Understanding the Math Behind Fraction Division | Maths Explanation for Perl Kids

Perl makes it easy to perform arithmetic operations like dividing fractions. Whether you're simplifying fractions, multiplying them, or coding a math class project, Perl provides clear syntax and powerful tools for beginners and students alike.

Dividing fractions in Perl is a great way to combine coding with math skills. In this tutorial, junior secondary students will learn how to use Perl to divide fractions step-by-step. We'll explore how to invert and multiply fractions, write a Perl class for fraction operations, and understand the logic behind the algorithm.

Division is the inverse operation of multiplication; That is exactly what we'll do with for fractions.
Invert the fractions that come after a division sign, as well as change the division sign to multiplication, and then follow through with multiplication.

Algorithm Steps to Divide Fractions in Perl

Say we are to implement a Perl algorithm to divide the given fractional expression
²¹/₈ ÷ ⁷/₂;

Inverting this will yield
²¹/₈ ÷ ⁷/₂;

Then we can go ahead and multiply.

Create a new Perl module file; Call it DivideFraction.pm.
Type out the adjoining Perl code for dividing fractions.

Note: You can comment out the MultiplyFraction Perl object code in the main class from the previous lesson or simply continue from where it stopped.

So! Perl Fun Practice Exercise - Divide Fractions

As a fun practice exercise, feel free to try out your own fractions with different numerators and denominators, and see how the Perl code divides those fractions.

Perl Code for Dividing Fractions - Module File

package DIVIDEFRACTION;

BEGIN {
    require Exporter;

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

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

use warnings;
use strict;
use parent "MULTIPLYFRACTION";

my (@numerators, @denominators);
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}};
}

# Returns a scalar of the new numerator
sub doDivide {
    my $temp;
    # Invert every other fraction but the first
    for (1 .. $#numerators) {
        $temp = $numerators[$_];
        $numerators[$_] = $denominators[$_];
        $denominators[$_] = $temp;
    }
    %fractions = (
        numerators     => \@numerators,
        denominators => \@denominators
    );
    my $call = MULTIPLYFRACTION->new(\%fractions);
    return $call->doMultiply();
}

1;

Perl Code for Dividing Fractions - Main Class

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

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

##
# Dividing fractions
##
@numerators      = (16, 9, 640, 7);
@denominators = (9, 20, 27, 20);
%fractions = (
    numerators     => \@numerators,
    denominators => \@denominators
);

print "\n    Solving:\n";
# Print as fraction
printf("%13u", $_) for @numerators;
printf("\n%11s", " ");
print "-      /     " for 1 .. $#numerators;
printf("%2s\n", "-");
printf("%13u", $_) for @denominators;
print "\n";

# use the DivideFraction class
my $div_fract = DIVIDEFRACTION->new(\%fractions);
%fraction = %{$div_fract->doDivide()};

printf("\n%25u\n", $fraction{numerator});
printf("%25s\n", "Answer =         -");
printf("%25u\n", $fraction{denominator});

print "\n\n";

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