Fraction Calculator
Add, Subtract, Multiply & Divide Fractions Instantly
📚 Understanding Fractions – A Complete Guide
A fraction represents a part of a whole. It consists of two numbers: the numerator (top number) and the denominator (bottom number). The numerator tells you how many parts you have, while the denominator tells you how many equal parts make up the whole. For example, in the fraction ¾, 3 is the numerator and 4 is the denominator — meaning you have 3 out of 4 equal parts.
➕ How to Add Fractions
Adding fractions requires a common denominator. Follow these steps:
- Find the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly (also called the LCM).
- Convert each fraction to an equivalent fraction with the LCD as the denominator. Multiply both numerator and denominator by the appropriate factor.
- Add the numerators while keeping the denominator the same.
- Simplify the result by dividing both numerator and denominator by their greatest common divisor (GCD).
Example: ¼ + ⅙ → LCD of 4 and 6 is 12 → ³⁄₁₂ + ²⁄₁₂ = ⁵⁄₁₂
➖ How to Subtract Fractions
Subtraction follows the same principle as addition — you need a common denominator before subtracting the numerators:
- Find the LCD of both denominators.
- Convert both fractions to equivalent fractions.
- Subtract the second numerator from the first.
- Simplify the result using the GCD.
Example: ⅔ − ¼ → LCD of 3 and 4 is 12 → ⁸⁄₁₂ − ³⁄₁₂ = ⁵⁄₁₂
✖️ How to Multiply Fractions
Multiplication is straightforward — no common denominator needed:
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the resulting fraction.
Pro Tip: You can cross-cancel before multiplying to make simplification easier. Look for common factors between any numerator and any denominator.
Example: ⅔ × ¾ = (2×3)/(3×4) = ⁶⁄₁₂ = ½
➗ How to Divide Fractions
Division uses the "Keep-Change-Flip" method:
- Keep the first fraction as is.
- Change the division sign to multiplication.
- Flip the second fraction (take its reciprocal — swap numerator and denominator).
- Multiply as usual and simplify.
Example: ⅔ ÷ ¾ → ⅔ × ⁴⁄₃ = ⁸⁄₉
🔄 Mixed Numbers & Improper Fractions
A mixed number combines a whole number with a proper fraction (e.g., 2½). An improper fraction has a numerator larger than its denominator (e.g., ⁵⁄₂). To convert between them:
- Mixed to Improper: Multiply the whole number by the denominator, add the numerator, and place over the original denominator.
- Improper to Mixed: Divide the numerator by the denominator — the quotient is the whole number, and the remainder becomes the new numerator.
Our calculator above automatically handles mixed numbers and displays results in both improper fraction and mixed number formats.
🎯 Tips for Simplifying Fractions
- Always find the GCD (Greatest Common Divisor) of the numerator and denominator.
- Divide both by the GCD to get the simplest form.
- A fraction is fully simplified when the numerator and denominator have no common factors other than 1.
- Use the Euclidean algorithm for large numbers: repeatedly subtract the smaller from the larger until you reach the GCD.
❓ Frequently Asked Questions
What if the denominator is zero?
A fraction with a denominator of zero is undefined in mathematics. Our calculator will alert you if you attempt to divide by zero.
Can I use negative fractions?
Yes! You can enter negative values in the whole number or numerator fields. The calculator handles negative fractions correctly and normalizes the sign.
How accurate is the decimal conversion?
The decimal equivalent is displayed with up to 8 decimal places of precision, which is more than sufficient for most practical applications.
Is this fraction calculator free to use?
Absolutely! This tool is 100% free and works directly in your browser with no downloads, sign-ups, or ads required.
