Solver Fractions Solver

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Algebra: Numeric Fractions

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Source code of 'Fractions Solver'

This Solver (Fractions Solver) was created by by jim_thompson5910(13794)

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About jim_thompson5910:

==section input
Enter the two fractions and choose which operation to perform on them. Make sure you only enter integers (whole numbers) for each numerator/denominator.

<table><tr><td>*[input input_num1=1]</td><td></td><td>*[input input_num2=3]</td></tr>
<tr><td>______</td><td>*[choice op + - * /]</td><td>______</td></tr>
<tr><td>*[input input_denom1=2]</td><td></td><td>*[input input_denom2=4]</td></tr>
</table>

==section solution

perl

sub mult{

my ($split,@arr1,@arr2,$temp1,$temp2, @hold);

$split=$_[0];
@hold=split(/;/,$split);
@arr1=split(/,/,$hold[0]);
$arr1[2]=$arr1[1];
$arr1[1]="/";

@arr2=split(/,/,$hold[1]);
$arr2[2]=$arr2[1];
$arr2[1]="/";

#print "arr1=@arr1\n\n";

$temp1=$arr1[0]*$arr2[0];
$temp2=$arr1[2]*$arr2[2];

#$temp1=$numer1*$numer2;
#$temp2=$denom1*$denom2;
return ($temp1,"/",$temp2);
}

sub add{

my ($split,@arr1,@arr2, @hold, @tempfrac, $gcf);

$split=$_[0];
@hold=split(/;/,$split);
@arr1=split(/,/,$hold[0]);
$arr1[2]=$arr1[1];
$arr1[1]="/";

@arr2=split(/,/,$hold[1]);
$arr2[2]=$arr2[1];
$arr2[1]="/";

if(($arr1[2]!=$arr2[2])&&(($arr1[2]!=0)&&($arr2[2]!=0)))
{
 for(my $count=1;$count<abs($arr1[2]*$arr2[2]);$count++)
  {if(($arr1[2]%$count==0)&&($arr2[2]%$count==0))
    {$gcf=$count;}
  }

my $lcm=($arr1[2]*$arr2[2])/$gcf;
my $temp=$lcm/$arr1[2];

$exported_lcm=$lcm;
$exported_gcf=$gcf;

$arr1[0]=($lcm/$arr1[2])*$arr1[0];
$arr2[0]=($lcm/$arr2[2])*$arr2[0];

$arr1[2]=($lcm/$arr1[2])*$arr1[2];
$arr2[2]=($lcm/$arr2[2])*$arr2[2];
}
$tempfrac1[0]=$arr1[0]+$arr2[0];
$tempfrac2[0]=$arr1[2];
return ($tempfrac1[0],"/",$tempfrac2[0]);
}

sub subtract{

my ($split,@arr1,@arr2, @hold, @tempfrac, $gcf);

$split=$_[0];
@hold=split(/;/,$split);
@arr1=split(/,/,$hold[0]);
$arr1[2]=$arr1[1];
$arr1[1]="/";

@arr2=split(/,/,$hold[1]);
$arr2[2]=$arr2[1];
$arr2[1]="/";

if(($arr1[2]!=$arr2[2])&&(($arr1[2]!=0)&&($arr2[2]!=0)))
{
 for($count=1;$count<abs($arr1[2]*$arr2[2]);$count++)
  {if(($arr1[2]%$count==0)&&($arr2[2]%$count==0))
    {$gcf=$count;}
  }
my $lcm=($arr1[2]*$arr2[2])/$gcf;
my $temp=$lcm/$arr1[2];

$exported_lcm=$lcm;
$exported_gcf=$gcf;

$arr1[0]=($lcm/$arr1[2])*$arr1[0];
$arr2[0]=($lcm/$arr2[2])*$arr2[0];

$arr1[2]=($lcm/$arr1[2])*$arr1[2];
$arr2[2]=($lcm/$arr2[2])*$arr2[2];
}
$tempfrac1[0]=$arr1[0]-$arr2[0];
$tempfrac2[0]=$arr1[2];
return ($tempfrac1[0],"/",$tempfrac2[0]);
}

sub reduce{

my (@arr1, @original_arr1, $flag);

#$arr1[0]=$_[0];
#$arr1[1]="/";
#$arr1[2]=$_[1];
@arr1=@_;
$arr1[2]=$arr1[1];
$arr1[1]="/";

@original_arr1=@arr1;

