fraction.js

Fraction.js supports repeating decimals using parentheses or single quotes to denote the repeating part. This allows for exact rational representation of numbers that would otherwise be imprecise in floating-point.

Supported syntax examples:

• "0.(3)" or "0.'3'" for $0.333...$
• "123.45(6)" for $123.45666...$
• "123.45'6'" for $123.45666...$
• "123.(456)" for $123.456456...$

var f = new Fraction("123.32");
// Dividing by a repeating decimal string
console.log(f.div("33.6(567)"));

You can install fraction.js using npm or yarn, or by cloning the repository directly.

npm

npm install fraction.js

yarn

yarn add fraction.js

Git

git clone https://github.com/rawify/Fraction.js

Depending on your environment, use one of the following methods to include Fraction.js in your project.

Node.js (CommonJS)

const Fraction = require('fraction.js');

ESM (ECMAScript Modules)

import Fraction from 'fraction.js';

Browser (Script Tag)

Include the minified file in your HTML:

<script src="path/to/fraction.min.js"></script>
<script>
  var x = new Fraction("13/4");
</script>

The standard .mod() method in Fraction.js behaves like typical computer science modulo (often resulting in different behavior for negative numbers than pure mathematics).

To achieve the mathematically correct modulo (where the result is always within the range of the divisor), use the following pattern:

new Fraction(a).mod(b).add(b).mod(b)

var a = -1;
var b = 10.99;

// Standard modulo (not mathematically correct for negative congruences)
console.log(new Fraction(a).mod(b)); 

// Mathematically correct modulo
console.log(new Fraction(a).mod(b).add(b).mod(b));

The FractionInput type defines what can be passed into most Fraction methods (like add, sub, equals, etc.). It supports:

• Fraction instance
• number
• bigint
• string (e.g., "1/2")
• [number | bigint | string, number | bigint | string] (a tuple of [numerator, denominator])
• NumeratorDenominator object: { n: number | bigint; d: number | bigint; }

Fraction.js throws exceptions for critical errors such as:

• Parsing errors (invalid input strings)
• Division by zero

Ensure you wrap your logic in try...catch blocks when dealing with untrusted input or mathematical operations that might result in division by zero.

Methods for converting fractions to integers or rounding them.

Fraction.js can convert decimal numbers into precise fraction strings. You can use .toFraction(true) for a mixed number string format (e.g., "1 22/25").

If you are working with imprecise decimals and want to find the closest rational representation within a certain error margin, use .simplify(error) before converting.

// Mixed number string
let x = new Fraction(1.88);
let res = x.toFraction(true); // "1 22/25"

// Simplify with error tolerance
let y = new Fraction(0.33333);
let simplified = y.simplify(0.001).toFraction(); // "1/3"

Use these methods to compare two rational numbers or check divisibility.

Equality and Comparison

• equals(n): Returns true if two rational numbers are equal.
• lt(n): Returns true if the fraction is less than n.
• lte(n): Returns true if the fraction is less than or equal to n.
• gt(n): Returns true if the fraction is greater than n.
• gte(n): Returns true if the fraction is greater than or equal to n.
• compare(n): Returns an integer:
  • < 0: n is greater than the actual number
  • > 0: n is smaller than the actual number
  • = 0: n is equal to the actual number

Divisibility

• divisible(n): Returns true if n divides the current fraction.