(C++) 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". This is what you will do in this lab assignment.

Class Specification

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 Functions 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 

Required Class Interface

class Rational { private: int numerator; int denominator; public: Rational(); 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 display() const; private: int gcd(int, int); }; 

Required main function

You must use this main function and global functions getRational and displayResult exactly as they are here. You may not change these functions at all. Copy-and-paste these into your main.cpp file and then add the Rational class.

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 << ")"; }