Fraction calculator

How to use the fraction calculator

1. Choose an operation: add, subtract, multiply, divide, or simplify.
2. Enter the numerator and denominator for each fraction.
3. The simplified result and its decimal value appear as soon as every field is filled in.
4. Toggle 'Show step-by-step' to see the full calculation.

Common uses

• Homework help: verify fraction arithmetic and follow the working to understand the method
• Cooking and baking: scale a recipe by multiplying each amount by 3/2, then convert an awkward result such as 9/8 cup into tablespoons
• Turning an answer into a percentage for a grade or survey: the result shows its decimal value, and you can convert it to a percentage from there. The math tools guide walks through recipe scaling and homework checks.

Technical specification

• Algorithm or formula: a/b + c/d = (a·(L/b) + c·(L/d)) / L with L = lcm(b, d) (subtraction likewise); a/b × c/d = ac / bd; a/b ÷ c/d = ad / bc. Every result is divided by the greatest common divisor, found with Euclid's algorithm (Euclid, Elements, Book VII, Propositions 1 and 2).
• Browser API or library: Pure JavaScript integer arithmetic on BigInt, so intermediate products stay exact. No external library.
• Input limits: Whole-number numerators and denominators within the safe integer range (up to 2^53 - 1). Denominator must be non-zero. Decimal input such as 1.5 shows an error; enter it as a fraction (3/2).
• Output: Simplified fraction (numerator over denominator), decimal equivalent (up to 6 decimal places, or exponential notation for very small or very large values), and optional step-by-step working.
• Known limitations: Mixed-number input must use a slash-separated improper form. Continued fractions and complex rational expressions are not supported.

Frequently asked questions

What is the simplest form of a fraction?

A fraction is in its simplest form when the numerator and denominator share no common factor other than 1. For example, 4/8 simplifies to 1/2 because both 4 and 8 are divisible by 4. The tool divides both values by their greatest common divisor (GCD) to find the simplest form.

How do you add fractions with different denominators?

To add fractions with different denominators, first find the least common multiple (LCM) of the denominators. Convert each fraction so it has that denominator, then add the numerators. For example, 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12.

Is this fraction calculator free?

Yes. The tool is completely free to use with no registration, no account, and no payment required.

Is my data sent to a server?

All calculations run locally in JavaScript in your browser. Our servers are not involved at any point.