Write a Fraction class– that is, write your own class that will represent a fraction in your program. Each variable of type Fraction represents a single fraction. That means that the class should have at least two data fields that should be private: the numerator and the denominator of the fraction. The class also must have the following public class methods:

•Fraction(int n, int d); // constructor that defines a fraction n/d

•Fraction(); // constructor that defines a default fraction of 0/1

•Fraction(Scanner s); // constructor that defines a fraction via Scanner input

•double toDecimal(); // returns the decimal value of the fraction

•String toString(); // returns the string form of the fraction

"numerator" if denominator is 1

"numerator/denominator (decimal, with three decimal places)" otherwise

•int getNumerator(); // returns the numerator of the fraction

•int getDenominator(); // returns the denominator of the fraction

•Fraction plus(Fraction f); // returns fraction + parameter

•Fraction minus(Fraction f); // returns fraction - parameter

•Fraction times(Fraction f); // returns fraction * parameter

•Fraction divides(Fraction f); // returns fraction / parameter

You have been provided a private method:

•int[] simplifyFraction(int[] f); // returns simplified version of parameter

Using this method, all constructors should make sure that the fraction is in reduced form. You may not change the public API –that is, any methods not listed above must be made private

You will also have to write a program to test your Fraction class.

The following output is an example run:

== F1 ==

Enter numerator: 1

Enter denominator: 2

== F2 ==

Enter numerator: 3

Enter denominator: 5

F1: 1/2 (0.500)

F2: 3/5 (0.600)

F1+F1: 1

F2+F2: 6/5 (1.200)

F1+F2: 11/10 (1.100)

F2+F1: 11/10 (1.100)

F1-F1: 0

F2-F2: 0

F1-F2: - 1/10 (-0.100)

F2-F1: 1/10 (0.100)

F1*F1: 1/4 (0.250)

F2*F2: 9/25 (0.360)

F1*F2: 3/10 (0.300)

F2*F1: 3/10 (0.300)

F1/F1: 1

F2/F2: 1

F1/F2: 5/6 (0.833)

F2/F1: 6/5 (1.200)

F1*F1-F2: -7/20 (-0.350)

The program should use the Scanner constructor, the plus/minus/times/divides methods (as opposed to directly computing the outputs), and implicitly the toString method.

Here is the base code provided:

package edu.wit.cs.comp1000;

// TODO : document this class

public class PA9a {

/**

* Program execution point:

* input two fractions via the keyboard

* (using the Scanner constructor),

* output the two fractions, all pairwise

* {+ - * /} operations, and the first squared

* minus the second

*

* @param args command-line arguments (ignored)

*/

public static void main(String[] args) {

// TODO : write your code here

}

}