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Assignment - Objects

Create a class called Rational for performing arithmetic with fractions. You will write this class to conform to the following specifications.

• The class has two attributes: numerator and denominator.
• Here is an example of the use of the constructor for this class.

  $fraction = Rational->new(numerator => 3, denominator => 4);

Methods

Implement the following methods:

• gcd()is a method which returns the greatest common divisor of the object’s numerator and denominator. If either the numerator or the denominator is zero, return zero. Example of use: $divisor = $fraction->gcd();

• numerator() to set and get the numerator attribute. (See page 273 for information about get-set methods.)

• denominator() will set and get the denominator attribute.

• reduce() reduces the rational number to lowest term using this algorithm:

  1. Find the GCD of the numerator and the denominator.
  2. If it is non-zero, divide numerator and denominator by GCD.

  This method changes the object’s attributes; it does not return a value.

• add() adds the rational number to another rational number. It returns a rational numer, reduced to lowest terms. Example of use: $fraction3 = $fraction1->add($fraction2);

  Algorithm: Where this Rational is a/b and the addend is c/d: if the denominators are equal then the result is (a+c)/b, otherwise ((a*d)+(b*c))/(b*d). Reduce this result to lowest terms.

• subtract() subtracts the rational number given as its argument from the current rational number. It returns a rational number, reduced to lowest terms. Example of use: $fraction3 = $fraction1->subtract($fraction2);. Thus, if $fraction1 had the value 3/4 and $fraction2 had the value 1/2, the result in $fraction3 would be 1/4.

  Algorithm 1: Where this rational number is a/b and the minuend is c/d, if the denominators are equal then the result is (a-c)/b, otherwise ((a*d)-(b*c))/(b*d). Reduce this result to lowest terms.

  Algorithm 2: Where this rational number is a/b and the minuend is c/d, create a new Rational with value -c/d. Calculate (a/b)+(-c/d) by using the add()s method.

• multiply() multiplies the rational number given as its argument by the current rational number. It returns the result, reduced to lowest terms. Example of use: $fraction3 = $fraction1->multiply($fraction2);

  Algorithm: Where this rational number is a/b and the multiplicand is c/d, calculate (a/b)*(c/d) as (a*c)/(b*d). Reduce this result to lowest terms.

• divide() divides the current rational number by the rational number given as its argument. It returns the result, reduced to lowest terms. Example of use: $fraction3 = $fraction1->divide($fraction2); In this example, if $fraction1 has the value 2/5 and $fraction2 has the value 3/7, the result in $fraction3 will be 14/15.

  Algorithm 1: Where this rational number is a/b and the divisor is c/d, calculate (a/b)/(c/d) as (a*d)/(b*c). Reduce this result to lowest terms.

  Algorithm 2: Where this rational number is a/b and the divisor is c/d, create a new Rational with value d/c, then calculate (a/b)*(d/c) using the multiply() method.

• to_string() returns the string representation of the rational number in the form numerator / denominator

  .

Reducing Fractions

To reduce a fraction to its lowest terms, you must divide both the numerator and denominator by their greatest common divisor. Here is code that calculates the greatest common divisor. You should copy and paste this into your Rational class.

sub gcd
{
	my $self = shift;
	my $a = $self->{numerator};
	my $b = $self->{denominator};
	my $mod;

	# ensure that both numbers are positive
	$a = -$a if ($a < 0);
	$b = -$b if ($b < 0);

	# avoid division by zero
	if ($a == 0 || $b == 0)
	{
		$b = 0;
	}
	else
	{
		if ($a < $b)	# a must always be greater than b
		{
			($b, $a) = ($a, $b); # swap them
		}
		while (($mod = $a % $b) != 0)
		{
			$a = $b;
			$b = $mod;
		}
	}
	return $b;
}

Testing your Class

You may download test_rational.pl, a program which lets you enter fractions and operations and see the results. (Enter fractions in the form 2/3.)

When You Finish

Email your file Rational.pm to david.eisenberg@evc.edu. The subject line of your email must include your full name, the class name, and the assignment title. Here are two correct examples:

CIT042 - Jane Bloggs - Objects
Objects program, CIT042, Jane Bloggs