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SSC CPO Fractions & Decimals

Study Material — 10 PYQs (2019–2019) · Concept Notes · Shortcuts

SSC CPO Fractions & Decimals is a frequently tested subtopic — 10 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SSC CPO Fractions & Decimals — Past Exam Questions

10 questions from actual SSC CPO papers · all shown free · click option to reveal solution

Exam Q 12019Previous Year Pattern

Express 0.625 as a fraction in its simplest form.

Exam Q 22019Previous Year Pattern

If 2/5 of a number is 48, what is the number?

Exam Q 32019Previous Year Pattern

If 3/7 of a tank is filled with water and the tank holds 280 litres, how many litres of water are in the tank?

Exam Q 42019Previous Year Pattern

A decimal number when multiplied by 8 gives 6.4. What is the decimal number?

Exam Q 52019Previous Year Pattern

If 7/9 of a tank is filled with water and contains 630 litres, how many litres does the full tank hold?

Exam Q 62019Previous Year Pattern

If 2.5 kg of sugar costs ₹150, what is the cost of 4 kg of sugar?

Exam Q 72019Previous Year Pattern

The decimal representation of 7/12 is 0.58̄3̄ (where 3 repeats). If this decimal is multiplied by 144, what is the result?

Exam Q 82019Previous Year Pattern

If 2/3 of a number is 18 more than 1/4 of the same number, what is 5/6 of that number?

Exam Q 92019Previous Year Pattern

A fraction becomes 4/5 when 3 is subtracted from both numerator and denominator. The same fraction becomes 5/6 when 2 is added to both numerator and denominator. Find the original fraction.

Exam Q 102019Previous Year Pattern

A decimal number 0.3̄6̄ (where both 3 and 6 repeat) is converted to a fraction. What is the denominator of this fraction when expressed in lowest terms?

Concept Notes

Fractions & Decimals— Rules & Concept

Core ConceptRead 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 RulesCore rules you must know cold

** 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. **

Formula BlockMemorise — 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)

Exam PatternsWhat 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.

Worked ExampleSolve 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. **

Exam TrapsCommon mistakes students make — avoid these

** 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 to Remember

  • 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-Specific Tips

  • 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 — Fractions & Decimals

  • 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)
←Number SeriesSimplification & Approximation→
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