$flag=$_[2];

if($arr1[0]==0)
{return $arr1[0];}

if($arr1[2]!=0)
{
$store=$arr1[0]/$arr1[2];

if($store>0)
{
  $arr1[0]=abs($arr1[0]);
  $arr1[2]=abs($arr1[2]);
}

if(($store<0)&&($arr1[2]<0))
{
  $arr1[0]=0-$arr1[0];
  $arr1[2]=abs($arr1[2]);
}

if($arr1[0]%$arr1[2]==0)
{
  if($flag==1)
   {$arr1[0]=$arr1[0]/$arr1[2];
   return $arr1[0];}

if($flag==2)
   {$arr1[0]=$arr1[0]/$arr1[2];
   $arr1[2]=1;
   return ($arr1[0],"/",$arr1[2]);}
#  if($flag==0)
#   {return $quotient;}

}

for (my $i=abs($arr1[0]*$arr1[2]); $i>1; $i--)
{
 if (($arr1[0]%$i==0)&&($arr1[2]%$i==0))
    {
       $arr1[0]/=$i;
       $arr1[2]/=$i;
       my $j=$i;

}
}

if($original_arr1[0]==$arr1[0])
{$exported_no_reduce=1;}

return ($arr1[0],"/",$arr1[2]);
}

sub invert{

my(@arr1,$temp);

@arr1=@_;

$temp=$arr1[0];
$arr1[0]=$arr1[1];
$arr1[1]=$temp;

return ($arr1[0], "/", $arr1[1]);
}

sub divide{

my ($split,@arr1,@arr2,$temp1,$temp2, @hold);

$split=$_[0];
@hold=split(/;/,$split);
@arr1=split(/,/,$hold[0]);
$arr1[2]=$arr1[1];
$arr1[1]="/";

@arr2=split(/,/,$hold[1]);
$arr2[2]=$arr2[1];
$arr2[1]="/";

#print "arr1=@arr1\n\n";

$temp1=$arr1[0]*$arr2[2];
$temp2=$arr1[2]*$arr2[0];

#$temp1=$numer1*$numer2;
#$temp2=$denom1*$denom2;
return ($temp1,"/",$temp2);
}

$in1="$input_num1/$input_denom1";
$in2="$input_num2/$input_denom2";

@in_array1=split(/\//,$in1);
@in_array2=split(/\//,$in2);

##################################################################

if($op eq '+')
{
@sum=add("$in_array1[0],$in_array1[1];$in_array2[0],$in_array2[1]");

$fact_num1=$exported_lcm/$in_array1[1];
$fact_num2=$exported_lcm/$in_array2[1];

if($fact_num1!=1)
{$fact1="(".$exported_lcm/$in_array1[1]."/".$exported_lcm/$in_array1[1].")";
$fact_exp1="Multiply {{{$in1}}} by {{{$fact1}}}";
$mult1="".($exported_lcm/$in_array1[1])*$in_array1[0]."/".($exported_lcm/$in_array1[1])*$in_array1[1]."";
$mult_exp1="Multiply {{{$in1}}} and {{{$fact1}}} to get {{{$mult1}}}";}
else
{$mult1=$in1;}
if($fact_num2!=1)
{$fact2="(".$exported_lcm/$in_array2[1]."/".$exported_lcm/$in_array2[1].")";
$fact_exp2="Multiply {{{$in2}}} by {{{$fact2}}}";
$mult2="".($exported_lcm/$in_array2[1])*$in_array2[0]."/".($exported_lcm/$in_array2[1])*$in_array2[1]."";
$mult_exp2="Multiply {{{$in2}}} and {{{$fact2}}} to get {{{$mult2}}}";}
else
{$mult2=$in2;}

print "

{{{$in1+$in2}}} Start with the given expression

if($in_array1[1]!=$in_array2[1])
{
print "

In order to add these two fractions, these fractions need to have a common denominator.

In order to do that, we simply find that the LCM of $in_array1[1] and $in_array2[1] is $exported_lcm (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)

Now we need to get each denominator to $exported_lcm

if($fact_num1!=1)
{

print "

{{{$fact1($in1)+$in2}}} $fact_exp1

{{{$mult1+$in2}}} $mult_exp1

";
}

if($fact_num2!=1)
{

print "

{{{$mult1+$fact2($in2)}}} $fact_exp2

{{{$mult1+$mult2}}} $mult_exp2

";
}
}
else
{$exported_lcm=$in_array1[1];}

print "

Since both fractions have a common denominator of $sum[2], we can now combine the fractions

{{{(",($exported_lcm/$in_array1[1])*$in_array1[0],"+",($exported_lcm/$in_array2[1])*$in_array2[0],")/$sum[2]}}} Combine the fractions

{{{",($exported_lcm/$in_array1[1])*$in_array1[0]+($exported_lcm/$in_array2[1])*$in_array2[0],"/$sum[2]}}}  Add the numerators

{{{$in1+$in2=@sum}}}

@final_fraction=@sum;
}

elsif($op eq '-')
{
@difference=subtract("$in_array1[0],$in_array1[1];$in_array2[0],$in_array2[1]");

$fact_num1=$exported_lcm/$in_array1[1];
$fact_num2=$exported_lcm/$in_array2[1];

print "

{{{$in1-$in2}}} Start with the given expression

if($in_array1[1]!=$in_array2[1])
{
print "

In order to subtract these two fractions, these fractions need to have a common denominator.

Now we need to get each denominator to $exported_lcm

if($fact_num1!=1)
{

print "

{{{$fact1($in1)-$in2}}} $fact_exp1

{{{$mult1-$in2}}} $mult_exp1

";
}

if($fact_num2!=1)
{

print "

{{{$mult1-$fact2($in2)}}} $fact_exp2

{{{$mult1-$mult2}}} $mult_exp2

";
}
}
else
{$exported_lcm=$in_array1[1];}

print "

Since both fractions have a common denominator of $difference[2], we can now combine the fractions

{{{(",($exported_lcm/$in_array1[1])*$in_array1[0],"-",($exported_lcm/$in_array2[1])*$in_array2[0],")/$difference[2]}}} Combine the fractions

{{{",($exported_lcm/$in_array1[1])*$in_array1[0]-($exported_lcm/$in_array2[1])*$in_array2[0],"/$difference[2]}}} Subtract the numerators

{{{$in1-$in2=@difference}}}

";
@final_fraction=@difference;
}

elsif($op eq '*')
{
@product=mult("$in_array1[0],$in_array1[1];$in_array2[0],$in_array2[1]");

print "

{{{($in1)($in2)}}} Start with the given expression

print "

In order to multiply these fractions, simply multiply the numerators and denominators separately like this:

{{{($in_array1[0]*$in_array2[0])/($in_array1[1]*$in_array2[1])}}} Multiply the numerators $in_array1[0] and $in_array2[0]. Place them as the numerator. Multiply the denominators $in_array1[1] and $in_array2[1]. Place them as the denominator

{{{",$in_array1[0]*$in_array2[0],"/",$in_array1[1]*$in_array2[1],"}}} Now multiply

{{{($in1)($in2)=@product}}}

";
@final_fraction=@product;
}

elsif($op eq '/')
{
@quotient=divide("$in_array1[0],$in_array1[1];$in_array2[0],$in_array2[1]");

print "

{{{($in1)/($in2)}}} Start with the given expression

@inverted_in2=invert($in_array2[0],$in_array2[1]);

print "

In order to divide these fractions, first we need to flip the second fraction {{{$in2}}} to get {{{@inverted_in2}}}.

Now multiply the first fraction {{{$in1}}} by the second fraction {{{@inverted_in2}}}

{{{($in1)(@inverted_in2)}}}

Now simply multiply the numerators and denominators separately like this:

{{{($in_array1[0]*$in_array2[1])/($in_array1[1]*$in_array2[0])}}} Multiply the numerators $in_array1[0] and $in_array2[1]. Place them as the numerator. Multiply the denominators $in_array1[1] and $in_array2[0]. Place them as the denominator

{{{",$in_array1[0]*$in_array2[1],"/",$in_array1[1]*$in_array2[0],"}}} Now multiply

{{{($in1)/($in2)=@quotient}}}

";
@final_fraction=@quotient;
}

else
{print "WRONG SELECTION!!";}

$final_fraction_string="@final_fraction";
$final_fraction_string=~s/\s//g;
$final_fraction[1]=$final_fraction[2];
pop(@final_fraction);

@reduced_final=reduce(@final_fraction);

if($exported_no_reduce!=1)
{
print "

If want to reduce the fraction, {{{$final_fraction_string}}} reduces to {{{@reduced_final}}} (note: click <a href=http://www.algebra.com/algebra/homework/NumericFractions/reduce-fraction.solver>here</a> if you need help with reducing fractions)

";
}

==section output

==section check
  angle=40 angle1=50