Simplification

1. What is Simplification (Advanced Level)?

Simplification (Advanced) refers to solving complex numerical expressions quickly and accurately by using shortcuts, estimation, and special rules. It checks your speed, accuracy, and understanding of arithmetic operations under exam pressure.

Quick & Accurate Problem Solving

Uses Shortcuts & Estimation

Tests Speed Under Pressure

Applies Special Rules

Simple Definition: Simplification (Advanced) means solving complex numerical problems using BODMAS, percentage, roots, powers, and approximations to find the correct answer in the shortest time.

Examples:

Example 1: √81 + 25% of 80 ÷ 4 = 9 + (20 ÷ 4) = 14

Example 2: (12² - 6²) ÷ 9 = (144 - 36) ÷ 9 = 108 ÷ 9 = 12

Example 3: 1 ÷ (1/3 + 1/6) = 1 ÷ (1/2) = 2

2. Important Shortcuts & Tricks

Trick	Description	Example
BODMAS Rule	Follow Bracket → Order → Division → Multiplication → Addition → Subtraction	(8+2)×3 = 10×3 = 30
Percentage Simplification	Replace % with ÷100	25% of 200 = (25/100) × 200 = 50
Square/Cube Values	Memorize 1–20 squares & cubes for speed	12² = 144, 7³ = 343
Root Simplification	√49 = 7, ³√27 = 3	Helps in fast solving
Reciprocal Rule	1 ÷ (1/a + 1/b) = (ab) / (a + b)	1/(1/3+1/6) = (3×6)/(3+6) = 2
Algebraic Identities	Use to simplify squares/cubes	(a+b)² - (a-b)² = 4ab
Estimation Trick	Round numbers to nearest 10 or 100	49.8 ≈ 50 for quick solve
Series Shortcut	1 + 2 + 3 + ... + n = n(n+1)/2	For pattern-based questions

3. Step-by-Step Method (Advanced Approach)

Step	Description
Step 1	Solve inner brackets ( (), {}, [] ) first
Step 2	Apply powers or roots next
Step 3	Perform Division and Multiplication (L → R)
Step 4	Perform Addition and Subtraction (L → R)
Step 5	Simplify decimals, percentages, or fractions
Step 6	Use approximation if exact answer isn't required

4. Real-Life Analogy

Think of Simplification like assembling a puzzle

Numbers & Operations

→ Puzzle pieces

(each has its place)

BODMAS Rule

→ Assembly instructions

(correct order matters)

Each number and operation is a piece — if you place them in the right order (BODMAS), the full picture (answer) appears correctly. If you mix them, the puzzle (calculation) breaks!

5. Common Delhi Police / SSC Exam Facts

Questions are based on BODMAS, roots, powers, and fractions

Most Simplification questions are 1–2 steps long but need accuracy

Approximation & estimation are often used in Data Interpretation

Shortcut techniques save time in lengthy calculations

Always verify signs (+/–) carefully, especially after brackets

Memorize squares and cubes up to 20 for faster calculation

6. Practice Questions (Exam-Type)

No.	Question	Solution	Answer
1	(15+3)×2–10÷2	18×2–5 = 36–5	31
2	√169 + 20	13 + 30 = 43	43
3	1/(1/4+1/6)	(4×6)/(4+6) = 24/10 = 2.4	2.4
4	(8²–6²)÷4	(64–36)÷4 = 28/4	7
5	(25×4) + ³√27	100 + 3	103

7. Quick Recap

Concept	Summary
Simplification (Advanced)	Quick solving of complex numerical problems
Key Rule	Always apply BODMAS
Shortcuts	Squares, roots, reciprocals, estimation
Common Topics	Fractions, decimals, powers, %
Exam Tip	Use approximation for speed & accuracy

You've completed Simplification (Advanced Level)!

Courage Tip: Practice these simplification techniques regularly to improve your speed and accuracy. Remember to apply BODMAS correctly and use approximation when exact calculation isn't necessary.