SSC CGL Preparation – Day 3

Quantitative Aptitude – Simplification and Approximation

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✅ What You’ll Learn Today

• Basic concepts of simplification
• BODMAS rule
• Approximations for faster calculation
• Use of identity tricks
• Square roots and cube roots
• Tips for quick mental math
• Solving complex expressions

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📌 1. Understanding Simplification

Simplification refers to reducing a mathematical expression to its simplest form to get the answer quickly and accurately.

🧮 Common Expressions:

• Fractions
• Decimals
• Brackets
• Surds
• Percentages
• Square/cube roots

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📌 2. The BODMAS Rule

BODMAS stands for:

B	O	D	M	A	S
Brackets	Orders (powers, roots)	Division	Multiplication	Addition	Subtraction

🔸 Types of Brackets:

• ( ) → Parentheses
• { } → Braces
• [ ] → Square Brackets

🧠 Tip: Always solve brackets from innermost to outermost.

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📌 3. Important Arithmetic Identities

Memorize and use these for speed:

• $$(a + b)^2 = a^2 + 2ab + b^2$$
• $$(a – b)^2 = a^2 – 2ab + b^2$$
• $$a^2 – b^2 = (a + b)(a – b)$$
• $$(x+a)(x+b) = x^2 + (a + b)x + ab$$

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📌 4. Approximation Techniques

In exams, you can save time by using approximate values where allowed.

🔸 When to Approximate:

• When options are far apart
• When expression has large or non-exact numbers
• When exact answer isn’t required (e.g., “approximately equal to”)

🔸 Rules of Thumb:

• Round off decimals:
  e.g., 5.82 ≈ 6, 3.49 ≈ 3.5
• Use known square roots:
  √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236
• Use known cube roots: ∛8 = 2, ∛27 = 3, ∛64 = 4

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📌 5. Surds & Decimals Simplification

Examples:

• √50 = √(25 × 2) = 5√2
• Simplify: $$\frac{√18}{√2} = √9 =3$$

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📌 6. Fractions to Decimals Conversion Table

Fraction	Decimal
1/2	0.5
1/3	0.333
1/4	0.25
1/5	0.2
3/4	0.75

🧠 Trick:

• Memorize decimals of common fractions to save time.

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📌 7. Tips for SSC CGL Simplification Questions

• Always check BODMAS rule
• Don’t jump to approximations unless explicitly mentioned
• Break complex expressions into parts
• Eliminate wrong options quickly using approximation
• Check units (especially in percentages or time questions)

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📌 8. Examples for Practice

Example 1:

Simplify: 24+36÷6×2−5
→ BODMAS:
= 24 + (6 × 2) – 5
= 24 + 12 – 5 = 31

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Example 2:

Approximate value of: $$\frac{149.8 \times 5.2}{9.9}​$$

$$Rounding: ≈ \frac{150 \times 5}{10} = \frac{750}{10} = 75$$

$$Answer: Approximately 75$$

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Example 3:

Simplify: $$\frac{2.4 × 1.5}{0.6}​$$

→ (2.4 × 1.5 = 3.6), 3.6 ÷ 0.6 = 6

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Example 4:

Simplify: $$\left( \frac{6}{7} + \frac{4}{21} \right) × 3$$

→ LCM of 7 and 21 = 21 $$=\left( \frac{18 + 4}{21} \right) × 3 = \frac{22}{21} × 3 = \frac{66}{21} = \frac{22}{7}​$$

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📌 9. What SSC CGL Asks?

✔ Expressions involving fractions, decimals, BODMAS
✔ Comparing approximate values
✔ Identifying simplification shortcut
✔ Real-world applications (interest, time, percentages)

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🧠 Shortcut Tricks

Practice with mental math daily

Multiply first, divide later

Use approximation only when answer options allow

Memorize squares till 30, cubes till 20