📖 What is a Fraction?
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).
Numerator / Denominator
Example: ¾ means 3 parts out of 4 equal parts
🔧 Types of Fractions
- Proper Fraction: Numerator < Denominator (e.g., ⅔)
- Improper Fraction: Numerator ≥ Denominator (e.g., ⁵⁄₃)
- Mixed Number: Whole number + fraction (e.g., 1⅔)
📝 Fraction Operations
1. Adding Fractions
Same denominator: Add numerators, keep denominator
⅕ + ⅖ = ⅗
Different denominators: Find common denominator first
½ + ⅓ = ³⁄₆ + ²⁄₆ = ⁵⁄₆
2. Subtracting Fractions
Same denominator: Subtract numerators, keep denominator
⅘ - ⅕ = ⅗
Different denominators: Find common denominator first
¾ - ½ = ¾ - ²⁄₄ = ¼
3. Multiplying Fractions
Multiply numerators, multiply denominators
⅔ × ⅘ = (2×4)/(3×5) = ⁸⁄₁₅
4. Dividing Fractions
Multiply by the reciprocal
⅔ ÷ ⅘ = ⅔ × ⁵⁄₄ = ¹⁰⁄₁₂ = ⁵⁄₆
💡 Simplifying Fractions
To simplify a fraction, divide numerator and denominator by their Greatest Common Factor (GCF).
Example: Simplify ⁶⁄₈
GCF of 6 and 8 is 2
⁶⁄₈ = (6÷2)/(8÷2) = ¾
GCF of 6 and 8 is 2
⁶⁄₈ = (6÷2)/(8÷2) = ¾
Pro Tips:
- Always simplify your final answer to its lowest terms
- Convert mixed numbers to improper fractions before calculating
- To find a common denominator, multiply the denominators
- For adding/subtracting, find the Least Common Multiple (LCM)
🎯 Real-Life Applications
- Cooking: Measuring ingredients (½ cup, ¾ teaspoon)
- Shopping: Discounts (¼ off, ½ price)
- Construction: Measuring lengths (⅛ inch)
- Time: Quarter hours, half hours
Ready to calculate? Use the calculator above to perform any fraction operation with step-by-step explanations!