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IBPS PO Simplification & Approximation

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Concept Notes

Simplification & Approximation— Rules & Concept

Core ConceptRead this first — the foundation of the topic

Core Concept

Simplification means solving expressions step by step using BODMAS rule. Approximation means finding values close to exact answers using rounding or estimation techniques. Both skills are essential for solving complex problems in limited exam time

Follow BODMAS strictly

Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction 2. Simplify fractions by finding common factors 3. Convert mixed numbers to improper fractions when needed 4. Use algebraic identities wherever possible Approximation Techniques: 1.

Round numbers to nearest 10, 100, or simple fractions 2. Use estimation for quick elimination of wrong options 3. Apply percentage approximations for decimal calculations

Formula BlockMemorise — at least one formula appears in every paper

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

• √(ab) = √a × √b

• Percentage approximation: 0.33 ≈ 1/3, 0.25 = 1/4, 0.125 = 1/8

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL typically asks 3-5 direct simplification questions worth 6-10 marks. Questions involve complex fractions, square roots, percentages, and mixed operations. Time allocation should be maximum 1-2 minutes per question. Powerful Shortcut - Fraction Multiplication Trick: When multiplying fractions, cancel common factors diagonally before multiplying. This reduces calculation time by 50%.

Worked ExampleSolve this step-by-step before moving on

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Step 1

Convert decimals to fractions = (24/10 × 16/10 × 5/10) / (8/10 × 3/10 × 4/1)

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Step 2

Simplify by canceling = (24 × 16 × 5) / (10 × 8 × 3 × 4 × 10)

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Step 3

Cancel common factors 24/8 = 3, 16/4 = 4, 5 cancels with denominator = (3 × 4) / (10 × 3 × 10) = 12/300 = 1/25 = 0.04 Worked Example 2: Approximate: √624 + √1444

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Step 1

Find perfect squares nearby √624 ≈ √625 = 25 (since 625 = 25²) √1444 ≈ √1444 = 38 (since 38² = 1444)

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Step 2

Add approximated values 25 + 38 = 63 Exact calculation gives 62.98, so approximation is highly accurate. Mega Shortcut - Options Elimination: In MCQs, approximate the answer first. Eliminate options that are far from your approximation. Then calculate precisely only for remaining close options. The #1 Most Common Trap: Students ignore BODMAS order and calculate left to right. For expression 2 + 3 × 4, wrong approach gives (2 + 3) × 4 = 20. Correct answer following BODMAS: 2 + (3 × 4) = 14. This single mistake can cost 2-4 marks in the exam. Another critical error is incorrect fraction handling. When adding fractions with different denominators, students often add numerators and denominators separately instead of finding LCM first.

Key Points to Remember

BODMAS rule is mandatory: Brackets → Orders → Division → Multiplication → Addition → Subtraction
Shortcut: (a + b)² = a² + 2ab + b² saves calculation time in complex expressions
Approximation formula: Round to nearest easy numbers first, then calculate
Fraction multiplication trick: Cancel common factors diagonally before multiplying
Time management: Spend maximum 1-2 minutes per simplification question
Options elimination: Use approximation to eliminate obviously wrong answers
Decimal conversion: 0.25 = 1/4, 0.33 = 1/3, 0.125 = 1/8, 0.2 = 1/5
Square root estimation: Memorize perfect squares 1² to 30² for quick approximation
Percentage shortcut: 10% of any number = number/10, 1% = number/100
Common trap: Never calculate left to right, always follow BODMAS strictly

Exam-Specific Tips

Perfect squares to memorize: 25² = 625, 26² = 676, 27² = 729, 28² = 784, 29² = 841, 30² = 900
Cube roots: ∛125 = 5, ∛216 = 6, ∛343 = 7, ∛512 = 8, ∛729 = 9, ∛1000 = 10
Fraction decimals: 1/7 = 0.142857 (repeating), 1/9 = 0.111... (repeating), 1/11 = 0.090909...
Value of √2 = 1.414, √3 = 1.732, √5 = 2.236 for approximation purposes
Percentage equivalents: 12.5% = 1/8, 16.67% = 1/6, 37.5% = 3/8, 62.5% = 5/8
Powers of 2: 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024
Common algebraic identity: (a + b)³ = a³ + b³ + 3ab(a + b)
Simplification weights 8-12% of total Quantitative Aptitude marks in SSC CGL

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