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{"name": "1.4.3. Task 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.4.3. Task 2", "tags": [], "metadata": {"description": "<p>Add two algebraic fractions. Part of HELM Book 1.4.3.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Express $\\displaystyle{\\frac{\\var{q2c[0]}}{\\var{latex(q2v[0])}}+\\frac{\\var{q2c[1]}}{\\var{latex(q2v[1])}}}$ as a single fraction.</p>", "advice": "<p>The simplest expression which has $\\var{latex(q2v[0])}$ and $\\var{latex(q2v[1])}$ as its factors is $\\var{latex(q2v[0])}\\var{latex(q2v[1])}$. This is the lowest common denominator. Both fractions are written using this common denominator. Noting that</p>\n<p>$\\displaystyle{\\frac{\\var{q2c[0]}}{\\var{latex(q2v[0])}}= \\frac{\\var{q2c[0]}\\var{latex(q2v[1])}}{\\var{latex(q2v[0])}\\var{latex(q2v[1])}} }$ and that $\\displaystyle{\\frac{\\var{q2c[1]}}{\\var{latex(q2v[1])}}= \\frac{\\var{q2c[1]}\\var{latex(q2v[0])}}{\\var{latex(q2v[1])}\\var{latex(q2v[0])}} }$ we find</p>\n<p>\\[\\frac{\\var{q2c[0]}}{\\var{latex(q2v[0])}}+\\frac{\\var{q2c[1]}}{\\var{latex(q2v[1])}}= \\frac{\\var{q2c[0]}\\var{latex(q2v[1])}}{\\var{latex(q2v[0])}\\var{latex(q2v[1])}}+\\frac{\\var{q2c[1]}\\var{latex(q2v[0])}}{\\var{latex(q2v[1])}\\var{latex(q2v[0])}} = \\var{q2ans}\\]</p>\n<p>No cancellation is now possible because neither $\\var{latex(q2v[0])}$ nor $\\var{latex(q2v[1])}$ is a factor in the numerator.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q1c": {"name": "q1c", "group": "Ungrouped variables", "definition": "shuffle([1,2,3,5,7,11])", "description": "", "templateType": "anything", "can_override": false}, "q1ans": {"name": "q1ans", "group": "Ungrouped variables", "definition": "expression(\n  \"(\"+(q1c[0]+q1c[2])+\"*x+\"+(q1c[0]*q1c[3]+q1c[1]*q1c[2])+\n  \")/((x+\"+q1c[1]+\")*(x+\"+q1c[3]+\"))\"\n)", "description": "", "templateType": "anything", "can_override": false}, "q2v": {"name": "q2v", "group": "Ungrouped variables", "definition": "shuffle([\"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}, "q2c": {"name": "q2c", "group": "Ungrouped variables", "definition": "shuffle([1,1,1,1,1,2,3,5,7,11])", "description": "", "templateType": "anything", "can_override": false}, "q2ans": {"name": "q2ans", "group": "Ungrouped variables", "definition": "simplify(expression(\n    \"(\"+q2c[0]+\"*\"+q2v[1]+\"+\"+q2c[1]+\"*\"+q2v[0]+\")/(\"+q2v[0]+\"*\"+q2v[1]+\")\"\n  ),\"all\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["q1c", "q1ans", "q2v", "q2c", "q2ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "{q2ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "($n`?*$v+$n`?*$v)/($v*$v)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "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/"}]}