Question

13.21 Lab: Rational class

This question has been asked here before, but every answer I have tested did not work, and I don't understand why, so I'm not able to understand how to do it correctly. I need to build the Rational.cpp file that will work with the main.cpp and Rational.h files as they are written.

Rational Numbers

It may come as a bit of a surprise when the C++ floating-point types (float, double), fail to capture a particular value accurately. Certainly double, which is usually stored as a 64-bit value, is far better than the old float, which is only 32 bits, but problems do arise. For example:

float n = 2.0;
float d = 3.0;
cout << precision(17);
cout << n / d << endl;

produces 0.6666668653488159, which is accurate to only 8 decimal places - a bit dirty for a discipline that prides itself on precision!

A solution that is often used when precision is of greatest importance and all of the numbers involved are going to be "rational" (that is, expressible as a 'ratio' of two integers - i.e. a fraction) is to use a custom data type - i.e. a class - that implements fractions, or "rational numbers". You will define the Rational class in this lab assignment.

Class Specification

Write all of your code in the Rational.cpp file.

Write a C++ program that performs the rational number operations addition, subtraction, multiplication and division on two fractions. The program should be written in a single file. You will need to design a "rational number" class named Rational whose value will be a fraction (e.g., 1/128, or 22/7), with appropriate constructors and member functions. A fraction will be specified as a numerator and a denominator - e.g. the pair (8, 109) represents the fraction 8/109. The member variables should be private and accessed using the accessor and mutator functions.

Constructors

Create 3 constructors:

• a constructor with two parameters (numerator and denominator)
• a constructor with one parameter (denominator set to 1)
• a constructor with no parameters (0/1)

Accessor Functions

• add
• subtract
• multiply
• divide
• display

Mutator Function

• simplify

The following are a list of the rules of arithmetic for fractions:

• (a/b) + (c/d) = (ad + bc) / (b*d)
• (a/b) - (c/d) = (ad - bc) / (b*d)
• (a/b) * (c/d) = (ac) / (bd)
• (a/b) / (c/d) = (ad) / (cb)

Note that for this lab, when you perform an operation, you do not need to simplify the resulting fraction, i.e., 4/5 * 5/10 = 20/50. You should not simplify this to 2/5 at this point.

The display function should output the Rational object in the format:

n / d

The simplify function should divide the numerator and denominator by the greatest common divisor. This function should call the private helper function gcd to get the greatest common divisor.

Feel free to use one of the gcd algorithms here: Euclidean algorithm

Required Class Interface

You must use the Rational class declaration exactly as it is provided. The Rational.h file cannot be changed.

Required main function

You must use the main function and global functions getRational and displayResult exactly as they are provided. The main.cpp file cannot be changed.

main.cpp

// Main

#include
#include "Rational.h"
using namespace std;

Rational getRational();
void displayResult(const string &, const Rational &, const Rational&, const Rational&);

int main() {
Rational A, B, result;
int choice;

cout << "Enter Rational A:" << endl;
A = getRational();
cout << endl;

cout << "Enter Rational B:" << endl;
B = getRational();
cout << endl;

cout << "Enter Operation (1 - 4):" << endl
<< "1 - Addition (A + B)" << endl
<< "2 - Subtraction (A - B)" << endl
<< "3 - Multiplication (A * B)" << endl
<< "4 - Division (A / B)" << endl
<< "5 - Simplify A" << endl;
cin >> choice;
cout << endl;

if (choice == 1) {
result = A.add(B);
displayResult("+", A, B, result);
} else if (choice == 2) {
result = A.subtract(B);
displayResult("-", A, B, result);
} else if (choice == 3) {
result = A.multiply(B);
displayResult("*", A, B, result);
} else if (choice == 4) {
result = A.divide(B);
displayResult("/", A, B, result);
} else if (choice == 5) {
A.simplify();
A.display();
} else {
cout << "Unknown Operation";
}
cout << endl;

return 0;
}

Rational getRational() {
int choice;
int numer, denom;

cout << "Which Rational constructor? (Enter 1, 2, or 3)" << endl
<< "1 - 2 parameters (numerator & denominator)" << endl
<< "2 - 1 parameter (numerator)" << endl
<< "3 - 0 parameters (default)" << endl;
cin >> choice;
cout << endl;

if (choice == 1) {
cout << "numerator? ";
cin >> numer;
cout << endl;
cout << "denominator? ";
cin >> denom;
cout << endl;
return Rational(numer, denom);
} else if (choice == 2) {
cout << "numerator? ";
cin >> numer;
cout << endl;
return Rational(numer);
} else {
return Rational();
}
}

void displayResult(const string &op, const Rational &lhs, const Rational&rhs, const Rational &result) {
cout << "(";
lhs.display();
cout << ") " << op << " (";
rhs.display();
cout << ") = (";
result.display();
cout << ")";
}

Rational.h

// Rational class declaration

#ifndef RATIONAL_H
#define RATIONAL_H

#include
using namespace std;

class Rational
{
private:
int numerator;
int denominator;
public:
Rational();
explicit Rational(int);
Rational(int, int);
const Rational add(const Rational &) const;
const Rational subtract(const Rational &) const;
const Rational multiply(const Rational &) const;
const Rational divide(const Rational &) const;
void simplify();
void display() const;
private:
int gcd(int, int) const;
};

#endif

Answer 1

Code For the Rational class along with the implementation of each function.

#include <iostream>

using namespace std;

class Rational{
private:
int numerator;
int denominator;
  
public:
Rational(){
this->numerator=0;
this->denominator=1;
}
  
Rational(int x){
this->numerator=x;
this->denominator=1;
}
  
Rational(int x, int y){
this->numerator=x;
this->denominator=y;
}
  
const Rational add(Rational & );
const Rational subtract(Rational & );
const Rational multiply(Rational & );
const Rational divide(Rational & );
void simplify();
void display() const{
cout<<numerator<<"/"<<denominator<<endl;
};
private:
int gcd(int, int) ;
};

const Rational Rational::add(Rational &r){
int lcm = (this->denominator*r.denominator)/gcd(this->denominator,r.denominator);
  
int result = ((lcm/this->denominator)*this->numerator)+((lcm/r.denominator)*r.numerator);
Rational r1=Rational(result,lcm);
return r1;
}

const Rational Rational::subtract(Rational &r){
int lcm = (this->denominator*r.denominator)/gcd(this->denominator,r.denominator);
  
int result = ((lcm/this->denominator)*this->numerator)-((lcm/r.denominator)*r.numerator);
Rational r1=Rational(result,lcm);
return r1;   
}

const Rational Rational::multiply(Rational &r){
int num = this->numerator*r.numerator;
int den = this->denominator*r.denominator;
Rational r1=Rational(num,den);
return r1;
}

const Rational Rational::divide(Rational &r){
int num = this->numerator*r.denominator;
int den = this->denominator*r.numerator;
Rational r1=Rational(num,den);
return r1;
}

void Rational::simplify(){
int gcm=gcd(this->numerator,this->denominator);
int num=this->numerator/gcm;
int den=this->denominator/gcm;
  
}

int Rational::gcd(int x, int y){
int result = 1;
for(int i =2;i<=x && i<=y ; ++i){
if(x%i==0 && y%i==0){
result = i;
}
}
  
return(result);
}