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Problem 6

(Rational Class) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private data of the classthe numerator and the denominator. Provide a constructor that enables an object of this class to be initialized when it is declared. The constructor should contain default values in case no initializers are provided and should store the fraction in reduced form. For example, the fraction \(\frac{2}{4}\) would be stored in the object as 1 in the numerator and 2 in the denominator. Provide public member functions that perform each of the following tasks: a. Adding two Rational numbers. The result should be stored in reduced form. b. Subtracting two Rational numbers. The result should be stored in reduced form. c. Multiplying two Rational numbers. The result should be stored in reduced form. d. Dividing two Rational numbers. The result should be stored in reduced form. e. Printing Rational numbers in the form a/b, where a is the numerator and b is the denominator. f. Printing Rational numbers in floating-point format.

Problem 15

(Tictactoe Class) Create a class Tictactoe that will enable you to write a complete program to play the game of tic-tac-toe. The class contains as private data a 3 -by-3 two-dimensional array of integers. The constructor should initialize the empty board to all zeros. Allow two human players. Wherever the first player moves, place a 1 in the specified square. Place a 2 wherever the second player moves. Each move must be to an empty square. After each move, determine whether the game has been won or is a draw. If you feel ambitious, modify your program so that the computer makes the moves for one of the players. Also, allow the player to specify whether he or she wants to go first or second. If you feel exceptionally ambitious, develop a program that will play three-dimensional tic-tac-toe on a \(4-b y-4-b y-4\) board. [Caution: This is an extremely challenging project that could take many weeks of effort!]

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