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

Load the contextFraction.pl for the fraction contexts that it provides.

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

The Fractions-NoDecimals context is selected which requires that answers be fractions and not decimals.

To ensure that students simplify answers, the operators other than division are undefined. Note that since these operators have been undefined for all MathObjects, the answer can not be defined as $frac = Compute("$b / ($c + $a^2)"). The operators + and ^ are undefined, so they are not available for the problem author either. So 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. This can be changed by setting the context flag reduceFractions => 0.

The option studentsMustReduceFractions => 1 that is passed to the cmp method means that fractions entered by students must be reduced in order to be accepted.

The option strictFractions => 1 that is passed to the cmp method means that division is only allowed between integers. Note that the options strictMinus => 1 and strictMultiplication => 1 are also needed to make the strictFractions option really work.

See contextFraction.pl for more details.

BEGIN_PGML
Find and simplify 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.