View of /trunk/webwork/courses/demoCourse/templates/set0/prob1b.pg

    1 ##DESCRIPTION
    2 ##  help for leaning precedence
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('functions')
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 TEXT(&beginproblem);
   18 $showPartialCorrectAnswers = 1;
   19 
   20 
   21 BEGIN_TEXT
   22 This problem will help you learn the rules of precedence, i.e. the order in which
   23 mathematical operations are preformed. You can use parentheses (and also square brackets
   24 [ ] and/or curly braces $LB $RB) if you want to change the normal way operations work.$PAR
   25 
   26 So first let us review the normal way operations are performed.$PAR
   27 
   28 The rules are simple.  Exponentiation is always done before multiplication
   29 and division and multiplication and division are always done before addition
   30 and subtraction. (Mathematically we say exponentiation takes precedence over
   31 multiplication and division, etc.). For example what is 1+2*3? $BR
   32 \{ ans_rule(25) \}
   33 END_TEXT
   34 
   35 $ans = 7;
   36 &ANS(std_num_cmp($ans));
   37 
   38 
   39 BEGIN_TEXT
   40 $BR and what is \( 2\cdot 3^2 \)? $BR
   41 \{ ans_rule(25) \}
   42 END_TEXT
   43 
   44 $ans = 2*3**2;
   45 &ANS(std_num_cmp($ans));
   46 
   47 BEGIN_TEXT
   48 
   49 $BR
   50 Now sometime you want to force things to be done in a different way. This is
   51 what parentheses are used for.  The rule is: whatever is enclosed in
   52 parentheses is done before anything else (and things in the inner most
   53 parentheses are done first).
   54 
   55 For example how do you enter \[ \frac {1+\sin(3)}{2+\tan(4)} \]? Hint: this is a good place to use
   56 [ ]'s and also to use the ${LQ}Preview${RQ} button. $BR
   57 \{ ans_rule(25) \}
   58 END_TEXT
   59 
   60 $ans = (1+sin(3))/(2+tan(4)) ;
   61 &ANS(std_num_cmp($ans));
   62 
   63 BEGIN_TEXT
   64 $BR
   65 Here are some more examples:
   66 
   67 (1+3)9 =36, (2*3)**2 = 6**2 = 36, 3**(2*2) = 3**4 = 81, (2+3)**2 = 5**2 = 25, 3**(2+2) = 3**4 = 81
   68 
   69 $BR
   70 (Here we have used ** to denote exponentiation and you can also use this instead of a ${LQ}caret${RQ} if you want).  Try entering some of these and use the "Preview" button to see the result.  The "correct"
   71 result for this answer blank is 36, but by using the ${LQ}Preview${RQ} button, you can enter whatever
   72 you want and use WeBWorK as a hand calculator.$BR
   73 \{ ans_rule(25) \}
   74 
   75 END_TEXT
   76 
   77 $ans =36;
   78 
   79 &ANS(std_num_cmp($ans));
   80 
   81 BEGIN_TEXT
   82 $BR
   83 
   84 There is one other thing to be careful of.  Multiplication and division have the
   85 same precedence and there are no universal rules as to which should be done first.
   86 For example, what does 2/3*4 mean?  (Note that / is the "division symbol", which
   87 is usually written as a line with two dots, but unfortunately, this "line with
   88 two dots" symbol is not on computer keyboards. Don't think of / as the horizontal
   89 line in a fraction. Ask yourself what 1/2/2 should mean.) WeBWorK and most other
   90 computers read things from left to right, i.e. 2/3*4 means (2/3)*4 or 8/3, IT DOES
   91 NOT MEAN 2/12.  Some computers may do operations from right to left.  If you
   92 want 2/(3*4) = 2/12, you have to use parentheses.  The same thing happens with
   93 addition and subtraction. 1-3+2 = 0 but 1-(3+2) = -4. This is one case where using
   94 parentheses even if they are not needed might be a good idea, e.g. write (2/3)*4
   95 even though you could write 2/3*4. This is also a case where previewing your answer
   96 can save you a lot a grief since you will be able to see what you entered.
   97 
   98 $BR
   99 Enter 2/3*4 and use the Preview button to see what you get.$BR
  100 \{ ans_rule(25) \}
  101 END_TEXT
  102 
  103 $ans = 8/3;
  104 &ANS(std_num_cmp($ans));
  105 
  106 ENDDOCUMENT();        # This should be the last executable line in the problem.