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. No data is sent to our servers.

Fraction calculator

Fraction calculator is a math tool that adds, subtracts, multiplies, divides, and simplifies fractions. It returns the result in its lowest terms, shows step-by-step working with GCD and LCM intermediates, and handles improper and mixed fractions. The tool runs in your browser.

Dedicated pages

Operation-specific fraction calculators.

Add fractions calculator

Add fractions with different denominators. Shows the simplified result and step-by-step working. Free, runs in your browser.

Multiply fractions calculator

Multiply two fractions and see the simplified result with step-by-step working. Free, runs in your browser.

Simplify fractions calculator

Simplify any fraction to its lowest terms. Enter numerator and denominator to see the simplified form and step-by-step working. Free, in-browser.

How to use the fraction calculator

Choose an operation: add, subtract, multiply, divide, or simplify.
Enter the numerator and denominator for each fraction.
The simplified result and step-by-step working appear instantly.
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 recipe measurements by multiplying or dividing ingredient fractions
Related tools: Roman numeral converter and percentage calculator

Technical specification

Algorithm or formula: Add and subtract use the LCM of denominators. Multiply uses straight numerator and denominator products. Divide multiplies by the reciprocal. Final simplification divides by GCD computed with Euclid's algorithm.
Browser API or library: Pure JavaScript integer arithmetic. No external library.
Input limits: Numerators and denominators within the safe integer range (up to 2^53). Denominator must be non-zero.
Output: Simplified fraction (numerator over denominator), decimal equivalent, 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. No data is sent to our servers.

Reviewed and tested May 25, 2026.