Fractions Calculator
Perform all operations with fractions including addition, subtraction, multiplication, division, and simplification with step-by-step calculations and automatic simplification.
Fraction Operations Calculator
Fraction Examples
Click on these links to see instant calculations with common fraction operations:
Fraction Operations
Fractions represent parts of a whole and are essential in mathematics. This calculator performs all basic operations with proper simplification and step-by-step explanations.
Fraction Operation Rules
- Addition/Subtraction: Find common denominator, then add/subtract numerators
- Multiplication: Multiply numerators together and denominators together
- Division: Multiply by the reciprocal of the second fraction
- Simplification: Divide numerator and denominator by their GCD
Step-by-Step Methods
| Operation | Method | Example |
|---|---|---|
| Addition | Find LCD, convert, add numerators | 1/4 + 1/6 = 3/12 + 2/12 = 5/12 |
| Subtraction | Find LCD, convert, subtract numerators | 3/4 - 1/2 = 3/4 - 2/4 = 1/4 |
| Multiplication | Multiply across: (a/b) × (c/d) = ac/bd | 2/3 × 3/5 = 6/15 = 2/5 |
| Division | Multiply by reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) | 1/2 ÷ 1/4 = 1/2 × 4/1 = 2 |
Common Denominators
For addition and subtraction, fractions need a common denominator. The least common denominator (LCD) is the smallest number that both denominators divide into evenly.
- Cooking: Recipe measurements, ingredient proportions, and scaling
- Construction: Measurements, material calculations, and blueprints
- Education: Math homework, fraction concepts, and problem solving
- Finance: Interest calculations, investment portions, and budgeting
- Crafts: Pattern scaling, material requirements, and proportions
Frequently Asked Questions
How do you add fractions?
To add fractions, find a common denominator, convert both fractions, then add the numerators. For example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and multiply the denominators together: (a/b) × (c/d) = (a×c)/(b×d). Then simplify if possible.
How do you simplify fractions?
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example: 6/8 = 3/4 (dividing by GCD of 2).