SSC CGL Preparation – Day 2

Quantitative Aptitude: Fractions and Decimals

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✏️ Fractions

A fraction represents a part of a whole. It is written in the form p/q, where:

• p = numerator
• q = denominator (q ≠ 0)

Types of Fractions:

1. Proper Fractions:
   • Numerator < Denominator (e.g., 3/5)
2. Improper Fractions:
   • Numerator > Denominator (e.g., 7/4)
3. Mixed Fractions:
   • Combination of a whole number and a proper fraction $$(e.g., 1\frac{3}{4})$$
4. Like Fractions:
   • Fractions with the same denominator (e.g., 2/7 and 5/7)
5. Unlike Fractions:
   • Fractions with different denominators (e.g., 2/3 and 5/4)

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✏️ Important Concepts:

• To add or subtract fractions:
  • Convert them to like fractions (common denominator) first.
• Multiplication of fractions:
  • Multiply numerators and multiply denominators directly.
• Division of fractions:
  • Multiply the first fraction by the reciprocal of the second.
• Converting improper to mixed:
  • Divide numerator by denominator, quotient becomes whole part.

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✏️ Decimals

A decimal represents a part of a whole using a point (.).
Examples: 0.5, 2.75, 1.002

Types of Decimals:

• Terminating Decimals:
  • Have a finite number of digits after the decimal point.
    (e.g., 0.25, 0.125)
• Non-Terminating Repeating Decimals:
  • Digits repeat infinitely.
    (e.g., 0.333…, 0.666…)
• Non-Terminating Non-Repeating Decimals:
  • Digits never repeat (Irrational numbers).
    (e.g., π = 3.1415926…)

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✏️ Important Concepts:

• Addition/Subtraction of Decimals:
  • Line up the decimal points before adding or subtracting.
• Multiplication of Decimals:
  • Multiply normally and count total decimal places from both numbers.
• Division of Decimals:
  • Adjust decimals to whole numbers if necessary (shift decimal points).
• Conversion:
  • Fraction to Decimal = divide numerator by denominator.
  • Decimal to Fraction = write in p/q form and simplify.

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🔥 Shortcuts and Tricks:

• 1/2 = 0.5
• 1/3 ≈ 0.333
• 1/4 = 0.25
• 1/5 = 0.2
• 1/6 ≈ 0.166
• 1/8 = 0.125
• 1/9 ≈ 0.111
• 1/10 = 0.1

Tip: Memorize common conversions to save time in exams!

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✍️ Common SSC CGL Patterns

• Simplifying fraction expressions
• Finding missing numbers in fractions
• Comparing fractions and decimals
• Word problems involving decimals and fractions
• Converting recurring decimals to fractions

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⚡ Example Problems:

Q1: Add 3/4 and 5/6.

Solution:
LCM of 4 and 6 = 12
$$\frac{(3×3)}{(4×3)} + \frac{(5×2)}{(6×2)} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}$$

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Q2: Multiply 0.25 × 0.04

Solution:
25 × 4 = 100
Count total 4 decimal places → 0.0100 = 0.01

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Q3: Convert 0.375 into a fraction.

Solution:
$$0.375 = \frac{375}{1000} = \frac{3}{8}$$

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Q4: Which is greater: 3/7 or 5/11?

Solution:
Cross multiply:
$$3×11 = 33
5×7 = 35 → 35 > 33 → \frac{5}{11} > \frac{3}{7}$$