Question

C++

Create a Rational Number (fractions) class like the one in Exercise 9.6 of the textbook. Provide the following capabilities:

1. Create a constructor that prevents a 0 denominator in a fraction, reduces or simplifies fractions (by dividing the numerator and the denominator by their greatest common divisor) that are not in reduced form, and avoids negative denominators.
2. Overload the addition, subtraction, multiplication, and division operators for this class.
3. Overload the relational and equality operators for this class.
4. Provide a function that returns the string representation of the rational number in the form a/b, where a is the numerator and b is the denominator.
5. Provide a function that returns the rational number as a double.

Also provide a main program to test your class.

Answer 1

Here is the c++ code for the above task:

#include <iostream>

using namespace std;

// function to compute gcd of two numbers

int _gcd(int x, int y) {

   x = abs(x);

   y = abs(y);

   if(x % y == 0) return y;

   else return _gcd(y, x % y);

}

// function to simplify the fraction

void simplify(int &n, int &d) {

   int gcd = _gcd(n, d);

   n /= gcd;

   d /= gcd;

   if(d < 0) {

       n = -n;

       d = -d;

   }

}

// Rational number class

class Rational {

   int num; // numerator

   int den; // denominator

   public:

   // constructor

   Rational(int n, int d) {

       if(d != 0) {

           num = n;

           den = d;

           simplify(num, den);

       }

   }

   // getters

   int getNum() {

       return num;

   }

   int getDen() {

       return den;

   }

   // setters

   int setNum(int n) {

       num = n;

   }

   int setDen(int d) {

       den = d;

   }

  

   // overloading operators

   Rational operator+(const Rational& rhs) {

       // make denominator equals to lcm and then add numerator

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       Rational result((lcm / den) * num + (lcm / rhs.den) * rhs.num, lcm);

       return result;

   }

   Rational operator-(const Rational& rhs) {

       // make denominator equals to lcm and then subtract

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       Rational result((lcm / den) * num - (lcm / rhs.den) * rhs.num, lcm);

       return result;

   }

   Rational operator*(const Rational& rhs) {

       // muliply

       Rational result(num * rhs.num, den * rhs.den);

       return result;

   }

   Rational operator/(const Rational& rhs) {

       // divide

       Rational result(num * rhs.den, den * rhs.num);

       return result;

   }

   bool operator==(const Rational& rhs) {

       // check for equlity

       return (num == rhs.num && den == rhs.den);

   }

   bool operator<(const Rational& rhs) {

       // check for less than after making denominator equal

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       return (lcm / den) * num < (lcm / rhs.den) * rhs.num;

   }

   bool operator>(const Rational& rhs) {

       // check for greater than after making denominator equal

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       return (lcm / den) * num > (lcm / rhs.den) * rhs.num;

   }

   bool operator<=(const Rational& rhs) {

       // check for less than or equal to after making denominator equal       

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       return (lcm / den) * num <= (lcm / rhs.den) * rhs.num;

   }

   bool operator>=(const Rational& rhs) {

       // check for greater than or equal to after making denominator equal       

       int lcm = (den * rhs.den) / _gcd(den, rhs.den);

       return (lcm / den) * num >= (lcm / rhs.den) * rhs.num;

   }

   bool operator!=(const Rational& rhs) {

       return !(*this == rhs);

   }

   // function for string representation

   string to_str() {

       return to_string(num) + "/" + to_string(den);

   }

   // function to return rational as double

   double eval() {

       return (double)num / (double)den;

   }

};

// main function to test out class

int main() {

   Rational r1(6, 10);

   cout << "r1 = " << r1.to_str() << endl;

   Rational r2(4, -6);

   cout << "r2 = " << r2.to_str() << endl;

   Rational r3 = r1 + r2;

   cout << "r1 + r2 = " << r3.to_str() << endl;

  

   r3 = r1 - r2;

   cout << "r1 - r2 = " << r3.to_str() << endl;

  

   r3 = r1 * r2;

   cout << "r1 * r2 = " << r3.to_str() << endl;

  

   r3 = r1 / r2;

   cout << "r1 / r2 = " << r3.to_str() << endl;

   cout << "r1 = " << r1.eval() << endl;

   cout << "r2 = " << r2.eval() << endl;

}

Code screenshot:

Sample output: