Fractions 7.2.1

There is a newer version of this package available.
See the version list below for details.
dotnet add package Fractions --version 7.2.1
NuGet\Install-Package Fractions -Version 7.2.1
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package.
<PackageReference Include="Fractions" Version="7.2.1" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add Fractions --version 7.2.1
#r "nuget: Fractions, 7.2.1"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package.
// Install Fractions as a Cake Addin
#addin nuget:?package=Fractions&version=7.2.1

// Install Fractions as a Cake Tool
#tool nuget:?package=Fractions&version=7.2.1


This package contains a data type to calculate with rational numbers. It supports basic mathematic operators such as:

  • addition
  • subtraction
  • multiplication
  • division
  • remainder
  • ..

The fraction data type implements operator overloads and implicit type conversion for convenience.


You can implicitly cast int, uint, long, ulong or BigInteger to Fraction:

Fraction a = 3;  // int
Fraction b = 4L; // long
Fraction c = new BigInteger(3);
// ..

You can explicitly cast decimal and double to Fraction:

var a = (Fraction)3.3m; // decimal
var b = (Fraction)3.3;  // double

You can explicitly cast from Fraction to any supported data type (int, uint, long, ulong, BigInteger, decimal, double). However, be aware that an OverflowException will be thrown, if the target data type's boundary values are exceeded.


There a three types of constructors available:

  • new Fraction (<value>) for int, uint, long, ulong, BigInteger, decimal and double.
  • new Fraction (<numerator>, <denominator>) using BigInteger for numerator and denominator.
  • new Fraction (<numerator>, <denominator>, <reduce>) using BigInteger for numerator and denominator + bool to indicate if the resulting fraction shall be normalized (reduced).

Static creation methods

  • Fraction.FromDecimal(decimal)
  • Fraction.FromDouble(double)
  • Fraction.FromDoubleRounded(double)
  • Fraction.FromString(string) (using current culture)
  • Fraction.FromString(string, IFormatProvider)
  • Fraction.FromString(string, NumberStyles, IFormatProvider)
  • Fraction.TryParse(string, out Fraction) (using current culture)
  • Fraction.TryParse(string, NumberStyles, IFormatProvider, out Fraction)

Creation from double

The double data type stores its values as 64bit floating point numbers that comply with IEC 60559:1989 (IEEE 754) standard for binary floating-point arithmetic. double cannot store some binary fractions. For example, 1/10, which is represented precisely by .1 as a decimal fraction, is represented by .0001100110011... as a binary fraction, with the pattern 0011 repeating to infinity. In this case, the floating-point value provides an imprecise representation of the number that it represents:

var value = Fraction.FromDouble(0.1);
/* Returns 3602879701896397/36028797018963968
 * which is 0.10000000000000000555111512312578 */ 

You can use the Fraction.FromDoubleRounded(double) method to avoid big numbers in numerator and denominator. But please keep in mind that the creation speed is significantly slower than using the pure value from Fraction.FromDouble(double). Example:

var value = Fraction.FromDoubleRounded(0.1);
// Returns 1/10 which is 0.1 

Creation from string

The following string patterns can be parsed:

  • [+/-]n where n is an integer. Examples: +5, -6, 1234, 0
  • [+/-]n.m where n and m are integers. The decimal point symbol depends on the system's culture settings. Examples: -4.3, 0.45
  • [+/-]n/[+/-]m where n and m are integers. Examples: 1/2, -4/5, +4/-3, 32/100 Example:
var value = Fraction.FromString("1,5", new CultureInfo("de-DE"))
// Returns 3/2 which is 1.5

You should consider the TryParse methods when reading numbers as text from user input. Furthermore it is best practice to always supply a culture information (e.g. CultureInfo.InvariantCulture). Otherwise you will sooner or later parse wrong numbers because of different decimal point symbols or included Thousands character.


You can convert a Fraction to any supported data type by calling:

  • .ToInt32()
  • .ToUInt32()
  • .ToInt64()
  • .ToUInt64()
  • .ToBigInteger()
  • .ToDecimal()
  • .ToDouble()
  • .ToString() (using current culture)
  • .ToString(string) (using format string and the system's current culture)
  • .ToString(string,IFormatProvider)

If the target's data type boundary values are exceeded the system will throw an OverflowException.


var rationalNumber = new Fraction(1, 3);
var value = rationalNumber.ToDecimal();
// result is 0.33333
Console.WriteLine(Math.Round(value, 5));

String format

Character Description
G General format: <numerator>/<denominator> e.g. 1/3
n Numerator
d Denominator
z The fraction as integer
r The positive remainder of all digits after the decimal point using the format: <numerator>/<denominator> or string.Empty if the fraction is a valid integer without digits after the decimal point.
m The fraction as mixed number e.g. 2 1/3 instead of 7/3

Note: The special characters #, and 0 like in #.### are not supported. Convert the Fraction to decimal if you want to display rounded decimal values.


var value = new Fraction(3, 2);
// returns 1 1/2
Console.WriteLine(value.ToString("m", new CultureInfo("de-DE")));

