SSC MTS Fractions & Decimals ā Study Material, 8 PYQs & Practice MCQs | ZestExam
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SSC MTS Fractions & Decimals
Study Material ā 8 PYQs (2019ā2019) Ā· Concept Notes Ā· Shortcuts
SSC MTS Fractions & Decimals is a frequently tested subtopic ā 8 previous year questions from 2019ā2019 papers are included below with concept notes, key rules and shortcut tricks.
If 1/3 of a number is 24, what is 1/4 of that number?
Exam Q 52019Previous Year Pattern
A number when divided by 8 gives a quotient of 12 and remainder 5. Express this number as a decimal when divided by 20.
Exam Q 62019Previous Year Pattern
The ratio of two numbers is 7:5. If their difference is 18, what is the sum of the two numbers expressed as a decimal?
Exam Q 72019Previous Year Pattern
A shopkeeper mixes two types of rice. Type A costs ā¹40 per kg and Type B costs ā¹60 per kg. If he mixes them in the ratio 3:2, what is the cost per kg of the mixture?
Exam Q 82019Previous Year Pattern
The sum of a fraction and its reciprocal is 25/12. If the fraction is greater than 1, what is the fraction?
Concept Notes
Fractions & Decimalsā Rules & Concept
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Core Concept
Read this first ā 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 ā at least one formula appears in every paper
Fraction to Decimal: Numerator Ć· 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 Ć c/d = (ac)/(bd)
Division: a/b Ć· c/d = (ad)/(bc)
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Exam Patterns
What examiners ask ā 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 aĆd and bĆc. If aĆd > bĆc, 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 - 7Ć6 = 42 and 9Ć5 = 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: 4Ć·11 = 0.363636... ā
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 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 aĆd with bĆc
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