<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>AlgMap-14.10</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[Express the following as a single fraction:
\[ \frac{@n1@}{@d1@}\cdot\frac{@n2@}{@d2@}. \]
<br>
(Hint: Try factorising the fractions.)
<br>
<br>

[[input:ans]] [[validation:ans]]]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text>When multiplying fractions you can save work if the denominator of one fraction has common factors with the numerator of another. In this example, if we factorise the denominator of the first fraction we obtain:
\[ \frac{@n1@}{@factor(d1)@}\cdot\frac{@n2@}{@d2@}. \]
It is clear that the factor \({@v+c@}\) is common in both fractions and so we can cancel \({@v+c@}\):
\[ \frac{@n1@}{@v+a@}\cdot\frac{1}{@d2@} = {@ta@}. \]</text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>v:rand([x,y,z,t]);
a:rand([1,4,7])*rand([1,-1]);
c:rand([2,5,8])*rand([1,-1]);
n1:rand(5)+1;
d1:expand((v+a)*(v+c));
n2:(v+c);
d2:rand(5)+2;
ta:factor((n1/d1)*(n2/d2));</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[ \frac{@n1@}{@d1@}\cdot\frac{@n2@}{@d2@} = {@ta@}. \]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans</name>
      <type>algebraic</type>
      <tans>ta</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
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      <allowwords/>
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      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
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        <text/>
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      <node>
        <name>0</name>
        <description/>
        <answertest>SingleFrac</answertest>
        <sans>ans</sans>
        <tans>ta</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>1</truenextnode>
        <trueanswernote>1-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
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        <falseanswernote>1-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>lowesttermsp(ans)</sans>
        <tans>true</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
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        <trueanswernote>1-1-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>1-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>1210123340</deployedseed>
    <deployedseed>669842388</deployedseed>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans</name>
        <value>ta</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>1-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans</name>
        <value>(n1/d1)*(n2/d2)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>1-0-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
