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Fractions & Decimals

UP Police Constable · Quantitative Aptitude

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Core Concept

Read this first — the foundation of the topic

Core Concept: Fractions represent parts of a whole. A fraction has two parts - numerator (top number) and denominator (bottom number). Decimals are another way to write fractions using place values after a decimal point.

Both are extensively tested in SSC CGL. Key Rules and Properties: Every fraction can be converted to decimal form by dividing numerator by denominator. Terminating decimals have denominators with only factors of 2 and 5. Non-terminating decimals have denominators with factors other than 2 and 5.

When adding fractions, find common denominator first. When multiplying fractions, multiply numerators together and denominators together. **

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Formula Block

Memorise — at least one formula appears in every paper

Fraction to Decimal: Numerator ÷ Denominator

Decimal to Fraction: Remove decimal, divide by appropriate power of 10

Addition: a/b + c/d = (ad + bc)/(bd)

Subtraction: a/b - c/d = (ad - bc)/(bd)

Multiplication: a/b × c/d = (ac)/(bd)

Division: a/b ÷ c/d = (ad)/(bc)

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL frequently asks fraction comparisons, decimal conversions, arithmetic operations with mixed numbers, and word problems involving parts of quantities. Questions often involve finding equivalent fractions, simplifying complex fractions, and converting recurring decimals to fractions. Shortcut - Cross Multiplication for Comparison: To compare fractions a/b and c/d, multiply a×d and b×c. If a×d > b×c, then a/b > c/d. This saves time over finding common denominators.

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Worked Example

Solve this step-by-step before moving on

1

Step 1

Cross multiply - 7×6 = 42 and 9×5 = 45

2

Step 2

Compare results - 42 < 45

3

Step 3

Therefore 7/9 < 5/6 Converting Recurring Decimal 0.363636... to Fraction:

1

Step 1

Let x = 0.363636...

2

Step 2

Multiply by 100 (since 2 digits repeat): 100x = 36.363636...

3

Step 3

Subtract original: 100x - x = 36

4

Step 4

Solve: 99x = 36, so x = 36/99 = 4/11

5

Step 5

Verify: 4÷11 = 0.363636... ✓ Another Shortcut - Decimal Place Memory: For quick conversions, remember that 1/8 = 0.125, 1/3 = 0.333..., 1/6 = 0.1666..., 1/7 = 0.142857... (repeating). These frequently appear in options. Common Mistake: Students often forget to simplify fractions to lowest terms or make errors with recurring decimals. Always reduce fractions by finding the highest common factor of numerator and denominator. Also, when dealing with mixed numbers, convert to improper fractions first before performing operations.

🔑 Key Points

Fraction = Numerator/Denominator represents parts of a whole number
Terminating decimals have denominators with only factors 2 and 5
Cross multiplication shortcut: a/b vs c/d compare a×d with b×c
To add fractions: a/b + c/d = (ad + bc)/(bd)
Recurring decimal with n repeating digits: multiply by 10^n then subtract
Mixed number operations: convert to improper fractions first
Always simplify final answers using HCF of numerator and denominator
1/7 = 0.142857... (6-digit repetition) appears frequently in SSC

📌 Exam Facts

1/3 = 0.333... (non-terminating recurring decimal)
1/8 = 0.125 (terminating decimal)
1/7 = 0.142857142857... (6-digit recurring pattern)
1/6 = 0.16666... (recurring decimal starting after first digit)
1/11 converts any 2-digit recurring decimal (like 0.363636... = 4/11)
Fractions with denominators having prime factors other than 2,5 give non-terminating decimals
1/9 = 0.111..., 2/9 = 0.222..., following pattern up to 8/9 = 0.888...
Any decimal with denominator as power of 10 can be directly written as fraction

🚀 60-Second Revision

Remember: Cross multiply to compare fractions quickly without finding LCM
Formula: Recurring decimal conversion - multiply by 10^n, subtract, solve
Trap: Always check if fraction can be simplified using HCF
Quick recall: 1/8=0.125, 1/3=0.333..., 1/7=0.142857..., 1/6=0.1666...
Method: Convert mixed numbers to improper fractions before operations
Check: Denominators with only factors 2,5 give terminating decimals
Shortcut: For addition a/b + c/d use cross multiplication formula (ad+bc)/(bd)

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