📘 Fractions – Complete Concept Guide
Sainik School | RMS | Navodaya | Competitive Exams
1️⃣ What is a Fraction?
A fraction represents a part of a whole.
a / b
a = Numerator (top number)
b = Denominator (bottom number, b ≠ 0)
Example: 3/4 means 3 parts out of 4 equal parts.
2️⃣ Types of Fractions
- Proper Fraction: Numerator < Denominator (3/5, 7/9)
- Improper Fraction: Numerator ≥ Denominator (9/4, 11/6)
- Mixed Fraction: 2 1/3, 5 3/4
- Like Fractions: Same denominator (3/8, 5/8)
- Unlike Fractions: Different denominators (3/4, 5/6)
Mixed → Improper = (Whole × Denominator + Numerator) / Denominator
3️⃣ Operations on Fractions
➕ Addition
1/3 + 1/4 → LCM = 12 → 4/12 + 3/12 = 7/12
➖ Subtraction
5/6 − 1/6 = 4/6 = 2/3
✖ Multiplication
2/3 × 4/5 = 8/15
➗ Division
2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6
Rule: Keep – Change – Flip
4️⃣ Important Concepts
Equivalent Fractions: 1/2 = 2/4 = 5/10
Simplest Form: 12/18 → HCF=6 → 2/3
Reciprocal of 3/5 = 5/3
5️⃣ Fraction to Decimal & Percentage
3/4 = 0.75
3/5 × 100 = 60%
6️⃣ Exam Tricks 🎯
✔ Convert mixed fractions first
✔ Take LCM for unlike fractions
✔ Cancel before multiplying
✔ Always simplify
✔ Cross multiply for comparison
7️⃣ Exercise - 1 (MCQs)
1) 2/3 + 1/4 = ?
Answer: 7/12
2) Equivalent of 3/5
Answer: 6/10
3) Simplest form of 10/20
Answer: 1/2
4) 1 − 5/8 = ?
Answer: 3/8
5) 2/3 × 3/4 = ?
Answer: 1/2 (Corrected)
6) Reciprocal of 2/3
Answer: 3/2
7) Smallest fraction:
Answer: 1/2
8) 3/4 ÷ 1/2 = ?
Answer: 3/2
🔥 Final Revision Box
• Proper → Numerator < Denominator
• Improper → Numerator ≥ Denominator
• Add unlike → Take LCM
• Multiply → Straight multiply
• Divide → Flip & multiply
• Always simplify final answer
