Subtract Fractions in Perl | Step-by-Step Guide with Code Examples

subtracting fractions with Different Denominators | Rationalising Fractions in Perl

Learning how to subtract fractions in Perl is an important step for junior secondary students who are beginning to combine mathematics with coding. In this tutorial, we'll walk through the process of subtracting fractions with different denominators, explain how to use the LCM (Lowest Common Multiple) method, and show you how to rationalise or canonise fractions before subtraction. By the end, you'll be able to write a simple Perl program to subtract fractions step by step, giving you both a solid maths foundation and practical coding skills to implement libraries like the built-in Perl fractions module.

Like with Adding Fractions in Perl, fractional numbers are also rationalised before subtraction. This means they are put in a form where their denominators become the same. This identical denominator is the LCM of the previous denominators of all the separate fractions.
After this is done, the new numerators can then be subtracted.

Steps for Subtraction of Fractions with Different Denominators - Perl Algorithm

The following steps will guide us in writing our Perl code for subtracting fractions.
Let's illustrate these steps with the example fractional expression ⁷/₄ - ²/₅

Step 1:

Using the Find LCM in Perl class from the Primary Category, find the LCM of the denominators.
⇒ LCM of 4 & 5 = 20

Step 2:

In a turn by turn fashion, divide the found LCM from Step 1 by each denominator, multiplying the quotient by the corresponding numerator.
⇒ ^{((7 x 5) - (2 x 4))}/₂₀
= ^{(35 - 8)}/₂₀

Step 3:

Go ahead and subtract the numerators.
⇒ ²⁷/₂₀

Create a new Perl module file; call it SubtractFraction.pm
Type out the adjoining Perl code for subtracting fractions.

Perl Code for Subtracting Fractions - Module File

package SUBTRACTFRACTION;

BEGIN {
    require Exporter;

    # for the sake of standard
    our $VERSION = 2016.12;

    # Functions and variables to be exported by default
    our @EXPORT_OK = qw(doSubtract);
}

use warnings;
use strict;
use parent "ADDFRACTION";

my $answer;
my (@numerators, @denominators, @new_numerators);
my %fractions;

# simulate an object construct
# takes one argument  -- besides its package name;
# hash reference to array references for numerators and denominators
sub new {
    no warnings "all";

    my $this = shift;
    my $parameters = shift; #this is already a hash reference
    bless $parameters, $this;
    $this->_init($parameters);
    return $this;
}

# Simulate a constructor
sub _init {
    my $self = shift;
    my $aux = shift;

    $fractions{numerators}        = $aux->{numerators};
    $fractions{denominators}    = $aux->{denominators};
    @numerators        = @{$fractions{numerators}};
    @denominators    = @{$fractions{denominators}};

    $answer = 0;
}

# returns an array --
# new numerator and new denominator(LCM) in that order
sub doSubtract {
    # STEPS 1, 2:
    my $call = ADDFRACTION->new(\%fractions);
    my @help = $call->canoniseFraction();
    @new_numerators = @{$help[0]};

    # STEP 3:
    # subtract all transformed numerators
    $answer = $new_numerators[0];
    $answer -= $new_numerators[$_] for 1 .. $#new_numerators;

    return ($answer, $help[1]);
}

1;

Perl Code for Subtracting Fractions - Main Class

#!/usr/bin/perl;
use strict;
use warnings;
use SUBTRACTFRACTION;

# Useful variables
my (@numerators, @denominators, @solutions);
my %fractions;

##
# Subtracting fractions
##
@numerators = (9, 3, 5, 7);
@denominators = (2, 4, 12, 18);
%fractions = (
    numerators     => \@numerators,
    denominators => \@denominators
);

print "\n    Solving:\n";
# Print as fraction
printf("%13u", $_) for @numerators;
printf("\n%12s", " ");
print "-     -      " for 1 .. $#numerators;
printf("%2s\n", "-");
printf("%13u", $_) for @denominators;
print "\n";

# use the SubtractFraction class
my $sub_fract = SUBTRACTFRACTION->new(\%fractions);
@solutions = $sub_fract->doSubtract();

printf("\n%25u\n", $solutions[0]);
printf("%25s\n", "Answer =     -");
printf("%25u\n", $solutions[1]);

print "\n\n";

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