rational numbers with operations


extended rational number type for javascript

Why I think this lib is great:

  • Representing fractions is not just easy, but it's natural. This is what rational numbers do best. Operations like 0.1 + 0.2 are a pain in js, but using rational numbers, it's just: r(1,10).plus(1,5) === r(3,10)

  • This lib provides a type of object which will work with 1/0 or 0/0 just as well. This is especially useful if you plan to plot values on a graph.

I've got the inspiration for this lib from here: MF105: The extended rational numbers in practice



var r = require('rationals');
// denominator of 1 is optional
r(1) === r(1); // true
r(1,1) === r(1); // true
// all rationals will be always reduced
r(2,4) === r(13,26); // true
r(100,50) === r(2); // true
// chaining works
r(1,2).plus(r(1,3)).minus(r(1,4)).times(r(1,5)).per(r(1,6)) === r(49,70); // true
// my personal favorite aproximation of Pi, from ancient china
r(355,113).val(); // 3.1415929203539825
// you can give floats and they will be converted into rationals
rats(0.4,0.1) == rats(4);


  • a & b are objects created with the rationals() function
  • in the parentheses you have some common aliases for the methods
  • add (plus)


  • subtract (minus, sub)


  • multiply (times, mul)


  • divide (per, div)


  • toString

    Examining an object can be hard, but if you cast it to a string: r(355,113)+'' will return '355/113'.

    So r(625,125).toString() will return '5/1'.

  • display

    Just like toString(), but the numerator will be shown only if it's not 1. That is, integers will appear without a slash symbol and a denominator.

    r(625,125).display() returns '5'.

  • val (value)

    Will return the numerator divided with the denominator.

    r(355,113).val(); //3.1415929203539825

  • compare (value)

    Will return -1, 0 or 1 if the rational is smaller, equal or larger than the rational it is compared to

    r(-999,605).compare(R(272,835)) // -1 r(-966,743).compare(R(-632,198)) // 1 r(-3,9).compare(R(12,-36)) // 0

  • compareAbs (value)

    Same as compare but without signs.

    r(-999,605).compareAbs(R(272,835)) // 1

Good to know

If you provide anything else as the numerator, than an integer, float or a numerica string an exception will be thrown. On the other hand, if you do the same with the denominator, it will be cast to 1. This is because I am lazy, and I do not want to handle wrong values and undefined values differently throwing for the former and casting to 1 for the latter.


npm install rationals

You can use it in the browser with browserify