// Numbas version: exam_results_page_options
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Recall that the factors of an expression are multiplied together, not added.</p>\n<p>(a): <span data-jme-visible=\"denlen=2\">$\\var{latex(q1denset[0])}$ is a common factor</span>&nbsp;&nbsp;<span data-jme-visible=\"denlen=3\">$\\var{latex(q1denset[0])}$ and $\\var{latex(q1denset[1])}$ are common factors</span>&nbsp;and can be cancelled.</p>\n<p>(b):&nbsp;The numerator and denominator do not share a common factor, so nothing can be cancelled.&nbsp;This fraction cannot be simplified.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "[\"a\",\"b\",\"c\",\"d\",\"f\",\"g\",\"h\",\"k\",\"m\",\"n\",\"p\",\"q\",\"r\",\"s\",\"t\",\"u\",\"v\",\"w\",\"x\",\"y\",\"z\"]", "description": "", "templateType": "anything", "can_override": false}, "q1numset": {"name": "q1numset", "group": "Q1", "definition": "shuffle(alphabet)[0..3]", "description": "<p>The numerator</p>", "templateType": "anything", "can_override": false}, "q1denset": {"name": "q1denset", "group": "Q1", "definition": "flatten([shuffle(q1numset)[0..random(1,2)],[random(1..100)]])", "description": "<p>The denominator</p>", "templateType": "anything", "can_override": false}, "q1simnumset": {"name": "q1simnumset", "group": "Q1", "definition": "filter(!(x isa \"number\"),x,\n  map(x[0],x,\n    filter(x[1]=1,x,\n      frequencies(flatten([q1numset,q1denset]))\n    )\n  )\n)", "description": "<p>numerator after simplification</p>", "templateType": "anything", "can_override": false}, "q1simden": {"name": "q1simden", "group": "Q1", "definition": "q1denset[length(q1denset)-1]", "description": "<p>Simplified denominator</p>", "templateType": "anything", "can_override": false}, "q1num": {"name": "q1num", "group": "Q1", "definition": "simplify(expression(\n    foldl(str + \"*\" + x,str,x,\"1\",q1numset)\n    ),\"unitFactor\")", "description": "", "templateType": "anything", "can_override": false}, "q1den": {"name": "q1den", "group": "Q1", "definition": "simplify(expression(\n    foldl(str + \"*\" + x,str,x,\"1\",q1denset)\n    ),[\"unitFactor\",\"constantsFirst\"])", "description": "", "templateType": "anything", "can_override": false}, "q1simnum": {"name": "q1simnum", "group": "Q1", "definition": "simplify(expression(\n    foldl(str + \"*\" + x,str,x,\"1\",q1simnumset)\n    ),\"unitFactor\")", "description": "", "templateType": "anything", "can_override": false}, "q1bden": {"name": "q1bden", "group": "Q1", "definition": "simplify(\n  expression(\n    q1denset[0] + \"+\" + q1denset[1]\n  ),[\"unitFactor\",\"constantsFirst\"]\n)", "description": "", "templateType": "anything", "can_override": false}, "denlen": {"name": "denlen", "group": "Q1", "definition": "length(q1denset)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet"], "variable_groups": [{"name": "Q1", "variables": ["q1num", "q1numset", "q1denset", "q1den", "q1simnumset", "q1simnum", "q1simden", "q1bden", "denlen"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "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>(a)&nbsp;</p>\n<table style=\"width: 241px;\">\n<tbody>\n<tr>\n<td style=\"border-bottom: 1pt solid; text-align: center; width: 35.6719px;\">$\\var{q1num}$</td>\n<td class=\"tdeq\" style=\"width: 11.4688px;\">=</td>\n<td style=\"border-bottom: 1pt solid; text-align: center; width: 49.5156px;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 35.6719px;\">$\\var{q1den}$</td>\n<td style=\"width: 11.4688px;\"></td>\n<td class=\"tddenom\" style=\"width: 49.5156px; text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p>(b)</p>\n<table>\n<tbody>\n<tr>\n<td style=\"border-bottom: 1pt solid; text-align: center; width: 35.6719px;\">$\\var{q1num}$</td>\n<td class=\"tdeq\" style=\"width: 11.4688px;\">=</td>\n<td style=\"border-bottom: 1pt solid; text-align: center; width: 49.5156px;\">[[2]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 35.6719px;\">$\\var{q1bden}$</td>\n<td style=\"width: 11.4688px;\"></td>\n<td class=\"tddenom\" style=\"width: 49.5156px; text-align: center;\">[[3]]</td>\n</tr>\n</tbody>\n</table>\n<p style=\"padding-left: 40px;\"></p>\n<p style=\"padding-left: 40px;\">When simplifying, remember only common factors can be cancelled.</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "(a) numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q1simnum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "(a) denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q1simden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "(b) numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q1num}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "(b) denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q1bden}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}