Restrict Answers to a Fraction

Restricting answers that should reduce to a fraction.

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Complete Code

Download file: RestrictAnswerToFraction.pg

POD for Macro Files

See Also

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'contextFraction.pl', 'PGcourse.pl');

Preamble

These standard macros need to be loaded. 
Context("Fraction-NoDecimals");
Context()->operators->undefine('+', '-', '*', '*', '**', '^');

$a    = random(2, 4);
$b    = random(1, 9);
$c    = random(1, 9);
$den  = $c + $a * $a;
$frac = Compute("$b/$den");
$ans  = $frac->cmp(
    studentsMustReduceFractions => 1,
    strictFractions             => 1,
    strictMinus                 => 1,
    strictMultiplication        => 1
);

Setup

Here we specify that we are using the Fractions-NoDecimals Context, which requires that answers be fractions and not decimals. To ensure that students do the simplification rather than typing the answer without expanding it, we undefine operators other than division (see Restricting Functions and Operators).

Note that because we’ve undefined these operators for all MathObjects, we can’t define the answer as $frac=Compute("$b/($c + $a^2)");. The operators + and ^ are undefined, so we don’t have them available. In this case we do the calculation of the denominator using Perl first, and then use the MathObject to create the answer.

Also note that by default a Fraction will be reduced to lowest terms.

BEGIN_PGML
Find and simplify completely the value of
[`f([$a])`] if [`` f(x) = \frac{[$b]}{[$c] + x^2}. ``]

[`f([$a]) = `] [__]{$ans}

_(Simplify your answer as much as possible, and enter a fraction instead of
a decimal.)_
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.