Solver Converting Mixed Fractions to Improper Fractions (and vice versa)

Source code of 'Converting Mixed Fractions to Improper Fractions (and vice versa)'

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==section input

This solver will show you how to convert mixed fractions to improper fractions. Also, it will show you how to convert an improper fractions to a mixed fractions.

Choose which fractions you want to convert: *[choice method mixed-fraction-to-improper-fraction improper-fraction-to-mixed-fraction]

Mixed Fractions to Improper Fractions

If you want to convert a mixed fraction to an improper fraction (for example {{{1&1/2}}} to {{{3/2}}}) then enter the given mixed fraction (make sure to choose the first choice of the drop box)<table>
<tr><td rowspan="2">*[input whole=1]</td>
<td>*[input mixed_num=1]</td></tr>
<tr><td>*[input mixed_denom=2]</td></tr>
</table>OR....

Improper Fractions to Mixed Fractions

If you want to convert from an improper fraction to a mixed fraction (eg {{{5/4}}} ---> {{{1&1/4}}}), enter the improper fraction (make sure to choose the second choice of the drop box)<table>
<tr><td>*[input imp_num=5]</td></tr>
<tr><td>*[input imp_denom=4]</td></tr>
</table>Note: Enter whole numbers only into each box (no decimals or fractions in any one box)

==section solution

perl

### -------------------------- Mixed to Improper

if($method eq "mixed-fraction-to-improper-fraction")
{

my $temp=$whole;
$temp=~s/\-//g;

## Error checking (Mixed Number)

if((($mixed_num=~m/\D/)||($mixed_denom=~m/\D/))||($temp=~m/\D/))
{
 print " Error: Please enter numerical values only ";
 return;
}

print "<h4>Mixed Fractions to Improper Fractions</h4>";

print " Remember, mixed fractions (or mixed numbers) are of the form: ";

print " <pre>";

print " numerator";
print " whole part ----------------";
print " denominator";

print " </pre>";

print " So we can see that: {{{whole_part=$whole}}}, {{{numerator=$mixed_num}}}, and {{{denominator=$mixed_denom}}} ";

print " Now follow these steps to convert the mixed fraction to an improper fraction ";

my $temp_product=$whole*$mixed_denom;
my $temp_sum;

print " Step 1) First, multiply the whole part {{{$whole}}} by the denominator {{{$mixed_denom}}} to get {{{$whole*$mixed_denom=$temp_product}}}. ";

if($whole=~m/\-/)
{
$temp_sum=$temp_product-$mixed_num;
print " Step 2) Now subtract the numerator {{{$mixed_num}}} from that result to get {{{$temp_product-$mixed_num=$temp_sum}}}. This result is the new numerator. The denominator will remain the same. ";
}
else
{
$temp_sum=$temp_product+$mixed_num;
print " Step 2) Now add that result to the numerator {{{$mixed_num}}} to get {{{$temp_product+$mixed_num=$temp_sum}}}. This result is the new numerator. The denominator will remain the same. ";
}

print " Step 3) Place the new numerator {{{$temp_sum}}} over the original denominator {{{$mixed_denom}}} to get {{{$temp_sum/$mixed_denom}}} ";

print " ============================= ";

print " Answer: ";

#print " So the mixed number {{{$whole&$mixed_num/$mixed_denom}}} converts to the improper fraction {{{($temp_sum)/($mixed_denom)}}} ";

print " So, {{{$whole&$mixed_num/$mixed_denom=$temp_sum/$mixed_denom}}}";

}

## improper to mixed
elsif($method eq "improper-fraction-to-mixed-fraction")
{

my $temp=$imp_num;
$temp=~s/\-//g;

## Error checking (Improper)

if($temp=~m/\D/||$imp_denom=~m/\D/)
{
 print " Error: Please enter numerical values only ";
 return;
}

my $new_whole=int($imp_num/$imp_denom);
my $remainder=$imp_num-$new_whole*$imp_denom;

my $temp_num=$new_whole*$imp_denom;

print " {{{$imp_num/$imp_denom}}} Start with the given improper fraction. ";

print " {{{($temp_num+$remainder)/$imp_denom}}} Break up {{{$imp_num}}} to get {{{$temp_num+$remainder}}}. Note: Make sure that the first number is a multiple of the denominator {{{$imp_denom}}} ";

print " {{{$temp_num/$imp_denom+$remainder/$imp_denom}}} Break up the fraction. ";

print " {{{$new_whole+$remainder/$imp_denom}}} Reduce ";

if($imp_num=~m/\-/)
{
 $remainder=~s/\-//g;
 print " {{{-($new_whole+$remainder/$imp_denom)}}} Factor out a -1 ";

}

print " ============================= ";

print " Answer: ";

print " So, {{{$imp_num/$imp_denom=$new_whole&$remainder/$imp_denom}}}";

}

==section output

==section check