Mathematic operators

The following mathematic operations are supported:

  • .Reduce() returns a normalized fraction (e.g. 2/41/2)
  • .Add(Fraction) returns the sum of (a + b)
  • .Subtract(Fraction) returns the difference of (a - b)
  • .Multiply(Fraction) returns the product of (a * b)
  • .Divide(Fraction) returns the quotient of (a / b)
  • .Remainder(Fraction) returns the remainder (or left over) of (a % b)
  • .Invert() returns an inverted fraction (same operation as (a * -1))
  • .Abs() returns the absolute value |a|
  • Fraction.Pow(Fraction, int) returns a base raised to a power (a ^ exponent) (e.g. 1/10^(-1) → 10/1)

As extension method:

  • FractionExt.Sqrt(this Fraction, int) returns the square root, specifying the precision after the decimal point.


 var a = new Fraction(1, 3);
 var b = new Fraction(2, 3);
 var result = a * b;
 // returns 2/9 which is 0,2222...

Equality operators

Fraction implements the following interfaces:

  • IEquatable<Fraction>,
  • IComparable,
  • IComparable<Fraction>

Please note that .Equals(Fraction) will compare the exact values of numerator and denominator. That said:

var a = new Fraction(1, 2, true);
var b = new Fraction(1, 2, false);
var c = new Fraction(2, 4, false);

// result1 is true
var result1 = a == a;

// result2 is true
var result2 = a == b;

// result3 is false
var result3 = a == c;

You have to use .IsEquivalentTo(Fraction) if want to test non-normalized fractions for value-equality.

Under the hood

The data type stores the numerator and denominator as BigInteger. Per default it will reduce fractions to its normalized form during creation. The result of each mathematical operation will be reduced as well. There is a special constructor to create a non-normalized fraction. Be aware that Equals relies on normalized values when comparing two different instances.

Build from source

Build status

Required software frameworks

  • .Net Core 6.0 SDK

Required build tools

Please run:

dotnet tool install fake-cli -g

to install fake as global tool. On Linux you may have to add the following lines into your .profile or .bashrc file:

if [ -d "$HOME/.dotnet/tools" ] ; then

Fractions uses the great FAKE DSL for build tasks. To build the solution, simply start the build.cmd on Windows or the shell script on Unix.

Product Compatible and additional computed target framework versions.
.NET net5.0 was computed.  net5.0-windows was computed.  net6.0 was computed.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  net7.0-android was computed.  net7.0-ios was computed.  net7.0-maccatalyst was computed.  net7.0-macos was computed.  net7.0-tvos was computed.  net7.0-windows was computed.  net8.0 was computed.  net8.0-android was computed.  net8.0-browser was computed.  net8.0-ios was computed.  net8.0-maccatalyst was computed.  net8.0-macos was computed.  net8.0-tvos was computed.  net8.0-windows was computed. 
.NET Core netcoreapp2.0 was computed.  netcoreapp2.1 was computed.  netcoreapp2.2 was computed.  netcoreapp3.0 was computed.  netcoreapp3.1 was computed. 
.NET Standard netstandard2.0 is compatible.  netstandard2.1 is compatible. 
.NET Framework net461 was computed.  net462 was computed.  net463 was computed.  net47 was computed.  net471 was computed.  net472 was computed.  net48 was computed.  net481 was computed. 
MonoAndroid monoandroid was computed. 
MonoMac monomac was computed. 
MonoTouch monotouch was computed. 
Tizen tizen40 was computed.  tizen60 was computed. 
Xamarin.iOS xamarinios was computed. 
Xamarin.Mac xamarinmac was computed. 
Xamarin.TVOS xamarintvos was computed. 
Xamarin.WatchOS xamarinwatchos was computed. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.
  • .NETStandard 2.0

    • No dependencies.
  • .NETStandard 2.1

    • No dependencies.

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GitHub repositories (2)

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Version Downloads Last updated
7.7.1 1,354 5/6/2024
7.7.0 1,847 4/17/2024
7.6.1 502 4/15/2024
7.6.0 408 4/13/2024
7.5.0 220 4/12/2024
7.4.1 3,201 3/31/2024
7.4.0 275 3/31/2024
7.3.0 637,954 10/1/2023
7.2.1 8,082,566 12/11/2022
7.2.0 302,353 11/9/2022
7.1.0 1,387,965 2/20/2022
7.0.0 7,013,394 10/6/2021
6.0.0 378,092 2/18/2021
5.0.1 10,052 11/13/2020
5.0.0 1,457 11/13/2020
4.0.1 24,491,099 6/3/2019
4.0.0 1,668 6/3/2019
3.0.1 297,904 5/1/2017
3.0.0 2,031 5/1/2017
2.0.1 4,550 10/29/2015
2.0.0 2,081 10/29/2015
1.2.0 2,429 1/14/2015
1.1.0 3,230 2/16/2014
1.0.1 2,545 11/16/2013 2,130 4/21/2013
1.0.0 2,467 4/14/2013