In this guide
Simplification is the part of SSC maths that aspirants tend to take for granted. The questions look like school arithmetic, so candidates rush — and lose marks to a bracket read in the wrong order or a sign dropped halfway through. At the same time, simplification is the foundation of speed in every other topic. A candidate who can simplify fractions, powers and roots quickly gains seconds on every question in the paper.
BODMAS
The order of operations:
- Brackets — innermost first: ( ), then { }, then [ ].
- Orders — powers and roots ("of" is also treated here in many SSC questions).
- Division and Multiplication — left to right.
- Addition and Subtraction — left to right.
Common error: 24 ÷ 4 × 2. Division and multiplication are done left to right: 24 ÷ 4 = 6, then 6 × 2 = 12 — not 24 ÷ 8 = 3.
Worked example: 18 − [5 − {6 + 2(7 − 8 − 1)}]
Innermost: 7 − 8 − 1 = −2; 2 × (−2) = −4; 6 + (−4) = 2; 5 − 2 = 3; 18 − 3 = 15.
Fractions and decimals
Know these conversions by heart:
| Fraction | Percentage / decimal |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/6 | 16.67% |
| 1/7 | 14.29% (approx.) |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/11 | 9.09% |
| 1/12 | 8.33% |
| 1/16 | 6.25% |
Recurring decimals
- 0.3333… (0.3 recurring) = 3/9 = 1/3.
- 0.272727… (0.27 recurring) = 27/99 = 3/11.
- 0.1666… (0.16 with 6 recurring) = (16 − 1)/90 = 15/90 = 1/6.
Rule: for a pure recurring decimal, put the repeating digits over as many 9s as there are repeating digits. For a mixed recurring decimal, subtract the non-repeating part and put 9s followed by 0s.
Laws of indices
| Law | Example |
|---|---|
| a^m × a^n = a^(m+n) | 2³ × 2⁴ = 2⁷ |
| a^m ÷ a^n = a^(m−n) | 5⁶ ÷ 5² = 5⁴ |
| (a^m)^n = a^(mn) | (3²)³ = 3⁶ |
| a⁰ = 1 | 7⁰ = 1 |
| a^(−n) = 1/a^n | 2^(−3) = 1/8 |
| a^(1/n) = nth root of a | 27^(1/3) = 3 |
Worked example: Find x if 2^(x+3) = 32.
32 = 2⁵, so x + 3 = 5 and x = 2.
Surds
A surd is an irrational root, such as √2 or ∛5.
- √a × √b = √(ab)
- √(a²b) = a√b — for example, √72 = √(36 × 2) = 6√2.
Rationalising the denominator
Multiply by the conjugate:
1/(√5 − √3) = (√5 + √3)/[(√5)² − (√3)²] = (√5 + √3)/2.
Comparing surds
To compare ∛4 and √3, raise both to the power 6: (∛4)⁶ = 16 and (√3)⁶ = 27. So √3 is larger.
Square roots and cube roots
- Know squares to 30 and cubes to 15.
- Square root of a perfect square: the unit digit narrows the possibilities; the size of the number fixes the tens digit. √7,056: 80² = 6,400 and 90² = 8,100, and a unit digit of 6 means the root ends in 4 or 6. 84² = 7,056, so the answer is 84.
Approximation
In "find the approximate value" questions, round numbers sensibly and look at how far apart the options are.
Worked example: 49.98 × 20.03 ÷ 4.99 ≈ 50 × 20 ÷ 5 = 200.
Habits that prevent errors
- Write each step of a nested bracket on the rough sheet — don't do it all mentally.
- Circle negative signs.
- Check your answer's size against the options before selecting.
Practice
- Simplify: 36 ÷ 6 × 3 + 4 − 2.
- Convert 0.454545… to a fraction.
- Find x if 3^(2x−1) = 243.
- Rationalise 2/(√7 + √5).
- Which is larger: ∛3 or √2?
- Approximate: 299.8 × 40.1 ÷ 60.2.
Answers: 1. 20. 2. 5/11. 3. x = 3. 4. √7 − √5. 5. ∛3 (raise both to the power 6: 9 vs 8). 6. About 200.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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