.NET 1.1+

Rational Number Arithmetic

Standard arithmetic uses integers or floating-point values for operands and results. Rational numbers, or fractions, are not amongst the standard data types. In this article, we will create a structure for fractions and add arithmetic functionality.

Rational Numbers

A rational number is a value that can be expressed as the ratio of two integer values. Such a number can be written as a fraction containing the two integers, one above the other, separated by a horizontal line. For example, ¼, ½ or ¾. The two numbers are called the numerator and denominator; the numerator appearing at the top of the fraction and the denominator at the bottom.

The use of rational numbers for arithmetic has some benefits over the use of decimal values. The main advantage is one of accuracy. With decimal values, rounding errors can occur in small numbers due to the manner in which the values are stored. This can be seen in the following sample code. Although the initial value is divided and then multiplied by the same number, the result is not the same as the original value. If rational numbers were used, this rounding problem would not be introduced.

decimal d = 1;
d /= 3;
d *= 3;

Console.WriteLine(d);   // Outputs "0.9999999999999999999999999999"

Creating the RationalNumber Structure

In this article we will develop a new structure to hold and manipulate rational numbers. The RationalNumber structure could just as easily be created as a class. However, in this case a structure is preferred so that rational numbers exhibit the behaviour of value types, rather than reference types.

For simplicity in this article, the RationalNumber structure will be created in a console application project. You may wish to create the collection in a class library instead for use within your own projects. To begin, create a new console application named "RationalNumberDemo". Add a new class file to the project named "RationalNumber".

The new code class will contain the standard declaration for a class. Replace this with the following structure definition.

struct RationalNumber
{
}

Creating the Properties

The RationalNumber structure requires two properties. These are the integer values representing the numerator and the denominator of the fraction. Each will be a read-only property as the setting of these values will be restricted to the constructor.

To add the properties, add the following code to the structure:

private int _numerator;
private int _denominator;

public int Numerator
{
    get { return _numerator; }
}

public int Denominator
{
    get { return _denominator; }
}