In this guide
Simplification is often among the first maths questions in an SSC CHSL paper, and the easiest to rush. A question like 24 ÷ 6 × 2 + 3 looks trivial, yet candidates regularly compute 24 ÷ 12 instead of working left to right. These questions reward a steady method more than cleverness, and they are worth protecting: each one is a mark that should cost you 20–30 seconds, not a penalty.
There are two skills here. The first is exact simplification: applying the order of operations without a slip. The second is seeing structure: noticing that a scary expression is really an identity in disguise, or that the options are far enough apart to estimate.
BODMAS, and what it really means
- Brackets, innermost first: ( ), then { }, then [ ].
- Of and Orders: powers, roots and "of".
- Division and Multiplication, left to right.
- Addition and Subtraction, left to right.
The most important words are "left to right". Division does not come before multiplication; they have equal rank, and you simply work across. The same holds for addition and subtraction.
"Of" means multiplication, but it is done before ordinary division. So 1/2 of 40 ÷ 5 is (1/2 × 40) ÷ 5 = 20 ÷ 5 = 4, not 1/2 × (40 ÷ 5).
Fractions and mixed numbers
- Convert mixed numbers first: 2⅓ = 7/3.
- Dividing by a fraction means multiplying by its reciprocal.
- To add or subtract, use the LCM of the denominators.
- Cancel before you multiply. It keeps numbers small and errors rare.
Decimals and percentages
- Multiplying by 0.25 is dividing by 4; by 0.125 is dividing by 8; by 0.2 is dividing by 5.
- In a product, count decimal places: 0.2 × 0.02 × 0.002 has 1 + 2 + 3 = 6 places, so it is 0.000008.
- Percentages are fractions: 25% of 80 = 80 ÷ 4 = 20. The percentage guide has the full fraction table.
Powers and roots
- aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, and (aᵐ)ⁿ = aᵐⁿ.
- √(a × b) = √a × √b, so √(64 × 25) = 8 × 5 = 40.
- A decimal square root halves the decimal places: √0.0144 = 0.12, because 0.12 × 0.12 = 0.0144.
- Surds combine like terms: √12 + √27 = 2√3 + 3√3 = 5√3.
Identities that collapse expressions
SSC likes expressions that look heavy but are just an identity. Learn to recognise these:
| Identity | Spot it when you see |
|---|---|
| a² − b² = (a + b)(a − b) | A difference of two squares, often divided by a sum or difference |
| (a + b)² = a² + 2ab + b² | Numbers near a round figure: 102², 999² |
| a³ + b³ = (a + b)(a² − ab + b²) | A sum of cubes divided by a² − ab + b² |
| a³ − b³ = (a − b)(a² + ab + b²) | A difference of cubes divided by a² + ab + b² |
Why it helps: instead of computing 0.87³ you cancel the whole denominator and are left with a single addition.
Approximation
Round each number to something convenient, then check how far apart the options are.
- If options differ by a lot (say 100, 150, 200, 250), rough rounding is enough.
- If they are close (say 146, 148, 150, 152), round less, or calculate exactly.
- For square roots, find the nearest perfect square: √1,090 ≈ 33, because 33² = 1,089.
Two checks that catch errors
- Size check. Before marking an answer, ask whether it is roughly the size you expected. If 39.9 × 20.1 ÷ 7.98 gave you 1,000, something went wrong, since the estimate is about 100.
- Digit-sum check (casting out nines). A number and its digit sum leave the same remainder when divided by 9, so digit sums must agree across a multiplication. For 34 × 21 = 714: 3 + 4 = 7 and 2 + 1 = 3, and 7 × 3 = 21 → 2 + 1 = 3. The answer's digit sum is 7 + 1 + 4 = 12 → 3. They match. A mismatch proves an error; a match makes one unlikely, though not impossible.
Six worked questions
Q1. Simplify 50 − [20 − {12 − (8 − 5)}].
Innermost first: 8 − 5 = 3. Then 12 − 3 = 9. Then 20 − 9 = 11. Then 50 − 11 = 39.
Q2. Simplify 3/4 of 120 − 25% of 80 + √144.
3/4 of 120 = 90. 25% of 80 = 20. √144 = 12. So 90 − 20 + 12 = 82.
Q3. Simplify (3/5 + 1/4) ÷ (1/2 − 1/5).
First bracket: 12/20 + 5/20 = 17/20. Second: 5/10 − 2/10 = 3/10. Then 17/20 × 10/3 = 17/6 = 2⅚.
Q4. Simplify (7.5 × 7.5 − 2.5 × 2.5) ÷ (7.5 − 2.5).
This is (a² − b²) ÷ (a − b) = a + b, so the answer is 7.5 + 2.5 = 10. Check: (56.25 − 6.25) ÷ 5 = 50 ÷ 5 = 10.
Q5. Simplify (0.87³ + 0.13³) ÷ (0.87² − 0.87 × 0.13 + 0.13²).
This is (a³ + b³) ÷ (a² − ab + b²) = a + b = 0.87 + 0.13 = 1.
Q6. Approximate 18% of 499 + 24% of 301.
18% of 500 = 90 and 24% of 300 = 72, so the answer is about 162. (Exactly: 89.82 + 72.24 = 162.06.)
Common errors
| Error | Fix |
|---|---|
| Multiplying before a division that comes first | Work left to right |
| Treating "of" as ordinary multiplication after division | Do "of" before ÷ |
| Dropping a minus sign inside brackets | Write each bracket's value on the rough sheet |
| Squaring a decimal wrongly (0.3² = 0.9) | Count places: 0.3² = 0.09 |
| Calculating exactly when options are far apart | Look at the options before you start |
Practice
- 36 ÷ 4 × 3 − 5
- 3/4 of 80 ÷ 6 + 2
- 100 − [40 − {15 − (9 − 4)}]
- 1½ ÷ 3/8
- √(81 × 49)
- Approximate: 59.8 × 4.95 ÷ 2.02
- (8.5² − 1.5²) ÷ 7
- 101 × 99
Answers:
- 22. 36 ÷ 4 = 9, then 9 × 3 = 27, then 27 − 5 = 22.
- 12. 3/4 of 80 = 60, then 60 ÷ 6 = 10, then 10 + 2 = 12.
- 70. 9 − 4 = 5; 15 − 5 = 10; 40 − 10 = 30; 100 − 30 = 70.
- 4. 3/2 × 8/3 = 4.
- 63. 9 × 7.
- About 150. 60 × 5 ÷ 2 = 150 (exactly, about 146.5).
- 10. (8.5 + 1.5)(8.5 − 1.5) = 10 × 7 = 70, and 70 ÷ 7 = 10.
- 9,999. (100 + 1)(100 − 1) = 10,000 − 1.
What to do next
- Do 20 BODMAS questions today, writing every intermediate value.
- Learn the four identities in the table and find one example of each in previous CHSL papers.
- Before each approximation question, glance at the options first and decide how precise you need to be.
- Add squares to 30 and cubes to 15 to your daily drill with the squares, cubes and roots guide, and see the maths plan for what comes next.
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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