Could you please help me with this Exercise? The language is JAVA. Thank You!
Exercise 11.4 A “rational number” is a number that can be represented as
the ratio of two integers. For example, 2/3 is a rational number, and you can
think of 7 as a rational number with an implicit 1 in the denominator.
The purpose of this exercise is to write a class definition that includes a va-
riety of methods, including constructors, static methods, instance methods,
modifiers, and pure methods:
1. Define a class called Rational. A Rational object should have two
integer instance variables that store the numerator and denominator.
2. Write a constructor that takes no arguments and sets the numerator to
0 and denominator to 1.
3. Write an instance method called printRational that displays a Rational
object in a reasonable format.
11.10 Exercises 199
4. Write a main method that creates a new object with type Rational,
sets its instance variables to the values of your choice, and displays the
object.
5. You now have a minimal testable program. Test it and, if necessary,
debug it.
6. Write a toString method for Rational and test it using println.
7. Write a second constructor that takes two arguments and uses them to
initialize the instance variables.
8. Write an instance method called negate that reverses the sign of a ra-
tional number. This method should be a modifier, so it should be void.
Add lines to main to test the new method.
9. Write an instance method called invert that swaps the numerator and
denominator. It should be a modifier. Add lines to main to test the new
method.
10. Write an instance method called toDouble that converts the rational
number to a double (floating-point number) and returns the result. This
method is a pure method; it does not modify the object. As always, test
the new method.
11. Write an instance method named reduce that reduces a rational number
to its lowest terms by finding the greatest common divisor (GCD) of the
numerator and denominator and dividing through. This method should
be a pure method; it should not modify the instance variables of the
object on which it is invoked.
Hint: Finding the GCD takes only a few lines of code. Search the web
for “Euclidean algorithm”.
12. Write an instance method called add that takes a Rational number as
an argument, adds it to this, and returns a new Rational object. There
are several ways to add fractions. You can use any one you want, but
you should make sure that the result of the operation is reduced so that
the numerator and denominator have no common divisor (other than 1).