Cheatsheet: Simplification | IBPS PO Prelims & Mains Preparation - Bank Exams PDF Download

Introduction

Simplification is a core concept in quantitative aptitude that appears in most competitive exams like Banking . It involves breaking down complex mathematical expressions into simpler forms using basic operations, algebraic rules, and smart calculation methods. Mastering simplification helps you solve problems faster and more accurately, giving you an edge in time-bound exams.

Key Concepts​

1. Understanding the Basics

Simplification problems test your ability to:

• Perform arithmetic operations quickly

• Apply the correct order of operations

• Convert between fractions, decimals, and percentages

• Use algebraic identities effectively

• Estimate and approximate values

2. The BODMAS Rule​

Always follow this order of operations:

1. Brackets (solve innermost first)

2. Orders (powers and roots)

3. Division

4. Multiplication

5. Addition

6. Subtraction

Example:
20 + 30 ÷ 5 × (7 - 2)^2
= 20 + 30 ÷ 5 × 25 (Brackets first)
= 20 + 6 × 25 (Division next)
= 20 + 150 (Multiplication)
= 170 (Final answer)

Important Formula​

1. Percentage Conversions

• To find x% of y: (x/100) × y

• What percent is y of x: (y/x) × 100

• Percentage change: [(New - Original)/Original] × 100

2. Important Fractions to Decimals

• 1/2 = 0.5 = 50%

• 1/4 = 0.25 = 25%

• 3/4 = 0.75 = 75%

• 1/5 = 0.2 = 20%

• 1/8 = 0.125 = 12.5%

3. Squares and Cubes 

4. Algebraic Shortcuts

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b)³ = a³ + 3a²b + 3ab² + b³

Smart Calculation Techniques​

1. Breaking Down Numbers

Example: 48 × 25
= (50 - 2) × 25
= 1250 - 50
= 1200

2. Unit Digit Verification

Check the last digit to verify answers:
Example: 347 × 9 → 7×9=63 → Answer must end with 3

3. Quick Estimation

Example: 499 × 21 ≈ 500 × 20 = 10,000

4. Cross-Cancellation in Fractions

Example: (15 × 4)/(5 × 3) = 60/15 = 4

5. Divisibility Checks

• Divisible by 2: Its last digit is even (0, 2, 4, 6, or 8) then number is divisible by 3

• Divisible by 3: Sum of digits divisible by 3

• Divisible by 4: Last two digits divisible by 4

• Divisible by 6: Divisible by both 2 and 3

• Divisible by 9: Sum of digits divisible by 9

Approximation Methods​

1. Rounding Off

• If next digit ≥5, round up

• If next digit <5, round down
  Example: 4.68 ≈ 4.7 (to one decimal place)

2. Nearest Compatible Numbers

Example: 398 + 213 ≈ 400 + 210 = 610

3. Percentage Approximations

Example: 23% of 499 ≈ 25% of 500 = 125

Common Pitfalls to Avoid​

1. Forgetting BODMAS order

2. Misplacing decimal points

3. Overlooking negative signs

4. Incorrectly applying algebraic rules

5. Rounding too early in multi-step problems

Final Tips for Exams

• Solve brackets and exponents first

• Break complex numbers into simpler parts

• Use estimation when exact calculation isn't needed

• Verify answers using unit digits

• Keep calm and avoid rushing

By mastering these techniques and practicing regularly, you'll significantly improve your speed and accuracy in simplification problems. Remember, consistent practice is the key to success in quantitative aptitude!