Question
Define a class for 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 and so on we mean the everyday fraction, not the integer division this expression would 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 member variables of an object to any legitimate values. Also include a constructor that has only a single parameter of type int ; call this single parameter wholeNumber and define the constructor so that the object will be initialized to the rational number wholeNumber /1. Include a default constructor that initializes an object to 0 (that is, to 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 /. Write a test program to test your lass. 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 .
Answer
C++ program code:
//header section
#include <iostream>
#include <cmath>
using namespace std;
//Create a class name, Rational
class Rational
{
private:
//Declare variables
int numerator;
int denominator;
public:
//Construtor with arguments
Rational(int num = 0, int den = 1)
{
numerator = num;
denominator = den;
normalize();
}
//The normalize function is defined to normalize the rational
//number by ensuring the denominator is positive and reducing
//the fraction to its simplest form.
void normalize()
{
if (denominator < 0)
{
numerator *= -1;
denominator *= -1;
}
int gcd =__gcd(abs(numerator), denominator);
numerator /= gcd;
denominator /= gcd;
}
//The operator<< function overloads the insertion operator
//to output the rational number in the form "numerator/denominator".
friend ostream& operator<<(ostream& os, const Rational& rational)
{
os << rational.numerator << "/" << rational.denominator;
return os;
}
//The operator>> function overloads the extraction operator
//to input the rational number in the form "numerator/denominator" and normalize it.
friend istream& operator>>(istream& is, Rational& rational)
{
char slash;
is >> rational.numerator >> slash >> rational.denominator;
rational.normalize();
return is;
}
//The comparison operators (==, <, <=, >, >=) are overloaded
//to compare two rational numbers based on their values.
bool operator==(const Rational& other) const
{
return (numerator == other.numerator) && (denominator == other.denominator);
}
bool operator<(const Rational& other) const {
return (numerator * other.denominator) < (denominator * other.numerator);
}
bool operator<=(const Rational& other) const {
return (*this < other) || (*this == other);
}
bool operator>(const Rational& other) const {
return !(*this <= other);
}
bool operator>=(const Rational& other) const {
return !(*this < other);
}
//The arithmetic operators (+, -, *, /) are overloaded to perform addition,
//subtraction, multiplication, and division on rational numbers.
Rational operator+(const Rational& other) const {
int num = (numerator * other.denominator) + (other.numerator * denominator);
int den = denominator * other.denominator;
return Rational(num, den);
}
Rational operator-(const Rational& other) const {
int num = (numerator * other.denominator) - (other.numerator * denominator);
int den = denominator * other.denominator;
return Rational(num, den);
}
Rational operator*(const Rational& other) const {
int num = numerator * other.numerator;
int den = denominator * other.denominator;
return Rational(num, den);
}
Rational operator/(const Rational& other) const {
int num = numerator * other.denominator;
int den = denominator * other.numerator;
return Rational(num, den);
}
};
int main()
{
//Create two Rational objects, r1 and r2, are created with initial values.
Rational r1(1, 2);
Rational r2(3, 4);
cout << "r1: " << r1 << endl;
cout << "r2: " << r2 << endl;
//Call the methods and output
cout << "r1 == r2: " << boolalpha << (r1 == r2) << endl;
cout << "r1 < r2: " << boolalpha << (r1 < r2) << endl;
cout << "r1 <= r2: " << boolalpha << (r1 <= r2) << endl;
cout << "r1 > r2: " << boolalpha << (r1 > r2) << endl;
cout << "r1 >= r2: " << boolalpha << (r1 >= r2) << endl;
Rational sum = r1 + r2;
Rational difference = r1 - r2;
Rational product = r1 * r2;
Rational quotient = r1 / r2;
cout << "Sum: " << sum << endl;
cout << "Difference: " << difference << endl;
cout << "Product: " << product << endl;
cout << "Quotient: " << quotient << endl;
return 0;
}
Output of the program code:
r1: 1/2
r2: 3/4
r1 == r2: false
r1 < r2: true
r1 <= r2: true
r1 > r2: false
r1 >= r2: false
Sum: 5/4
Difference: -1/4
Product: 3/8
Quotient: 2/3