implement an immutable data type rational for

Question

Implement an immutable data type Rational for rational numbers that supports addition, subtraction, multiplication and division.

public class Rational

	Rational(int numerator, int denominator)
Rational	plus(Rational b)	sum of this number and b
Rational	minus(Rational b)	difference of this number and b
Rational	times(Rational b)	product of this number and b
Rational	divides(Rational b)	quotient of this number and b
boolean	equals(Rational that)	is this number equal to that?
String	toString()	string representation

Notes

1. You do not have to worry about testing for overflow, but use as instance variables two long values that represent the numerator and denominator to limit the possibility of overflow.
2. Use Euclid's algorithm to ensure that the numerator and denominator never have any common factors.
3. Include a test client that exercises all of your methods.