In this project, a rational number is defined as a fraction in which the numerator and denominator are integers with the denominator being non-zero. Requirements To ensure consistency among solutions each implementation must implement the following requirements. • Your implementation should reflect the definition of a simplified rational number at all times. • A long (integer) is used to represent both the numerator and denominator. • The Rational class must be able to handle both positive and negative numbers. • The rational number must be in simplest form after every operation; that is, 8 6 shall be immediately reduced to 4 3 . In order to simplify a rational number properly, use the the Euclidean Algorithm to determine the greatest common divisor of the two numbers. • All methods that have an object as parameter must be able to handle an input of null. • By definition, the denominator of a fraction cannot be zero since it leads to an undefined value. In Java, this division by zero results in an ArithmeticException; the Rational class must throw an ArithmeticException when division by zero is attempted. • The denominator should be initialized to a sensible and consistent value. The numerator shall be initialized to zero. • The denominator should always be positive leaving the numerator to indicate the sign of the number (positive or negative). • The Rational class shall reside in the default package. Methods There are many methods that one would expect to be supported in a Rational class; unless specified, you will have to implement all of the described methods. Constructors • Rational() o Description: constructs a Rational initializing the value to 0. • Rational(long a) o Parameters: a – the default value for the Rational number. o Description: constructs a Rational initializing the value to 1a . • Rational(long a, long b) throws ArithmeticException o Parameters:
a – an integer specifying the initial value of the numerator.
b – an integer specifying the initial value of the denominator. o Description: constructs a Rational number initializing the object to a b . Accessors • long getNumerator() o Description: returns the current value of the numerator. o Returns: as an accessor method, it only returns the current value of the numerator. • long getDenominator() o Description: returns the current value of the denominator. o Returns: as an accessor method, it only returns the current value of the denominator. Mathematical Operations With each of the following methods, if the input object r is null, you may treat the input as the value zero (0). • Rational add(Rational r) o Parameters: r – the rational number to be added to this rational. o Description: adds r and this, returning a new object with the reduced sum. A common denominator is required to complete this operation. o Returns: returns a new object with the reduced sum. • Rational subtract(Rational r) o Parameters: r – the rational number to be subtracted from this rational. o Description: subtracts r from this, returning a new object with the reduced difference. A common denominator is required to complete this operation. o Returns: returns a new object with the reduced difference. • Rational multiply(Rational r) o Parameters: r – the rational number to be multiplied with thisrational o Returns: returns a new object with the reduced product. • Rational divide(Rational r) throws ArithmeticException o Parameters: r – the rational number that is to divide this rational. o Description: divides this by r, returning a new object with the reduced quotient. o Returns: returns a new object with the reduced quotient. The Greatest Common Divisor Algorithm • private long gcd(long p, long q) o Parameters:
p – an integer.
q – an integer. o Description: determines the greatest common divisor of the two input integers according to the Euclidean Algorithm; a quick implementation is easily available online. o Returns: the (positive) GCD of the two input integers. o Notes: It is easier to implement this method if both integers are positive values. Supplied Methods Besides the interface specification described above, there are other methods that have been provided; feel free to use them as required in your implementation and testing. Do not modify these methods. o Returns: a String representation of this rational value. • int compareTo(Object obj) o Parameters: obj – an object to compare against this rational value. o Description: determines whether the content of obj is smaller (or larger) than this rational value; the result returned is compliant with the Comparable interface that the Rational class implements. o Returns: -1, 0, or 1 when this object is less than, equal, or greater than obj. • boolean equals(Object obj) o Parameters: obj – an object to compare against this rational value. o Description: determines whether the content of obj equals this rational value. • public static void main(String args[]) o Parameters: args – a rational of values that specifies.