Fraction Calculator
Perform arithmetic operations with fractions, mixed numbers, and decimals. Add, subtract, multiply, and divide fractions with step-by-step solutions.
Calculator
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How It Works
How Fraction Calculations Work
Fraction calculations follow specific mathematical rules for each operation.
Addition & Subtraction
a/b + c/d = (ad + bc) / bd
Find common denominator, then add numerators
a/b - c/d = (ad - bc) / bd
Find common denominator, then subtract numerators
Multiplication & Division
a/b × c/d = ac / bd
Multiply numerators and denominators
a/b ÷ c/d = ad / bc
Multiply by reciprocal of second fraction
Simplification Process
1. Find the Greatest Common Divisor (GCD) of numerator and denominator
2. Divide both numerator and denominator by the GCD
3. The result is the simplified fraction in lowest terms
Examples
Fraction Calculation Examples
Addition Example
1/4 + 1/6
Common denominator: 12
3/12 + 2/12 = 5/12
Result: 5/12
Multiplication Example
2/3 × 3/4
Multiply: (2×3)/(3×4) = 6/12
Simplify: 6/12 = 1/2
Result: 1/2
Division Example
3/4 ÷ 1/2
Multiply by reciprocal: 3/4 × 2/1
Calculate: (3×2)/(4×1) = 6/4
Result: 3/2 or 1½
Mixed Number Example
2¼ + 1⅓
Convert: 9/4 + 4/3
Add: 27/12 + 16/12 = 43/12
Result: 3⁷⁄₁₂
Compare
Fraction vs Decimal Comparison
| Aspect | Fractions | Decimals |
|---|---|---|
| Precision | Exact | Approximate |
| Calculation | More Complex | Simpler |
| Representation | Ratio Form | Place Value |
| Common Use | Math, Cooking | Money, Science |
When to Use Fractions
- • Exact measurements in cooking
- • Mathematical proofs and equations
- • When precision is critical
- • Representing parts of a whole
When to Use Decimals
- • Money calculations
- • Scientific measurements
- • Quick approximations
- • Calculator operations
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