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 ½, etc we mean the everyday meaning of the 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 rationalNum
Include a constructor with two arguments that can be used to set the member variables of an object to any legitimate value. Also include a constructor that has only a single parameter of type int; call this single parameter whole_number and define the constructor so that the object will be initialized to the rational number whole_number/1. Also 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, -300/-400 are all possible input. The input operator, >>, reads the string 15/32 as
Overload all of the following operators so that they correctly apply to the type rationalNum: ==, <, >, +, -, *, and /.
Write a test program to test your class.
[Hints: Two rational numbers a/b and c/d are equal if a*d equals c*b. If b and d are positive numbers, a/b is less than c/d provided a*d is less than c*b.
- (a/b + c/d) is given by:
Numerator =a*d + c*b
Denominator = b*d
- (a/b – c/d) is given by
Numerator = a*d – c*b
Denominator = b*d
- (a/b * c/d) is given by
Numerator = a*c
Denominator = b*d
- (a/b divided by c/d) is given by
Numerator = a*d
Denominator = b*c
]
The numerators and denominators of rational numbers tend to become large, so it is better to normalize intermediate results. This is achieved by calling a method, normalize(), on the number as shown:
cout << “The sum of the two numbers is: “ << result.normalize() << endl;
Here’s the function that you call to normalize the number. Make it a member function of the rationalNum class. It is called in the driver program to:
- Display each input number read
- Display the results of the arithmetic operations.
rationalNumber rationalNumber::normalize()
{
rationalNum temp;
int x,y,z;
x=numerator;
y=denominator;
z=(x*x < y*y)? (z=x):(z=y);
for (int i=2; i*i<=z*z; i++){
while ((x%i)==0 && (y%i)==0 )
{
x=x/i;
y=y/i;
z=z/i;
}
}
if (y<0){
temp.numerator=-x;
temp.denominator=-y;
}
else {
temp.numerator=x;
temp.denominator=y;
}
return temp;
}
Here’s the output of test run of the driver program using rationalNum objects.
E:neu>rationalMain
Enter the first value: 2/3
Enter the second value: 3/5
value1 is 2/3
Normalized value1: 2/3
value 2 is: 3/5
Normalized value2: 3/5
addition 19/15
Normalized sum: 19/15
subtraction 1/15
Normalized difference: 1/15
multiplication 6/15
Normalized product: 2/5
division 10/9
Normalized quotient: 10/9
is 2/3 < 3/5 ? no
is 2/3 > 3/5 ? yes
is 2/3 = 3/5 ? no
Press any key to continue . . .
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