In parts 1 and 2 of this 3 part challenge, you were asked to develop a Rational number struct. A rational number, as the name suggests, is a ratio between two natural numbers and is usually represented as a fraction in the form 1/2, 5/4, -79/13, etc.

In part 1, the task was to create a C# struct with:

• A constructor which takes two integer parameters,
• two read-only properties Numerator and Denominator which return the numerator and denominator of the fraction respectively, reduced to there lowest common form.
• An override of the ToString() method giving a string representation of the rational number as described in the preceding paragraph.

In part 2, the code was extended to:

• Allow arithmetic operations +, -, *, and / between rational numbers (including unary - operator)
• A Sign property that returned the sign of the fraction.

Before completing this part, make sure your class meets the conditions described in parts 1 and 2. The best way to do this is to complete those challenges first and use the code to start this challenge.

Task

Your task now is to add comparison operators to your class so that rational numbers can be compared with each other using the comparison operators ==, !=, <, <=, > and >=. A further requirement is to implement implicit and explicit conversion to and from the C# decimal value type. For information on how to implement these functionalities, check the Resources tab.

Examples

var r1 = new Rational(1, 2);
var r2 = new Rational(10, 8);
var r3 = new Rational(2, -1);

// Comparison operations
r1 == r2 ➞ false
r2 >= r1 ➞ true
r2 != r3 ➞ true
r1 == new Rational(17/34) ➞ true

// Type conversion
var r4 = (Rational)6.5572m; ➞ explicit conversion from decimal
var d = (decimal)r2;  ➞ explicit conversion to decimal
r4 == 6.5572m ➞ true (implicit conversion to decimal)
r4.ToString() ➞ "16393/2500"

Notes

When overloading comparison operators == and !=, you'll also be expected to override the Equals() and GetHashCode() methods (see the Resources tab for further information).