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<text><![CDATA[<p>Express the following, as a single fraction: \[{@a/b@}+{@c/d@}.\] <br /> [[input:ans]] <br /> <br /> Leave your answer in it's lowest terms in the form \(\frac{a}{b}\). [[validation:ans]]</p>]]></text>
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<text><![CDATA[<p>Express the following, as a single fraction: \[{@a/b@}+{@c/d@}.\] </p>
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<p>[[input:ans]] [[validation:ans]]</p>
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Leave your answer in it's lowest terms in the form \(\frac{a}{b}\). </p>]]></text>
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</questiontext>
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<generalfeedbackformat="html">
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<text><![CDATA[<p>In this case the denominators of the fractions are equal so you simply add the numerators to obtain the numerator and the denominator stays the same.</p>
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<text><![CDATA[<p>In this case the denominators of the fractions are equal so you simply add the numerators to obtain the numerator and the denominator stays the same.</p>
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<p>The general rule is: \[\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} \] In this exmaple: \[{@a/b@}+{@c/d@} = \frac{{@a@}+{@c@}}{@b@} = {@ta@}.\]</p>]]></text>
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</generalfeedback>
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<defaultgrade>1</defaultgrade>
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<penalty>0.1</penalty>
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<hidden>0</hidden>
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<idnumber/>
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<idnumber></idnumber>
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<stackversion>
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<text/>
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<text>2026010500</text>
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</stackversion>
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<questionvariables>
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<text>simp:true;
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b:rand(5)+3;
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a:b-1;
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d:b;
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c:d+1;
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ta:(a/b)+(c/d);
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lcm:lcm(b,d);
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<text>simp:true;
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b:rand(5)+3;
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a:b-1;
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d:b;
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c:d+1;
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ta:(a/b)+(c/d);
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lcm:lcm(b,d);
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simp:false;</text>
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</questionvariables>
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<specificfeedbackformat="html">
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<text>\[{@a/b@}+{@c/d@} = {@ta@}.\]</text>
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</questionnote>
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<questiondescriptionformat="moodle_auto_format">
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<text/>
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<text></text>
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</questiondescription>
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<questionsimplify>0</questionsimplify>
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<assumepositive>0</assumepositive>
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<logicsymbol>lang</logicsymbol>
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<matrixparens>[</matrixparens>
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<isbroken>0</isbroken>
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<variantsselectionseed/>
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<variantsselectionseed></variantsselectionseed>
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<input>
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<name>ans</name>
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<type>algebraic</type>
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<tans>ta</tans>
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<boxsize>15</boxsize>
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<strictsyntax>1</strictsyntax>
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<insertstars>0</insertstars>
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<syntaxhint/>
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<syntaxhint></syntaxhint>
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<syntaxattribute>0</syntaxattribute>
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<forbidwords/>
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<allowwords/>
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<forbidwords></forbidwords>
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<allowwords></allowwords>
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<forbidfloat>1</forbidfloat>
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<requirelowestterms>0</requirelowestterms>
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<checkanswertype>1</checkanswertype>
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<mustverify>1</mustverify>
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<showvalidation>1</showvalidation>
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<options/>
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<options></options>
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</input>
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<prt>
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<name>prt1</name>
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<value>1.0000000</value>
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<autosimplify>0</autosimplify>
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<feedbackstyle>1</feedbackstyle>
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<feedbackvariables>
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<text/>
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<text></text>
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</feedbackvariables>
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<node>
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<name>0</name>
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<description/>
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<answertest>EqualComAss</answertest>
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<description>Correct answers</description>
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<answertest>EqualComAssRules</answertest>
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<sans>ans</sans>
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<tans>ta</tans>
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<testoptions/>
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<testoptions>[ID_TRANS]</testoptions>
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<quiet>0</quiet>
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<truescoremode>=</truescoremode>
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<truescore>1.0000000</truescore>
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<truepenalty/>
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<truescore>1</truescore>
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<truepenalty></truepenalty>
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<truenextnode>-1</truenextnode>
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<trueanswernote>1-0-T </trueanswernote>
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<trueanswernote>prt1-1-T</trueanswernote>
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<truefeedbackformat="html">
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<text/>
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<text></text>
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</truefeedback>
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<falsescoremode>=</falsescoremode>
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<falsescore>0.0000000</falsescore>
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<falsepenalty/>
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<falsenextnode>2</falsenextnode>
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<falseanswernote>1-0-F </falseanswernote>
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<falsescore>0</falsescore>
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<falsepenalty></falsepenalty>
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<falsenextnode>1</falsenextnode>
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<falseanswernote>prt1-1-F</falseanswernote>
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<falsefeedbackformat="html">
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<text/>
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<text></text>
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</falsefeedback>
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</node>
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<node>
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<name>1</name>
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<description/>
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<description></description>
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<answertest>AlgEquiv</answertest>
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<sans>ans</sans>
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<tans>(a+c)/(b+d)</tans>
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<testoptions/>
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<tans>ta</tans>
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<testoptions></testoptions>
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<quiet>0</quiet>
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<truescoremode>=</truescoremode>
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<truescore>0.0000000</truescore>
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<truepenalty/>
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<truescore>0</truescore>
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<truepenalty></truepenalty>
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<truenextnode>-1</truenextnode>
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<trueanswernote>1-1-T (naive adding of fractions)</trueanswernote>
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<trueanswernote>prt1-2-T</trueanswernote>
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<truefeedbackformat="html">
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<text><![CDATA[<p>Remember that the first step in adding fractions is to make both denominators equal. It is not simply adding the numerators and the denominators.</p>]]></text>
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<text><![CDATA[<p>Simplify the fraction fully into the form \(\frac{a}{b}\) and leave in it's lowest terms.</p>]]></text>
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</truefeedback>
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<falsescoremode>=</falsescoremode>
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<falsescore>0.0000000</falsescore>
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<falsepenalty/>
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<falsenextnode>-1</falsenextnode>
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<falseanswernote>1-1-F </falseanswernote>
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<falsescore>0</falsescore>
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<falsepenalty></falsepenalty>
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<falsenextnode>2</falsenextnode>
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<falseanswernote>prt1-2-F</falseanswernote>
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<falsefeedbackformat="html">
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<text/>
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<text></text>
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</falsefeedback>
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</node>
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<node>
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<name>2</name>
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<description/>
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<description>Naive adding of fractions/mediant</description>
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<answertest>AlgEquiv</answertest>
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<sans>ans</sans>
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<tans>ta</tans>
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<testoptions/>
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<tans>(a+c)/(b+d)</tans>
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<testoptions></testoptions>
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<quiet>0</quiet>
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<truescoremode>=</truescoremode>
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<truescore>0.0000000</truescore>
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<truepenalty/>
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<truescore>0</truescore>
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<truepenalty></truepenalty>
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<truenextnode>-1</truenextnode>
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<trueanswernote>1-2-T </trueanswernote>
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<trueanswernote>prt1-3-T</trueanswernote>
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<truefeedbackformat="html">
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<text><![CDATA[<p>Simplify the fraction fully into the form \(\frac{a}{b}\) and leave in it's lowest terms.</p>]]></text>
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<text><![CDATA[<p>Remember that the first step in adding fractions is to make both denominators equal. It is not simply adding the numerators and the denominators.</p>]]></text>
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</truefeedback>
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<falsescoremode>=</falsescoremode>
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<falsescore>0.0000000</falsescore>
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<falsepenalty/>
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<falsenextnode>1</falsenextnode>
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<falseanswernote>1-2-F </falseanswernote>
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<falsescore>0</falsescore>
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<falsepenalty></falsepenalty>
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<falsenextnode>-1</falsenextnode>
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<falseanswernote>prt1-3-F</falseanswernote>
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<falsefeedbackformat="html">
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<text/>
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<text></text>
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</falsefeedback>
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</node>
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</prt>
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<deployedseed>944404612</deployedseed>
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<qtest>
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<testcase>1</testcase>
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<description/>
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<description></description>
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<testinput>
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<name>ans</name>
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<value>ta</value>
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<name>prt1</name>
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<expectedscore>1.0000000</expectedscore>
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<expectedpenalty>0.0000000</expectedpenalty>
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<expectedanswernote>1-0-T</expectedanswernote>
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<expectedanswernote>prt1-1-T</expectedanswernote>
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</expected>
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</qtest>
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<qtest>
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<testcase>2</testcase>
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<description/>
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<description></description>
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<testinput>
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<name>ans</name>
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<value>(a+c)/(b+d)</value>
@@ -191,12 +194,12 @@ simp:false;</text>
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<name>prt1</name>
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<expectedscore>0.0000000</expectedscore>
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<expectedpenalty>0.1000000</expectedpenalty>
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<expectedanswernote>1-1-T (naive adding of fractions)</expectedanswernote>
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