Fraction Calculator
Perform fraction operations with ease. Add, subtract, multiply, and divide fractions with step-by-step solutions and automatic simplification.
Fraction Calculator
🔢 Input Fractions
📊 Preview
💡 Quick Tips
- • Fractions are automatically simplified
- • Use negative numbers for negative fractions
- • Mixed numbers show whole + fractional parts
- • Decimal equivalents are shown for reference
Fraction Operations Reference
Addition & Subtraction
1. Find common denominator (LCD)
2. Convert fractions to equivalent fractions
3. Add or subtract numerators
4. Simplify the result
Multiplication
1. Multiply numerators together
2. Multiply denominators together
3. Simplify the result
Division
1. Flip the second fraction (reciprocal)
2. Multiply the fractions
3. Simplify the result
Simplification
1. Find GCD of numerator and denominator
2. Divide both by the GCD
3. Result is the simplified fraction
Understanding Fraction Operations
🔢 Basic Concepts
Numerator: The top number (how many parts you have)
Denominator: The bottom number (total number of parts)
Proper Fraction: Numerator is smaller than denominator (like ½)
Improper Fraction: Numerator is larger than denominator (like ⁵⁄₃)
Mixed Number: Whole number plus a fraction (like 1 ²⁄₃)
⚙️ How Operations Work
Addition/Subtraction: Find common denominator, then add/subtract numerators
Multiplication: Multiply numerators together, denominators together
Division: Multiply by the reciprocal (flip the second fraction)
Simplification: Divide both parts by their greatest common divisor
📚 Study Tips
- • Always simplify your final answer
- • Find the LCD (Least Common Denominator) for addition/subtraction
- • Convert mixed numbers to improper fractions before calculating
- • Check your work by converting to decimals
🎯 Real-World Uses
- • Cooking and recipe measurements
- • Construction and woodworking
- • Time calculations (parts of hours)
- • Financial calculations (portions of money)
💡 Quick Rules
- • Same denominator? Just add/subtract numerators
- • Multiplying? Straight across (num × num, den × den)
- • Dividing? Flip and multiply
- • Always reduce to lowest terms
📖 Step-by-Step Examples
Addition Example: ¼ + ⅓
1. Find LCD: 4 and 3 → LCD = 12
2. Convert: ¼ = ³⁄₁₂, ⅓ = ⁴⁄₁₂
3. Add: ³⁄₁₂ + ⁴⁄₁₂ = ⁷⁄₁₂
4. Simplify: ⁷⁄₁₂ (already simplified)
Division Example: ½ ÷ ¼
1. Flip second fraction: ¼ → ⁴⁄₁
2. Multiply: ½ × ⁴⁄₁
3. Calculate: (1×4)/(2×1) = ⁴⁄₂
4. Simplify: ⁴⁄₂ = 2