CSC 309 Object-Oriented Programming in C++
Homework #5
Due: Feb 7 [Loop], 8 [DL] (1 week)

Write a class called Fraction and an application program which tests the class.  Your job is to write 3 files, completely from scratch.

1. Fraction.h -- header file
2. Fraction.cpp -- implementation file
3. FractApp.cpp -- application file

To set up the header file and implementation file (with macroguard and #include's), review the previous homework assignments.

1. Class Fraction (in "Fraction.h" and "Fraction.cpp")

Fractions are of the form a / b, where a is the numerator and b is the denominator, and a,b are integers (and b is not 0). In addition to the two int data members, provide the following methods (16 class methods and 1 regular function):

• Class methods:
  1. Fraction(int n = 0, int d = 1);
  2. int getNum() const;
  3. int getDenom() const;
  4. Fraction operator+(const Fraction& f2) const; 
  5. Fraction operator-(const Fraction& f2) const;   // binary subtraction
  6. Fraction operator*(const Fraction& f2) const; 
  7. Fraction operator/(const Fraction& f2) const; 
  8. Fraction operator-() const;  // unary minus
  9. bool operator==(const Fraction& f2) const; 
  10. bool operator!=(const Fraction& f2) const; 
  11. bool operator<(const Fraction& f2) const; 
  12. bool operator<=(const Fraction& f2) const; 
  13. bool operator>(const Fraction& f2) const; 
  14. bool operator>=(const Fraction& f2) const;
  15. void reduce(); 
  16. void standardize();
• Regular functions:
  17. ostream& operator<<(ostream& out, const Fraction& f);

Notes on the methods and functions:

• The constructor and two get methods should be straight-forward.  
  As a reminder, the full definition of the constructor (in the implementation file) should not have default values in the parameter.
• Arithmetic operations on fractions are defined by the following rules:
  • a / b + c / d = (ad + bc) / bd
  • a / b - c / d = (ad - bc) / bd
  • a / b * c / d = ac / bd
  • (a / b) / (c / d) = ad / bc (where c/d is not 0)
  • -(a / b) = (-a) / b
• Relational operators should be obvious, after understanding the arithmetic operations. 
  NOTE: Do NOT convert a Fraction to a double in order to compare two Fraction's. That's because a double can express only up to 15 decimal digits, while a Fraction can express numbers of higher precisions.
• The reduce() method modifies 'this' object to a reduced form.  For example, 10/15 ==> 2/3.
  To write this method, you will need to find the greatest common divisor (gcd) of the numerator and denominator.  You are welcome to use the following.  You can put it as a private method (since it will only be called by other member functions, not from outside).

  class Fraction
  {
  public:
    ...
  private:
    ...
    int gcd(int a, int b) const;
  };
  
  int Fraction::gcd(int a, int b) const
  {
    if (b == 0)
      return a;
    else
      return gcd(b, a % b);
  }

• The standardize() method modifies 'this' object to a standardized form (with a positive denominator).  For example,

  2/-3 ==> -2/3
  -2/-3 ==> 2/3

• The output operator (<<) should print the fraction as "a/b" to the parameter out.

2. Application (in "FracApp.cpp")

Write an application which tests all the methods you wrote.  The output of the program should be:

1/3 + 5/8 = 23/24
1/3 - 5/8 = -7/24
1/3 * 5/8 = 5/24
1/3 / 5/8 = 8/15
-(1/3) = -1/3

24/21, after reduce(), 8/7
5/8, after reduce(), 5/8

2/-3, after standardize(), -2/3
-2/-3, after standardize(), 2/3

11/15 < 17/23 is true
11/15 <= 17/23 is true
11/15 > 17/23 is false
11/15 >= 17/23 is false
11/15 == 17/23 is false
11/15 != 17/23 is true

11/15 < 22/30 is false
11/15 <= 22/30 is true
11/15 > 22/30 is false
11/15 >= 22/30 is true
11/15 == 22/30 is true
11/15 != 22/30 is false

Write necessary code to produce this output.  Of course you must create appropriate Fraction objects and call methods to produce the results.
NOTE: There is no interaction with the user in the program.

Submission

• Zip all source files involved (.cpp and .h), and submit the zip file through Course OnLine (COL).