Fraction Calculator — Add, Subtract, Multiply & Divide Fractions | CalculHub
Fraction Calculator
Add, subtract, multiply, or divide fractions. Results are automatically simplified.
Result
Fraction Calculator — Add, Subtract, Multiply & Divide Fractions
A Fraction Calculator helps you perform arithmetic operations on fractions instantly and accurately. Whether you're a student solving math homework, a parent helping your child with K-12 assignments, or a professional dealing with ratios and proportions, this tool simplifies any fraction operation — and automatically reduces results to their simplest form.
Fractions are used everywhere: cooking recipes (½ cup, ¾ teaspoon), measurements (3/8 inch), financial ratios, probability calculations, and more. Knowing how to add, subtract, multiply, and divide fractions is a fundamental mathematical skill.
Fraction Operations — Quick Reference
| Operation | Method | Example |
|---|---|---|
| Addition (a/b + c/d) | (a×d + c×b) / (b×d), then simplify | 1/2 + 1/3 = 5/6 |
| Subtraction (a/b − c/d) | (a×d − c×b) / (b×d), then simplify | 3/4 − 1/4 = 1/2 |
| Multiplication (a/b × c/d) | (a×c) / (b×d), then simplify | 2/3 × 3/4 = 1/2 |
| Division (a/b ÷ c/d) | (a×d) / (b×c), then simplify | 3/4 ÷ 1/2 = 3/2 |
How to Simplify Fractions (Finding GCD)
A fraction is simplified (in lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it.
Example: Simplify 12/18. GCD(12, 18) = 6. So 12/18 = 2/3.
This calculator uses the Euclidean algorithm to find the GCD automatically, ensuring all results are in their simplest form.
Frequently Asked Questions — Fraction Calculator
How do you add fractions with different denominators?
To add fractions with different denominators (unlike fractions), find the Least Common Denominator (LCD), convert both fractions to equivalent fractions with that LCD, then add the numerators. This calculator handles all of that automatically.
What is a proper vs improper fraction?
A proper fraction has the numerator smaller than the denominator (e.g., 3/4). An improper fraction has the numerator equal to or larger than the denominator (e.g., 5/3). An improper fraction can also be written as a mixed number (1 and 2/3).
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%.
What happens when you divide by zero?
Division by zero is undefined in mathematics. A fraction with a denominator of 0 (like 5/0) does not have a valid value. This calculator will display an error if you enter 0 as a denominator.