Question

C++ and/or using Xcode...

Define a class of rational numbers. A rational number is a number that can be represented as the quotient of two integers. For example, 1/2, 3/4, 64/2, and so forth are all rational numbers. (By 1/2, etc., we mean the everyday meaning of the fraction, not the integer division this expression could produce in a C++ program). Represent rational numbers as two values of type int, one for the numerator and one for the denominator. Call the class Rational.

Include a constructor with two arguments that can be used to set the members variables of an object to any legitimate values. Also include a constructor that has only a single parameter of type int; call the single parameter whole_number and define the constructor so that the object will be initialized to the rational number whole_number/1. Also include a default constructor that initializes an object to 0 (that is, 0/1).

Overload the input and output operators >> and <<. Numbers are to be input and output in the form 1/2, 15/32, 300/401, and so forth. Note that the numerator, the denominator, or both may contain a minus sign, so -1/2, 15/32, and -300/-401 are also possible inputs. Overload all the following operators so that they correctly apply to the type Rational: ==, <, <=, >, >=, +, -, *, and /. Also write a test program to test your class.

(HINTS: Two rational numbers a/b and c/d are equal if a*d equals c*b. If b and d are positive rational numbers, a/b is less than c/d provided a*d is less than c*b. You should include a function to normalize the values stored so that, after normalization, the denominator is positive and the numerator and denominator are as small as possible. For example, after normalization 4/-8 would be represented the same as -1/2. You should also write a test program to test the class.)     

// Display the three values to test cout
    cout << "\nTest1 equals " << test1;
    cout << "\nTest2 equals " << test2;
    cout << "\nTest3 equals " << test3;
// Test our operators
    cout << "\nTest1 * Test2 equals " << test1*test2;
    cout << "\nTest1 / Test3 equals " << test1/test3;
    cout << "\nTest2 + Test3 equals " << test2+test3;
    cout << "\nTest3 - Test1 equals " << test3-test1;
    if (test1 == test2)
        cout << "\nTest1 is equal to Test2";
    if (test1 < test2)
        cout << "\nTest1 is less than Test2";

Answer 1

Rational.h

#ifndef H_Rational
#define H_Rational

#include <iostream>
using namespace std;

//Rational class
class Rational
{
   //private members
   private:
int nm, dm;
//public members
public:
   Rational();
Rational(int n);
Rational(int n,int d);
Rational(const Rational& fx);

void operator=(Rational fx);
Rational operator+(Rational fx);
Rational operator-(Rational fx);
Rational operator*(Rational fx);
Rational operator/(Rational fx);

bool operator==(Rational fx);
bool operator!=(Rational fx);
bool operator<=(Rational fx);
bool operator>=(Rational fx);
bool operator<(Rational fx);
bool operator>(Rational fx);

void simplify();
friend ostream& operator<<(ostream& os,const Rational& ob);
friend istream& operator>>(istream& is,Rational& ob);
};

#endif

Rational.cpp

#include <iostream>
#include<math.h>
#include"Rational.h"
using namespace std;

//default constructor
Rational::Rational()
{
   nm = 0;
   dm = 1;
}

//parameterized constructor
Rational::Rational(int n)
{
   nm = n;
dm = 1;
}

//parameterized constructor
Rational::Rational(int n, int d)
{
   nm = n;
   if(d==0) throw "denominators error";
dm = d;
}

//copy constructor
Rational::Rational(const Rational& t)
{
nm = t.nm;
dm = t.dm;
}

//= operator overloading
void Rational::operator=(Rational fx)
{
nm = fx.nm;
dm = fx.dm;
}

//+ operator overloading
Rational Rational::operator+(Rational fx)
{
   int k, j;

k=fx.dm *dm;
j=fx.nm * dm + fx.dm * nm;
Rational tx(j,k);
tx.simplify();
return tx;
}

//- operator overloading
Rational Rational::operator-(Rational fx)
{
   int j, k;

k=fx.dm *dm;
j=fx.nm * dm - fx.dm * nm;
Rational tx(j,k);
tx.simplify();
return tx;
}

//* operator overloading
Rational Rational::operator*(Rational fx)
{
   int j, k;

   j = fx.nm * nm;
   k = fx.dm *dm;
Rational tx(j,k);
tx.simplify();
return tx;
}

// / operator overloading
Rational Rational::operator/(Rational fx)
{
   int j, k;

   j = fx.dm * nm;
   k = fx.nm * dm;
Rational tx(j,k);
tx.simplify();
return tx;
}

// == operator overloading
bool Rational::operator==(Rational fx)
{
return (nm==fx.nm && dm==fx.dm);
}

// != operator overloading
bool Rational::operator!=(Rational fx)
{
return (nm!=fx.nm || dm!=fx.dm);
}

// <= operator overloading
bool Rational::operator<=(Rational fx)
{
return (nm*fx.dm<=fx.nm*dm);
}

// >= operator overloading
bool Rational::operator>=(Rational fx)
{
return (nm*fx.dm>=fx.nm*dm);
}

// < operator overloading
bool Rational::operator<(Rational fx)
{
return (nm*fx.dm<fx.nm*dm);
}

// > operator overloading
bool Rational::operator>(Rational fx)
{
return (nm*fx.dm>fx.nm*dm);
}

// << operator overloading
ostream& operator<<(ostream& os,const Rational& ob)
{
os<<ob.nm<<"/"<<ob.dm<<"\n";
return os;
}

// >> operator overloading
istream& operator>>(istream& is, Rational& ob)
{
is>>ob.nm>>ob.dm;
return is;
}

//function to simplify the Rational
void Rational::simplify()
{
   int i, j, k;

   j = abs(nm);
   k = abs(dm);

   for(i=j; j%i!=0 || k%i!=0; i--);

   nm = nm/i;
   dm = dm/i;

   if(nm<0 && dm<0 ||dm<0)
   {
       nm = -nm;
       dm = -dm;
   }
}

Main.cpp

#include <iostream>
#include"Rational.h"

using namespace std;

//main function
int main()
{
   Rational test1(2,3), test2(1,3), test3(1,2);

cout << "\nTest1 equals " << test1;
cout << "\nTest2 equals " << test2;
cout << "\nTest3 equals " << test3;
// Test our operators
cout << "\nTest1 * Test2 equals " << test1*test2;
cout << "\nTest1 / Test3 equals " << test1/test3;
cout << "\nTest2 + Test3 equals " << test2+test3;
cout << "\nTest3 - Test1 equals " << test3-test1;
if (test1 == test2)
cout << "\nTest1 is equal to Test2";
if (test1 < test2)
cout << "\nTest1 is less than Test2";

   return 0;
}

Output: