Fractions & Decimals
SSC GD Exam - Quantitative Aptitude
1. What is a Fraction?
A fraction represents a part of a whole. It is written as:
Fraction = Numerator / Denominator
Example: 3/4
means 3 parts out of 4 equal parts
Numerator → 3
Denominator → 4
Visual Representation
3 colored out of 4 parts
2. Types of Fractions
| Type | Definition | Example |
|---|---|---|
| Proper Fraction | Numerator < Denominator | 3/5 |
| Improper Fraction | Numerator ≥ Denominator | 7/4 |
| Mixed Fraction | Combination of whole number and fraction | 2 ½ |
| Like Fractions | Same denominators | 3/8, 5/8 |
| Unlike Fractions | Different denominators | 2/3, 5/7 |
| Unit Fraction | Numerator = 1 | 1/9 |
3. Conversion Between Mixed & Improper Fractions
Mixed → Improper
a b/c = (a × c) + b / c
Example: 3½ = (3×2)+1 / 2 = 7/2
Improper → Mixed
Divide numerator by denominator
Example: 11/4 = 2¾
11 ÷ 4 = 2 remainder 3
4. Operations on Fractions
| Operation | Rule | Example |
|---|---|---|
| Addition | Make denominators same | ½ + ⅓ = (3+2)/6 = 5/6 |
| Subtraction | Make denominators same | ¾ – ⅖ = (15–8)/20 = 7/20 |
| Multiplication | Multiply numerators and denominators | ⅔ × ¾ = 6/12 = ½ |
| Division | Multiply by the reciprocal | ¾ ÷ ⅖ = ¾ × 5/2 = 15/8 |
5. What is a Decimal?
A decimal is another way to represent fractions using powers of 10.
0.5
= ½
0.25
= ¼
0.75
= ¾
6. Types of Decimals
| Type | Definition | Example |
|---|---|---|
| Terminating Decimal | Ends after some digits | 0.5, 2.75 |
| Non-Terminating Repeating Decimal | Digits repeat infinitely | 0.333…, 2.1212… |
| Non-Terminating Non-Repeating | Digits never repeat (Irrational) | √2 = 1.4142… |
7. Conversion Between Fractions & Decimals
Fraction → Decimal
Divide numerator by denominator
Example: 3/4 = 3 ÷ 4 = 0.75
Decimal → Fraction
Write as per place value
Example: 0.25 = 25/100 = 1/4
8. Comparing Fractions
Method: Make denominators same, then compare numerators
Example: Compare ⅗ and ¾
⅗ = 12/20
¾ = 15/20
Since 12/20 < 15/20 → ¾ is greater
9. Quick Recap - Key Points
Fractions
- • Proper: Numerator < Denominator
- • Improper: Numerator ≥ Denominator
- • Mixed: Whole number + Fraction
- • Like: Same denominators
Decimals
- • Terminating: Ends (0.5, 2.75)
- • Repeating: Digits repeat (0.333…)
- • Non-repeating: Irrational numbers
- • Conversion: Divide for fraction→decimal
10. Practice Questions
Test your knowledge with these practice questions. Click on "View Answer" to check your understanding.
Q1. Convert 3/4 into decimal.
View Answer
3 ÷ 4 = 0.75 ✅
Q2. Convert 0.6 into fraction.
View Answer
0.6 = 6/10 = 3/5 ✅
Q3. Add 1/2 + 1/3.
View Answer
(3+2)/6 = 5/6 ✅
Q4. Subtract 5/8 – 3/8.
View Answer
(5–3)/8 = 2/8 = 1/4 ✅
Q5. Multiply 2/3 × 3/4.
View Answer
(2×3)/(3×4) = 6/12 = 1/2 ✅
Q6. Divide 3/5 ÷ 9/10.
View Answer
3/5 × 10/9 = 30/45 = 2/3 ✅
Q7. Convert 2⅔ into improper fraction.
View Answer
(2×3)+2 = 8/3 ✅
Q8. Convert 11/4 into mixed fraction.
View Answer
2¾ ✅
Q9. Which is greater: 3/5 or 4/7?
View Answer
3/5 = 0.6; 4/7 ≈ 0.571 → 3/5 is greater ✅
Q10. Simplify: ½ + ¼ + ⅛.
View Answer
= 4/8 + 2/8 + 1/8 = 7/8 ✅
Q11. Convert 0.125 into fraction.
View Answer
125/1000 = 1/8 ✅
Q12. If 2/5 of a number = 16, find the number.
View Answer
Number = (16×5)/2 = 40 ✅
Q13. Convert 0.75 into simplest fraction.
View Answer
75/100 = 3/4 ✅
Q14. Find reciprocal of 5/8.
View Answer
Reciprocal = 8/5 ✅
Q15. Express ⅗ as a percentage.
View Answer
(3/5)×100 = 60% ✅
✅ Exam Strategy Tip
🟢 Practice LCM calculation for adding/subtracting fractions quickly
🟢 Memorize common fraction-decimal conversions (½=0.5, ¼=0.25, ¾=0.75)
🟢 For division, remember to multiply by reciprocal
🟢 Use cross-multiplication for comparing fractions quickly
You've completed Fractions & Decimals Concepts!
Courage Tip: Mastering fractions and decimals is fundamental for quantitative aptitude. Practice converting between different forms and performing operations quickly. Remember that fractions represent parts of a whole while decimals provide an alternative representation using powers of 10. Regular practice with real-world problems will help you apply these concepts effectively in competitive exams.
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