Fractions & Decimals

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 Concepts, Conversions, Tricks & Examples

Welcome back to Concept Studies — Because Concepts Matter!
If you’ve followed the previous chapters on Number System and HCF–LCM, then congratulations! You’re now ready for one of the most scoring and important topics for SSC, Banking, Railways, MPSC, UPSC Prelims and all competitive exams:




⭐ Fractions & Decimals

As a student, I used to get confused between conversions, comparisons and operations. But trust me — once you understand the concept core, everything becomes unbelievably easy.

🔹 What is a Fraction?

A fraction represents a part of a whole and has two parts:

             Numerator (Top)
Fraction =  ----------------
             Denominator (Bottom)

Example: 3/4 means three parts out of four equal parts.

Types of Fractions

  • Proper Fraction: Numerator < Denominator → (3/5)
  • Improper Fraction: Numerator > Denominator → (9/4)
  • Mixed Fraction: 2½, 5⅓
  • Like Fractions: Same denominator → (5/9, 2/9)
  • Unlike Fractions: Different denominators → (3/4, 5/6)

🔹 What is a Decimal?

A number with a decimal point, representing tenths, hundredths, thousandths, etc.

Example: 0.5 = 5/10 = 1/2

🔹 Conversion: Fractions ⇆ Decimals (Super Easy!)

Fraction → Decimal

Divide numerator by denominator.

3/4 = 3 ÷ 4 = 0.75
1/8 = 0.125

Decimal → Fraction

Write the decimal over its place value.

0.6 = 6/10 = 3/5
0.125 = 125/1000 = 1/8

🔹 Shortcut Box — Must Remember Fractions

1/2 = 0.5
1/3 = 0.333…
1/4 = 0.25
1/5 = 0.2
1/8 = 0.125
1/16 = 0.0625

🔹 Comparing Fractions – Fastest Exam Trick

Cross Multiplication Method

For fractions a/b and c/d:

If a × d > b × c → a/b is greater 
Which is greater: 3/7 or 4/9?  
3 × 9 = 27  
4 × 7 = 28  
28 > 27 → 4/9 is greater

🔹 Converting Mixed Fractions

Mixed → Improper Whole × Denominator + Numerator

Improper → Mixed Divide numerator by denominator.

🔹 Operations on Fractions

✔ Addition / Subtraction (Unlike Fractions)

LCM of denominators → Convert → Solve

3/4 + 5/6  
LCM = 12  
(9/12 + 10/12) = 19/12

✔ Multiplication

2/3 × 4/5 = 8/15

✔ Division

Multiply by reciprocal.

3/5 ÷ 7/9 = 3/5 × 9/7 = 27/35

🔹 Decimal Operations

✔ Addition/Subtraction

Align decimals vertically.

✔ Multiplication

Multiply normally → Count decimal places.

✔ Division

Shift the decimal to make divisor a whole number.

🔹 Shortcut Box – Decimal % to Fraction

25% = 1/4
12.5% = 1/8
37.5% = 3/8
62.5% = 5/8
75% = 3/4

🔹 Real Exam-Type Questions

  1. Convert 7/12 into decimal.
  2. Which is greater: 5/8 or 7/12?
  3. Convert 0.375 into fraction.
  4. Add: 3/5 + 7/10
  5. Divide: 4/9 ÷ 8/27

🔹 Coming Next (Lesson 6)

In the next post, we will cover:

  • Ratio & Proportion
  • Shortcut ratio tricks
  • Conversion between ratio & fraction
  • Exam-level applications

Stay tuned for the next post — and always remember, Because Concepts Matter!

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