Fractions #

For calculations with fractions, math.js supports a Fraction data type. Fraction support is powered by fraction.js. Unlike numbers and BigNumbers, fractions can store numbers with infinitely repeating decimals, for example 1/3 = 0.3333333..., which can be represented as 0.(3), or 2/7 which can be represented as 0.(285714).

Usage #

A Fraction can be created using the function fraction:

math.fraction('1/3')   // Fraction, 1/3
math.fraction(2, 3)    // Fraction, 2/3
math.fraction('0.(3)') // Fraction, 1/3

And can be used in functions like add and multiply like:

math.add(math.fraction('1/3'), math.fraction('1/6'))      // Fraction, 1/2
math.multiply(math.fraction('1/4'), math.fraction('1/2')) // Fraction, 1/8

Note that not all functions support fractions. For example trigonometric functions doesn’t support fractions. When not supported, the functions will convert the input to numbers and return a number as result.

Most functions will determine the type of output from the type of input: a number as input will return a number as output, a Fraction as input returns a Fraction as output. Functions which cannot determine the type of output from the input (for example math.evaluate) use the default number type number, which can be configured when instantiating math.js. To configure the use of fractions instead of numbers by default, configure math.js like:

// Configure the default type of number: 'number' (default), 'BigNumber', or 'Fraction'
math.config({
  number: 'Fraction'
})

// use the expression parser
math.evaluate('0.32 + 0.08') // Fraction, 2/5

Support #

The following functions support fractions:

• Arithmetic functions: abs, add, ceil, cube, divide, dotDivide, dotMultiply, fix, floor, gcd, mod, multiply, round, sign, square, subtract, unaryMinus, unaryPlus.
• Construction functions: fraction.
• Relational functions: compare, deepEqual, equal, larger, largerEq, smaller, smallerEq, unequal.
• Utils functions: format.

Conversion #

Fractions can be converted to numbers and vice versa using the functions number and fraction. When converting a Fraction to a number, precision may be lost when the value cannot represented in 16 digits.

// converting numbers and fractions
const a = math.number(0.3)                       // number, 0.3
const b = math.fraction(a)                       // Fraction, 3/10
const c = math.number(b)                         // number, 0.3

// loosing precision when converting to number: a fraction can represent
// a number with an infinite number of repeating decimals, a number just
// stores about 16 digits and cuts consecutive digits.
const d = math.fraction('2/5')                   // Fraction, 2/5
const e = math.number(d)                         // number, 0.4