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.
If 0.75 is expressed as a fraction in lowest terms, what is the denominator?
Practice 6easy
If 2/5 of a number is 24, what is the number?
Practice 7easy
What is 7/9 ÷ 14/27?
Practice 8easy
If 2/5 of a number is 24, what is the number?
Practice 9easy
Express 0.625 as a fraction in its simplest form.
Practice 10easy
Subtract 0.375 from 1.5. What is the result?
Practice 11easy
Express 0.625 as a fraction in simplest form.
Practice 12easy
If 5/6 of a number is 50, what is the number?
Practice 13medium
If 3/7 of a number is 48, what is 5/8 of that number?
Practice 14medium
If 2.5 metres of cloth costs ₹187.50, what is the cost of 6 metres of the same cloth?
Practice 15medium
If 2.5 × a = 15, and 3/4 × b = 15, what is the ratio of a to b?
Practice 16medium
What is the difference between 0.75 and 3/5 expressed as a decimal?
Practice 17medium
A number when divided by 0.5 gives 84. What is the number when expressed as a decimal?
Practice 18medium
A shopkeeper mixes two types of rice. Type A costs ₹40 per kg and Type B costs ₹60 per kg. If he mixes them in the ratio 3:2 by weight, what is the cost per kg of the mixture as a decimal?
Practice 19medium
A fraction becomes 4/5 when 1 is subtracted from both numerator and denominator. When 5 is added to both numerator and denominator, the fraction becomes 5/6. Find the original fraction.
Practice 20medium
The sum of a decimal number and its reciprocal is 2.9. If the decimal number is greater than 1, what is the decimal number?
10 more practice questions in the Study Panel
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