Fraction Calculator - Add, Subtract, Multiply, Divide
Free fraction calculator. Add, subtract, multiply, and divide fractions with step-by-step solutions. Simplify fractions and convert between mixed numbers and improper fractions.
Find a common denominator: 4
Convert ½ to ²⁄₄
Add: ²⁄₄ + ¾ = ⁵⁄₄
Simplify: ⁵⁄₄ = 1 ¼
Our free fraction calculator performs addition, subtraction, multiplication, and division of fractions with step-by-step explanations. It simplifies results, converts between improper fractions and mixed numbers, and shows decimal equivalents.
How to calculate with fractions
Working with fractions requires understanding a few basic principles:
Adding and subtracting fractions
To add or subtract fractions, they must have the same denominator (the bottom number):
- Find the least common denominator (LCD) — the smallest number both denominators divide into evenly
- Convert each fraction to an equivalent fraction with the LCD
- Add or subtract the numerators (top numbers)
- Keep the denominator the same
- Simplify the result if possible
Example: ½ + ¼ = ²⁄₄ + ¼ = ¾
Multiplying fractions
Multiplication is straightforward:
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result if possible
Example: ½ × ⅔ = ²⁄₆ = ⅓
Dividing fractions
To divide fractions, multiply by the reciprocal:
- Flip the second fraction (find its reciprocal)
- Change the division to multiplication
- Multiply as normal
Example: ½ ÷ ¼ = ½ × ⁴⁄₁ = ⁴⁄₂ = 2
Simplifying fractions
A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify:
- Find the greatest common divisor (GCD) of the numerator and denominator
- Divide both numbers by the GCD
Example: To simplify ⁶⁄₈, find GCD(6,8) = 2, then ⁶⁄₈ = ¾
Mixed numbers and improper fractions
Mixed number: A whole number combined with a fraction (e.g., 2 ½)
Improper fraction: A fraction where the numerator is larger than the denominator (e.g., ⁵⁄₂)
To convert mixed to improper: multiply the whole number by the denominator, add the numerator, keep the denominator.
To convert improper to mixed: divide numerator by denominator, the quotient is the whole number, the remainder is the new numerator.
Common fraction to decimal conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ⅓ | 0.333... | 33.3% |
| ¼ | 0.25 | 25% |
| ⅕ | 0.2 | 20% |
| ⅙ | 0.166... | 16.7% |
| ⅛ | 0.125 | 12.5% |
| ¾ | 0.75 | 75% |
Tips for working with fractions
- Always simplify your final answer
- Check if your answer makes sense (estimation)
- When in doubt, convert to decimals to verify
- Look for common factors before multiplying large numbers
- Use mixed numbers for final answers greater than 1