In Java plz
Constructors, getters Define a class called Rational. A Rational object should have two integer instance variables that store the numerator and denominator. - Write a constructor that takes no arguments and that sets the numerator to 0 and denominator to 1. - Write a function getNumerator() that returns the numerator for the rational number. - Write a function getDenominator() that returns the denominator for the rational number. - Write a second constructor that takes two arguments p and q, and uses them to initialize the instance variables for the numerator and denominator. Rational r= new Rational (10,15); // initializes the number 10/15 Rational s= new Rational () ; // initializes the number 0/1 tostring - Write a tostring method for Rational. This method takes no arguments, and returns the string representation of the rational. For example, the rational number 4/3 should be represented as the string "4/3" (no spaces). - Write a main function. Create some rationals and testing that it works with println is a good idea at this stage. When you call println on an object, the object is converted to a string using its to String method, and the result is what is printed. Reduce 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. It should return a new Rational number that has been reduced. You can use this function to return the GCD of two numbers. public static int findGcd(int n1, int n2){ int gcd=1; for ( int i=1;in1&i=n2;++i){ // Checks if is factor of both integers if (n1%i=0&&n2i=0){ \} gcd=i; 3 3 return gcd; For example: Rational r= new Rational (2,10);// This is 2/10 Rational s=r. reduce(); // Reduce to lowest terms System.out.println(s); // This should print 1/5 Add Write an instance method called add that takes a Rational number as an argument, adds it to this, and returns a new Rational object. This is a pure method and should not modify itself. To add fractions, think back to elementary school. You should make sure that the result of the operation is reduced (by calling the reduce function above) so that the numerator and denominator have no common divisor (other than 1). For example: Rational r= new Rational (1,4); // This is 1/4 Rational s= new Rational (1,4);// This is 1/4 Rational t=radd(s);// add r and s:1/4+1/4=2/4 System.out.println(t); // This should print 1/2 Harmonic In mathematics, the nth Harmonic number is defined as H(n)=1+1/2+1/3++1 So H(1)=1,H(2)=1+1/2,H(3)=1+1/2+1/3, and so on. Write the following functions in Harmonic.java. harmonicDouble Write a recursive function harmonicDouble that takes an integer n and returns (as a double) the nth Harmonic number. // Return the nth harmonic number as a double using recursion public static double harmonicDouble(int n){ \} Hints - Figure out what the first Harmonic number is. This is the base case. - Figure out what the recurrence relationship is. - Write the code. harmonicRational Using the Rational number class we built earlier, write the recursive function harmonicRational that return as a Rational number the nth Harmonic number, again using recursion. Note: harmonicRational calls itself -- it does not call harmonicDouble. // Return the nth harmonic number as an object of the Rational class using recursion public static Rational harmonicRational(int n){
