 step, ~5s.
For a mixed fraction $a\frac{b}{c}$, the improper fraction is $\frac{ac + b}{c}$. Do the multiplication first, then add.
$2\frac\{5\}\{8\}$: 2×8=16, 16+5=21, answer 21/8. Write the denominator first (it doesn't change), then compute numerator. This sequence is faster because you don't have to hold as many numbers in working memory simultaneously.
Standard method (full fraction notation): 3 sub-steps, ~15s. Fast-convert (denominator-first): 2 mental steps, ~6s.
The six most-tested perfect cubes in SSC CGL are 8, 27, 64, 125, 216, 343. Associate each with its root: ∛8=2, ∛27=3, ∛64=4, ∛125=5, ∛216=6, ∛343=7. When you see a cube root in a simplification question, your first action is pattern-match to this list, not compute.
Micro-example: ∛27 + √144 — match ∛27=3 and √144=12 from recall → 3+12=15. Total time: 4s.
Without recall (computing from scratch): 20s+. With pattern-match: 4s.
In the exam hall, apply this decision sequence every time you see a simplification question:
Step 1 — Scan for surds. If you see √ or ∛, evaluate them immediately using recall. Replace with the integer value before doing anything else.
Step 2 — Convert all mixed fractions to improper fractions or decimals. Pick the form that matches the majority of other numbers in the expression. If most terms are decimals, convert everything to decimals.
Step 3 — Identify bracket depth. Count how many layers of brackets exist. Work strictly inside-out.
Step 4 — Tag signs before every bracket removal. Never remove a bracket preceded by a minus sign without tagging the internal signs first.
Step 5 — Apply DMAS left to right within each bracket level once brackets are resolved: Division, then Multiplication, then Addition/Subtraction.
Step 6 — Answer check. For expressions with only integers, the answer should be an integer. For mixed decimals, ballpark the answer before checking options — if your answer is 2.025 and two options are above 2 and two below, a rough estimate tells you immediately if you're in the right zone.
Total time target for a standard BODMAS question with one level of nesting: under 45 seconds.
Why this question: Tests pure surd recognition. If you're computing rather than recalling, you're over 30 seconds on a question that should take 5.
Solving path: Identify √144 — this is 12×12=144, so √144=12. Identify ∛27 — this is 3×3×3=27, so ∛27=3. Add: 12+3=15. No computation required beyond recall.
Why this question: Tests decimal-to-fraction conversion with GCD cancellation. The trap is option (b) which looks right if you forget to simplify.
Solving path: 3.375 × \frac\{1\}\{1000\} = \frac\{3375\}\{1000\}. Now factor: 3375 = 27 × 125, 1000 = 8 × 125. Cancel 125: \frac\{27\}\{8\}. Note — 3.375 is itself \frac\{27\}\{8\} as a known decimal. If you had memorized \frac\{27\}\{8\} = 3.375, this question takes 3 seconds: the × \frac\{1\}\{1000\} does nothing to simplify — wait, it divides by 1000... actually reread: 3.375 × \frac\{1\}\{1000\} is NOT 3.375 itself. Compute: \frac\{3375\}\{1000\} = \frac\{27\}\{8\} after the 125-cancellation. Answer: 27/8.
Why this question: Tests mixed number conversion + decimal arithmetic in a bracketed expression. The trap is computing the bracket incorrectly by forgetting to fully convert 2(5/8).
Solving path: Convert 2\frac\{5\}\{8\} to decimal: \frac\{21\}\{8\} = 2.625. Now evaluate the bracket: 2.625 + 1.75 = 4.375. Finally: 6.4 − 4.375 = 2.025. Answer: 2.025.
Why this question: Tests decimal benchmark recall for fractions with denominator 8 and 16.
Solving path: Recall benchmarks directly: \frac\{1\}\{8\} = 0.125 and \frac\{1\}\{16\} = 0.0625. Add: 0.125 + 0.0625 = 0.1875. Answer: 0.1875. Total time with benchmarks memorized: under 8 seconds.
Why this question: Tests division by a decimal (0.5) which trips students who treat it as division by 5.
Solving path: Convert 2\frac\{1\}\{4\} to improper fraction: \frac\{9\}\{4\}. Dividing by 0.5 is the same as dividing by \frac\{1\}\{2\}, which is the same as multiplying by 2. So: \frac\{9\}\{4\} \times 2 = \frac\{9\}\{2\} = 4.5. Answer: 4.5. The trap is dividing by 5 instead of 0.5, giving 0.45 — not an option, but students second-guess themselves.
Why this question: Multi-step nested bracket question — the hardest type. Every bracket level must be evaluated strictly inside-out.
Solving path: Start from the innermost round bracket:
\frac\{3\}\{4\} - \frac\{1\}\{4\} = \frac\{2\}\{4\} = \frac\{1\}\{2\}\frac\{1\}\{2\} \times \frac\{1\}\{2\} = \frac\{1\}\{4\}\frac\{1\}\{3\} - \frac\{1\}\{4\} = \frac{4-3}\{12\} = \frac\{1\}\{12\}\frac\{5\}\{6\} \div \frac\{1\}\{12\} = \frac\{5\}\{6\} \times 12 = 107\frac\{1\}\{4\} - 10 = \frac\{29\}\{4\} - 10 = \frac{29 - 40}\{4\} = \frac{-11}\{4\} = -2\frac\{3\}\{4\}Answer: −2\frac\{3\}\{4\}.
Removing outer brackets before inner ones. This is the single most costly error. No matter how "simpler" the outer bracket looks, resolve inward first. Every time, no exceptions.
Forgetting to flip all signs when removing a minus-prefixed bracket. Students flip the first term and leave the rest unchanged. If −{a − b + c} becomes −a − b + c, you've lost marks. It must become −a + b − c.
Treating ÷ and × as if division has absolute priority over multiplication. They are equal priority, resolved left to right. 12 ÷ 3 × 2 = 8, not 2.
Converting mixed fractions incorrectly. 2\frac\{5\}\{8\} is NOT \frac{2 \times 5}\{8\} = \frac\{10\}\{8\}. The whole number multiplies the denominator, then adds the numerator: \frac{(2 \times 8)+5}\{8\} = \frac\{21\}\{8\}.
Dividing by a decimal without converting it to a fraction first. ÷ 0.5 means × 2, not ÷ 5. Students under time pressure read 0.5 and divide by 5. Write 0.5 = \frac\{1\}\{2\} explicitly before operating.
Skipping the ballpark check on multi-step decimal questions. After a 4-step calculation, spend 3 seconds confirming your answer is in the right order of magnitude. If the expression is roughly 6 − 4, your answer should be near 2, not 0.2 or 20. A ballpark check catches arithmetic slips that happen in the final subtraction step.