Simplification and Approximation
Overview
These questions test your ability to perform rapid calculations using BODMAS rules, handle fractions and decimals, and make intelligent approximations to save time.
The reason this topic dominates Clerk-level exams is straightforward: it directly measures calculation speed and accuracy—the core skills needed for a clerical banking role. Unlike complex word problems, these questions reward students who have mastered mental math shortcuts and know when to calculate exactly versus when to approximate.
Speed is everything here—you should aim to solve each question in 30–45 seconds.
Key Concepts
- BODMAS Rule: Operations must follow the order—Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Division and Multiplication are equal priority (left to right); same for Addition and Subtraction.
- Simplification vs Approximation: Simplification demands exact answers; Approximation allows rounding numbers to nearby convenient values (usually to nearest 5, 10, or whole number) before calculating.
- Fraction-Decimal Equivalents: Memorize common conversions (1/8 = 0.125, 1/6 = 0.167, 3/8 = 0.375, etc.) to instantly switch between forms based on what's easier to compute.
- Percentage-Fraction Link: Recognize that 25% = 1/4, 33.33% = 1/3, 12.5% = 1/8. This lets you convert percentage calculations into simpler fraction operations.
- Rounding Strategy: In approximation questions, round each number in the same direction initially, then adjust if answer options are close. Round 4999 to 5000, 7.89 to 8, 19.6% to 20%.
- Square and Cube Recognition: Know squares up to 30 and cubes up to 15 instantly. Recognizing 729 as 27² or 9³ saves crucial seconds.
- Estimation Boundaries: When options are spread apart (e.g., 450, 520, 610, 680), rough approximation suffices. When options are close (e.g., 512, 518, 524, 530), calculate more precisely.
Formulas / Key Facts
BODMAS Priority (left to right within same level) Brackets → Orders → Division/Multiplication → Addition/Subtraction
Fraction to Decimal Conversions (memorize these)
- 1/2 = 0.5, 1/3 = 0.333, 1/4 = 0.25, 1/5 = 0.2
- 1/6 = 0.167, 1/7 = 0.143, 1/8 = 0.125, 1/9 = 0.111
- 2/3 = 0.667, 3/4 = 0.75, 3/8 = 0.375, 5/8 = 0.625
Percentage Shortcuts
- 10% of x = x/10
- 5% of x = x/20 = half of 10%
- 15% = 10% + 5%
- 1% of x = x/100
Square Values (must know)
- 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225
- 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400
- 25² = 625, 30² = 900
Cube Values (must know)
- 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216
- 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000
Worked Examples
Example 1: Pure Simplification Find the value of: 48 ÷ 12 × 3 + 18 − 6 × 2
Step 1: Handle Division and Multiplication (left to right)
- 48 ÷ 12 = 4
- 4 × 3 = 12
- 6 × 2 = 12
Step 2: Rewrite expression
- 12 + 18 − 12
Step 3: Addition and Subtraction (left to right)
- 12 + 18 = 30
- 30 − 12 = 18
Answer: 18
Example 2: Approximation Find approximate value of: 4999 ÷ 49.9 × 9.9 + 1001
Step 1: Round to convenient numbers
- 4999 ≈ 5000
- 49.9 ≈ 50
- 9.9 ≈ 10
- 1001 ≈ 1000
Step 2: Calculate
- 5000 ÷ 50 = 100
- 100 × 10 = 1000
- 1000 + 1000 = 2000
Answer: ≈ 2000
Example 3: Fraction and Percentage Mix Find: 3/8 of 4800 + 25% of 1600 − 240
Step 1: Convert and calculate each part
- 3/8 of 4800 = (3 × 4800)/8 = 14400/8 = 1800
- 25% of 1600 = 1600/4 = 400
Step 2: Combine
- 1800 + 400 − 240 = 1960
Answer: 1960
Common Mistakes
- Ignoring BODMAS order → Students add before multiplying. Fix: Always scan the expression for × and ÷ first, mark them mentally, then proceed left to right.
- Over-approximating when options are close → Rounding 7.2 to 7 when options differ by 10 causes wrong answers. Fix: Check option spread first—if tight, approximate less aggressively.
- Forgetting to convert mixed fractions → Treating 2 1/4 as 2.14 instead of 2.25. Fix: Convert mixed fractions to improper fractions (2 1/4 = 9/4) or decimals immediately.
- Wrong bracket handling → Solving inner operations before resolving nested brackets. Fix: Work from innermost bracket outward—{[( )]} means solve ( ) first, then [ ], then { }.
- Decimal point errors in division → Getting 50 instead of 500 when dividing 5000 by 10. Fix: Count decimal places or zeros explicitly; verify magnitude makes sense.
Quick Reference
- BODMAS: Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction (L→R)
- For approximation: round to nearest 5 or 10, then adjust based on option spread
- 1/8 = 0.125 = 12.5%; 1/6 = 0.167 ≈ 16.67%; 3/8 = 0.375 = 37.5%
- Memorize squares (1–30) and cubes (1–15) for instant recognition
- Target time: 30–45 seconds per question; skip and return if stuck beyond 60 seconds
- When multiplying/dividing by 25: use × 100 ÷ 4 or × 4 ÷ 100 for speed