// Numbas version: exam_results_page_options
{"name": "Fractions: adding and subtracting, algebraic, already with common denominator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Fractions: adding and subtracting, algebraic, already with common denominator", "tags": [], "metadata": {"description": "<p>Fractions already have a common denominator. Addition and subtraction 50:50 split. Students shouldn't have to worry about reducing fractions by design.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Express the following as a single fraction. Use / as the fraction bar and use brackets to group the numerator and denominator separately, e.g. $\\dfrac{m+1}{2n}$ is written (m+1)/(2n)</p>", "advice": "<p>Since both denominators are the same, i.e. $\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}$. We can simply <span data-jme-visible=\"addSub=1\">add</span><span data-jme-visible=\"addSub=-1\">subtract</span> the numerators, and put that over the common denominator.</p>\n<p></p>\n<p><span data-jme-visible=\"addSub=1\">$\\begin{align*}\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}-{ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}+\\dfrac{\\simplify{{numbers[3]}x-{numbers[0]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}&amp;=\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}+{addSub*numbers[3]}x+{-addSub*numbers[0]-ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}\\end{align*}$</span></p>\n<p><span data-jme-visible=\"addSub=-1\">$\\begin{align*}\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}-{ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}-\\dfrac{\\simplify{{numbers[3]}x-{numbers[0]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}&amp;=\\dfrac{\\simplify{ {ynnum1[0]*numbers[0]}-{ynnum1[1]*numbers[1]}y} -(\\simplify{{numbers[3]}x-{numbers[0]}y})}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}\\\\[3pt]&amp;=\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}+{addSub*numbers[3]}x+{-addSub*numbers[0]-ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}\\end{align*}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"addSub": {"name": "addSub", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "<p>adding or subtracting</p>", "templateType": "anything", "can_override": false}, "numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "shuffle([3,5,7,11,13,17,19,23,29])[0..4]", "description": "", "templateType": "anything", "can_override": false}, "ynden": {"name": "ynden", "group": "Ungrouped variables", "definition": "shuffle([0,1,1])", "description": "<p>yes/no for denominator. Used to turn terms on or off</p>", "templateType": "anything", "can_override": false}, "ynnum1": {"name": "ynnum1", "group": "Ungrouped variables", "definition": "shuffle([0,1,1])", "description": "<p>shuffle([0,1,1])</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbers", "addSub", "ynnum1", "ynden"], "variable_groups": [], "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><span data-jme-visible=\"addSub=1\">$\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}-{ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}+\\dfrac{\\simplify{{numbers[3]}x-{numbers[0]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}$</span> <span data-jme-visible=\"addSub=-1\">$\\dfrac{\\simplify{{ynnum1[0]*numbers[0]}-{ynnum1[1]*numbers[1]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}-\\dfrac{\\simplify{{numbers[3]}x-{numbers[0]}y}}{\\simplify{{ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]}}}$</span>&nbsp; $=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({ynnum1[0]*numbers[0]}+{addSub*numbers[3]}x+{-addSub*numbers[0]-ynnum1[1]*numbers[1]}y)/({ynden[0]*numbers[2]}x+{ynden[1]*numbers[3]})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`! m_anywhere((?/?) + (?/?)) `& (?/?)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "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/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}