View of /trunk/NationalProblemLibrary/maCalcDB/setAlgebra01RealNumbers/sw1_2_15b.pg

    1 #DESCRIPTION
    2 ##  Algebra problem: simplifying fraction
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'fraction')
    6 ## hcao tagged and PAID on 2-20-2004
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Basic Algebra')
   10 ## DBsection('Real Numbers')
   11 ## Date('6/3/2002')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('College Algebra')
   15 ## EditionText1('3')
   16 ## AuthorText1('Stewart, Redlin, Watson')
   17 ## Section1('1.2')
   18 ## Problem1('15b')
   19 DOCUMENT();        # This should be the first executable line in the problem.
   20 
   21 loadMacros(
   22 "PG.pl",
   23 "PGbasicmacros.pl",
   24 "PGchoicemacros.pl",
   25 "PGanswermacros.pl",
   26 "PGauxiliaryFunctions.pl"
   27 );
   28 TEXT(beginproblem());
   29 $showCorrectPartialAnswers = 1;
   30 
   31 $n1 = random(2,10,1);
   32 $n2 = random(1,10,1);
   33 $d2 = random(2,10,1);
   34 
   35 BEGIN_TEXT
   36 Add the fractions, and reduce your answer.
   37              \[ \left($n1\div\frac{$n2}{$d2}\right)-\frac{$n2}{$d2} \]
   38 The reduced answer is \{ans_rule(5)\} / \{ans_rule(5)\}
   39 END_TEXT
   40 @factors = ();
   41 @commonfactors = ();
   42 $fac = $d2*$n2;
   43 for($i=2; $i<=($d2*$n2)/2; $i++){
   44   if($fac % $i == 0){
   45     $fac =$fac/$i;
   46     push @factors,$i;
   47                 $i = $i-1;
   48   };
   49 };
   50 $fac = $n1*$d2*$d2-$n2*$n2;
   51 foreach $i (@factors){
   52   if($fac % $i == 0){
   53     $fac = $fac / $i;
   54     push @commonfactors,$i;
   55   };
   56 };
   57 $den = $d2*$n2;
   58 $num = $n1*$d2*$d2-$n2*$n2;
   59 foreach $i (@commonfactors){
   60   $num = $num / $i;
   61   $den = $den / $i;
   62 };
   63 
   64 ANS(num_cmp($num, mode=>"strict"));
   65 ANS(num_cmp($den, mode=>"strict"));
   66 
   67 ENDDOCUMENT();        # This should be the last executable line in the problem.