# Answered Essay: In a language that supports operator overloading, build support for rational numbers. Each number should be repres

In a language that supports operator overloading, build support for rational numbers. Each number should be represented internally as a (numerator, denominator) pair in simplest form, with a positive denominator. Your code should support unary negation and the four standard arithmetic operators. Also, create a conversion routine that accepts two floating-point parameters – a value and an error bound-and returns the simplest (smallest denominator) rational number within the given error bound of the given value. The application must be submitted as a NetBeans project or Microsoft Visual Studio (VS 2013 or VS 2015) project which includes the source codes of your program. In addition to the NetBeans project or Microsoft Visual Studio project, use Microsoft Word to provide OLNY ONE assignment/user-documentation file. Documentation should include: A report which clearly describes the design and description of your software components. A logical flow diagram describes the logical flow structure of the application using any diagramming/graphic software such as Microsoft Visio. A logical flow diagram for every method, functions, and procedures defined in the application using any diagramming/graphic software such as Microsoft Visio. A description of any input files to test the application. (a file with valid data and a file with invalid data). A detailed instruction of how the program can be compiled and executed. Screenshots of execution sessions processing valid inputs and invalid inputs.

//Rational.java
public class Rational
{

private int numerator;
private int denominator;

//constructors
Rational()
{
numerator = 0;
denominator = 1;
}
Rational(int num, int den)
{
numerator = num;
denominator = den;
}

//getters
public int getNumerator()
{
return numerator;
}

public int getDenominator()
{
return denominator;
}

//modifiers
public void setNumerator(int num)
{
numerator = num;
}

public void setDenominator(int den)
{
denominator = den;
}

public String toString()
{
return numerator + “/” + denominator;
}

private int gcd(int num, int den)
{
int r;
while(den != 0)
{
r = num % den;
num = den;
den = r;
}
return num;
}

{
int n;
int d;
n = (numerator * f.denominator) + (f.numerator * denominator);
d = denominator * f.denominator;
return new Rational(n/gcd(n, d),d/gcd(n, d));
}

//subtract 2 rational numbers
public Rational sub(Rational f)
{
int n;
int d;
n = (numerator * f.denominator)
– (f.numerator* denominator);
d= denominator * f.denominator;
return new Rational(n/gcd(n, d),d/gcd(n, d));
}

//multiply 2 rational numbers
public Rational mul(Rational f)
{
int n;
int d;
n = numerator * f.numerator;
d = denominator * f.denominator;
return new Rational(n/gcd(n, d),d/gcd(n, d));
}

public Rational div(Rational f)
{
int n;
int d;
n = numerator * f.denominator;
d = f.denominator * numerator;
return new Rational(n/gcd(n, d),d/gcd(n, d));
}
}

—————————————————————————————————————-

/**
* The java program TestRational that tests
* the methods of Rational class
* */
//TestRational.java
public class TestRational
{
public static void main(String[] args)
{
//create two objects of type Rational
Rational r1=new Rational(1, 2);
Rational r2=new Rational(1, 2);

//print to console
System.out.println(“Rational,r1 = ”
+r1.toString());
System.out.println(“Rational,r2 = ”
+r2.toString());

System.out.println(“Subtraction of two rational numbers”);
//calling sub method
System.out.println(r1.sub(r2));
System.out.println(“Multiplication of two rational numbers”);
//calling mul method
System.out.println(r1.mul(r2));
System.out.println(“Division of two rational numbers”);
//calling div method
System.out.println(r1.div(r2));
}
}

—————————————————————————————————————-

Sample Output:

Rational,r1 = 1/2
Rational,r2 = 1/2
1/1
Subtraction of two rational numbers
0/1
Multiplication of two rational numbers
1/4
Division of two rational numbers
1/1

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