// Numbas version: finer_feedback_settings
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"listsquare", "group": "Ungrouped variables", "definition": "shuffle(listsquares)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "arg2": {"name": "arg2", "group": "Ungrouped variables", "definition": "square2[1]*prime2", "description": "", "templateType": "anything", "can_override": false}, "gcff": {"name": "gcff", "group": "Ungrouped variables", "definition": "gcd(questnum,questden)", "description": "", "templateType": "anything", "can_override": false}, "ansnummult": {"name": "ansnummult", "group": "using", "definition": "questnum/cancel", "description": "", "templateType": "anything", "can_override": false}, "cancel": {"name": "cancel", "group": "using", "definition": "gcd(questnum,tempden)", "description": "", "templateType": "anything", "can_override": false}, "listsquares": {"name": "listsquares", "group": "Ungrouped variables", "definition": "map([n,n^2],n,1..12)", "description": "", "templateType": "anything", "can_override": false}, "questden": 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"templateType": "anything", "can_override": false}, "questdensurd": {"name": "questdensurd", "group": "using", "definition": "random(2,3,5,6,7,10,11,13,14,15,17)", "description": "", "templateType": "anything", "can_override": false}, "prime1": {"name": "prime1", "group": "Ungrouped variables", "definition": "listprime[0]", "description": "", "templateType": "anything", "can_override": false}, "prime2": {"name": "prime2", "group": "Ungrouped variables", "definition": "listprime[1]", "description": "", "templateType": "anything", "can_override": false}, "ansden": {"name": "ansden", "group": "using", "definition": "tempden/cancel", "description": "", "templateType": "anything", "can_override": false}, "square1": {"name": "square1", "group": "Ungrouped variables", "definition": "listsquare[0]", "description": "", "templateType": "anything", "can_override": false}, "square2": {"name": "square2", "group": "Ungrouped variables", "definition": "listsquare[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["listsquares", "listprimes", "listsquare", "fcf", "square1", "square2", "listprime", "arg2", "prime1", "prime2", "extra", "ansmult", "ansarg", "questnum2", "questden", "gcff", "num_wo_cf", "den_wo_cf"], "variable_groups": [{"name": "using", "variables": ["questnum", "questdenmult", "questdensurd", "tempden", "cancel", "ansnummult", "ansden"]}], "functions": {}, "preamble": {"js": "", "css": ".fractiontable table {\n  width: 20%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size: x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the fraction $\\dfrac{\\var{questnum}}{\\var{questdenmult}\\sqrt{\\var{questdensurd}}}$ we can rationalise the denominator and rewrite the fraction in the simplified equivalent form&nbsp;</p>\n<div class=\"fractiontable\">\n<table cellpadding=\"0\" style=\"text-align: right;\">\n<tbody>\n<tr>\n<td class=\"tdnum\" style=\"text-align: center;\">[[0]]</td>\n<td class=\"tdnum\" style=\"text-align: center; background-image: url('resources/question-resources/sqrt_Irff7Ni.png'); background-repeat: no-repeat;\">&nbsp; &nbsp;$\\,\\,\\,\\,$[[1]]</td>\n</tr>\n<tr>\n<td class=\"tddenom\" colspan=\"2\" style=\"text-align: center;\">[[2]]</td>\n</tr>\n</tbody>\n</table>\n</div>", "stepsPenalty": "3", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In the above&nbsp;case, to rationalise the denominator we can multiply the top and bottom of the fraction by the surd part. This will rationalise the denominator since $\\sqrt{a}\\times\\sqrt{a}=a$.&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\dfrac{\\var{questnum}}{\\var{questdenmult}\\sqrt{\\var{questdensurd}}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{questnum}}{\\var{questdenmult}\\sqrt{\\var{questdensurd}}}\\times\\dfrac{\\sqrt{\\var{questdensurd}}}{\\sqrt{\\var{questdensurd}}}$</td>\n<td style=\"text-align: left;\">&nbsp; &nbsp; (multiplying top and bottom by the surd part of the denominator)</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{questnum}\\sqrt{\\var{questdensurd}}}{\\var{questdenmult}\\times\\var{questdensurd}}$</td>\n<td style=\"text-align: left;\">&nbsp; &nbsp;&nbsp;</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{questnum}\\sqrt{\\var{questdensurd}}}{\\var{tempden}}$</td>\n<td style=\"text-align: left;\">&nbsp; &nbsp;&nbsp;</td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"cancel&gt;1 and abs(ansnummult)&lt;&gt;1\">$\\,$</span></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"cancel&gt;1 and abs(ansnummult)&lt;&gt;1\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"cancel&gt;1 and abs(ansnummult)&lt;&gt;1\">$\\dfrac{\\var{ansnummult}\\sqrt{\\var{questdensurd}}}{\\var{ansden}}$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"cancel&gt;1 and abs(ansnummult)&lt;&gt;1\">&nbsp; &nbsp; (cancelling the common factor of $\\var{cancel}$)</span></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ansnummult=-1\">$\\,$</span></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"ansnummult=-1\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"ansnummult=-1\">$-\\dfrac{\\sqrt{\\var{questdensurd}}}{\\var{ansden}}$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"ansnummult=-1\">&nbsp; &nbsp; (cancelling the common factor of $\\var{cancel}$)</span></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ansnummult=1\">$\\,$</span></td>\n<td style=\"text-align: center;\"><span data-jme-visible=\"ansnummult=1\">$=$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"ansnummult=1\">$\\dfrac{\\sqrt{\\var{questdensurd}}}{\\var{ansden}}$</span></td>\n<td style=\"text-align: left;\"><span data-jme-visible=\"ansnummult=1\">&nbsp; &nbsp; (cancelling the common factor of $\\var{cancel}$)</span></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>A nice result of this process is that $\\dfrac{1}{\\sqrt{n}}=\\dfrac{\\sqrt{n}}{n}$ for all $n&gt;0$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansnummult", "maxValue": "ansnummult", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "questdensurd", "maxValue": "questdensurd", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansden", "maxValue": "ansden", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": ["question-resources/sqrt_Irff7Ni.png", "question-resources/fracsqrts.png"]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}