// Numbas version: exam_results_page_options
{"name": "1.4.1. Task: Cancelling common factors 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.4.1. Task: Cancelling common factors 4", "tags": [], "metadata": {"description": "<p>Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify the following fraction as much as possible.</p>", "advice": "<p>Find the common factors between the numbers.</p>\n<p>Find the common factors for each of the variables.</p>\n<p>Then simplify by cancelling the common factors.</p>\n<p>$\\var{q4num}$ and $\\var{q4den}$ have a greatest common factor of $\\var{commonfactor}$ which can be cancelled out.</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}, "q4v": {"name": "q4v", "group": "Q4", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q4idx": {"name": "q4idx", "group": "Q4", "definition": "sort(shuffle(1..10)[0..2])", "description": "", "templateType": "anything", "can_override": false}, "q4ab": {"name": "q4ab", "group": "Q4", "definition": "[random(1..20),random(1..20)]", "description": "", "templateType": "anything", "can_override": false}, "q4c": {"name": "q4c", "group": "Q4", "definition": "[q4ab[0]/gcd(q4ab[0],q4ab[1]),q4ab[1]/gcd(q4ab[0],q4ab[1]), random(2..10)]", "description": "<p>Two coprime numbers and a common multiplier</p>", "templateType": "anything", "can_override": false}, "q4num": {"name": "q4num", "group": "Q4", "definition": "simplify(expression(q4c[0]*q4c[2]+\"*\"+q4v+\"^\"+q4idx[0]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q4den": {"name": "q4den", "group": "Q4", "definition": "simplify(expression(q4c[1]*q4c[2]+\"*\"+q4v+\"^\"+q4idx[1]),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "q4simnum": {"name": "q4simnum", "group": "Q4", "definition": "expression(string(q4c[0]))", "description": "", "templateType": "anything", "can_override": false}, "q4simden": {"name": "q4simden", "group": "Q4", "definition": "simplify(expression(q4c[1]+\"*\"+q4v+\"^\"+(q4idx[1]-q4idx[0])),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "commonfactor": {"name": "commonfactor", "group": "Ungrouped variables", "definition": "simplify(expression(q4c[2]+\"*\"+q4v+\"^\"+q4idx[0]),\"all\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["alphabet", "commonfactor"], "variable_groups": [{"name": "Q4", "variables": ["q4v", "q4idx", "q4ab", "q4c", "q4num", "q4den", "q4simnum", "q4simden"]}], "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></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q4num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q4den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q4simnum}", "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": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q4simden}", "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/"}]}