Fractional Numbers
As before, fractional numbers can either be Proper (e.g. 2/5), Improper (e.g. 5/2), or Mixed (e.g. 21/2),
Improper to Mixed Fraction Code in Perl
Say we have the fraction 10/3 - which is an improper fraction - we can convert this fraction to a mixed fraction by following a number of steps:
Step 1:
Find the largest number smaller than the numerator (10),
that can divide the denominator - 3 - without remainder.
⇒ 9
Step 2:
Subtract the found number (9) - from Step 1 -
from the numerator (10)
⇒ 10 - 9 = 1;
This yields the whole number.
Step 3:
Divide the found number (9) - from Step 1 -
by the denominator (3)
⇒ 9/3 = 3;
This yields the new numerator.
Step 4:
Reuse the denominator (3) to get our mixed fraction
⇒ 31/3
Create a new perl module file;
call it ImproperToMixed.pm
Type out the adjoining Perl code for converting improper to mixed fractions.
Note: You can comment out the MixedToImproper Perl object code in the main class from the previous lesson or simply continue from where it stopped.
So!
Feel free to try out your own numerator and denominator.
Perl code for ImproperToMixed Module File
package IMPROPERTOMIXED;
BEGIN {
require Exporter;
# for the sake of standard
our $VERSION = 2016.12;
# Inherit from exporter to export functions and variables
our @ISA = qw(Exporter);
# Functions and variables to be exported by default
our @EXPORT_OK = qw(doConvert);
}
use warnings;
use strict;
my ($whole_number, $numerator, $denominator);
# simulate an object construct
# takes two arguments -- besides its name;
# numerator and denominator values
sub new {
no warnings "all";
my $this = shift;
my $parameters = {@_};
bless $parameters, $this;
$this->_init(@_);
return $this;
}
# Simulate a constructor
sub _init {
my $self = shift;
($numerator, $denominator) = @_;
}
# Returns a hash reference of the new whole number and numerator
sub doConvert {
my $new_numerator;
my $whole_number;
# STEP 1:
for (reverse 2 .. $numerator - 1) {
if (($_ % $denominator) == 0) {
# STEP 2:
$new_numerator = $numerator - $_;
# STEP 3:
$whole_number = $_ / $denominator;
last;
}
}
return {numerator => $new_numerator, whole_number => $whole_number};
}
1;
BEGIN {
require Exporter;
# for the sake of standard
our $VERSION = 2016.12;
# Inherit from exporter to export functions and variables
our @ISA = qw(Exporter);
# Functions and variables to be exported by default
our @EXPORT_OK = qw(doConvert);
}
use warnings;
use strict;
my ($whole_number, $numerator, $denominator);
# simulate an object construct
# takes two arguments -- besides its name;
# numerator and denominator values
sub new {
no warnings "all";
my $this = shift;
my $parameters = {@_};
bless $parameters, $this;
$this->_init(@_);
return $this;
}
# Simulate a constructor
sub _init {
my $self = shift;
($numerator, $denominator) = @_;
}
# Returns a hash reference of the new whole number and numerator
sub doConvert {
my $new_numerator;
my $whole_number;
# STEP 1:
for (reverse 2 .. $numerator - 1) {
if (($_ % $denominator) == 0) {
# STEP 2:
$new_numerator = $numerator - $_;
# STEP 3:
$whole_number = $_ / $denominator;
last;
}
}
return {numerator => $new_numerator, whole_number => $whole_number};
}
1;
Algebra Main class
#!/usr/bin/perl;
use strict;
use warnings;
use IMPROPERTOMIXED;
# Useful variables
my ($numerator, $denominator, $whole_number, $solution);
my %fraction;
##
# Convert fractions from Improper to Mixed
##
$numerator = 10;
$denominator = 3;
print "\n Converting from Improper to Mixed the fraction:\n";
# Print as fraction
printf("%55u\n", $numerator);
printf("%55s\n", "-");
printf("%55u\n", $denominator);
# use the ImproperToMixed class
my $imp2mix = IMPROPERTOMIXED->new($numerator, $denominator);
%fraction = %{$imp2mix->doConvert()};
printf("\n%52u\n", $fraction{numerator});
printf("%50s%u%s\n", "Answer = ", $fraction{whole_number}, "-");
printf("%52u\n", $denominator);
print "\n\n";
use strict;
use warnings;
use IMPROPERTOMIXED;
# Useful variables
my ($numerator, $denominator, $whole_number, $solution);
my %fraction;
##
# Convert fractions from Improper to Mixed
##
$numerator = 10;
$denominator = 3;
print "\n Converting from Improper to Mixed the fraction:\n";
# Print as fraction
printf("%55u\n", $numerator);
printf("%55s\n", "-");
printf("%55u\n", $denominator);
# use the ImproperToMixed class
my $imp2mix = IMPROPERTOMIXED->new($numerator, $denominator);
%fraction = %{$imp2mix->doConvert()};
printf("\n%52u\n", $fraction{numerator});
printf("%50s%u%s\n", "Answer = ", $fraction{whole_number}, "-");
printf("%52u\n", $denominator);
print "\n\n";