// Numbas version: finer_feedback_settings
{"name": "7b. Adding simple algebraic fractions with multiple variables", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "7b. Adding simple algebraic fractions with multiple variables", "tags": [], "metadata": {"description": "<p>simplifying pL1^a/n+kL2^bL1^c/m</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Express the following as a single fraction:</p>\n<p>\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{{Frac1}+{Frac2}}\\]</p>\n<p></p>\n<p><em>Simplify your answer where possible.</em></p>", "advice": "<p>Adding algebraic fractions is the same as adding ordinary fractions. First we need to write both fractions over the same denominator by multiplying the top and bottom of both fractions</p>\n<p>\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{{Frac1}+{Frac2}}<br/>=\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2})/({Denominator1}{Denominator2})+({Numerator2}{Denominator1})/({Denominator1}{Denominator2})}\\]</p>\n<p>Finally we add the numerators together and simplify to get</p>\n<p>\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2})/({Denominator1}{Denominator2})+({Numerator2}{Denominator1})/({Denominator1}{Denominator2})}<br/>=\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2}+{Numerator2}{Denominator1})/({Denominator1}{Denominator2})}<br/>=\\simplify{({Numerator1}{Denominator2}+{Numerator2}{Denominator1})/({Denominator1}{Denominator2})}.\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "<p>pL1^a/n+kL2^bL1^c/m</p>", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..12 except [-n*k,k])", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "L1": {"name": "L1", "group": "Ungrouped variables", "definition": "expression(random('x','y','a','w','c','z','n'))", "description": "", "templateType": "anything", "can_override": false}, "L2": {"name": "L2", "group": "Ungrouped variables", "definition": "expression(random(['x','y','a','w','c','z','n'] except string(L1)))", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-1..1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-2..2 except a)", "description": "", "templateType": "anything", "can_override": false}, "Frac1": {"name": "Frac1", "group": "Ungrouped variables", "definition": "if(a>0,\n  exec(op(\"/\"),[exec(op(\"*\"),[p,exec(op(\"^\"),[L1,a])]),n]),\n  if(a<0,\n    exec(op(\"/\"),[p,exec(op(\"*\"),[n,exec(op(\"^\"),[L1,-a])])]),\n    1))", "description": "", "templateType": "anything", "can_override": false}, "letter": {"name": "letter", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "Frac2": {"name": "Frac2", "group": "Ungrouped variables", "definition": "if(b>=0 && c>=0,\n  exec(op(\"/\"),[exec(op(\"*\"),[k,exec(op(\"*\"),[exec(op(\"^\"),[L1,c]),exec(op(\"^\"),[L2,b])])]),m]),\n  if(b<0 && c>=0,\n    exec(op(\"/\"),[exec(op(\"*\"),[k,exec(op(\"^\"),[L1,c])]),exec(op(\"*\"),[m,exec(op(\"^\"),[L2,-b])])]),\n    if(b>=0 && c<0,\n      exec(op(\"/\"),[exec(op(\"*\"),[k,exec(op(\"^\"),[L2,b])]),exec(op(\"*\"),[m,exec(op(\"^\"),[L1,-c])])]),\n      if(b<0 && c<0,\n        exec(op(\"/\"),[k,exec(op(\"*\"),[m,exec(op(\"*\"),[exec(op(\"^\"),[L1,-c]),exec(op(\"^\"),[L2,-b])])])]),\n1))))", "description": "", "templateType": "anything", "can_override": false}, "Numerator1": {"name": "Numerator1", "group": "Ungrouped variables", "definition": "if(a>0,\n  exec(op(\"*\"),[p,exec(op(\"^\"),[L1,a])]),\n  if(a<0,\n    p,\n    1))", "description": "", "templateType": "anything", "can_override": false}, "Denominator1": {"name": "Denominator1", "group": "Ungrouped variables", "definition": "if(a>0,\n  n,\n  if(a<0,\n    exec(op(\"*\"),[n,exec(op(\"^\"),[L1,-a])]),\n    1))", "description": "", "templateType": "anything", "can_override": false}, "Numerator2": {"name": "Numerator2", "group": "Ungrouped variables", "definition": "if(b>=0 && c>=0,\n  exec(op(\"*\"),[k,exec(op(\"*\"),[exec(op(\"^\"),[L1,c]),exec(op(\"^\"),[L2,b])])]),\n  if(b<0 && c>=0,\n    exec(op(\"*\"),[k,exec(op(\"^\"),[L1,c])]),\n    if(b>=0 && c<0,\n      exec(op(\"*\"),[k,exec(op(\"^\"),[L2,b])]),\n      if(b<0 && c<0,\n        k,\n1))))", "description": "", "templateType": "anything", "can_override": false}, "Denominator2": {"name": "Denominator2", "group": "Ungrouped variables", "definition": "if(b>=0 && c>=0,\n  m,\n  if(b<0 && c>=0,\n    exec(op(\"*\"),[m,exec(op(\"^\"),[L2,-b])]),\n    if(b>=0 && c<0,\n      exec(op(\"*\"),[m,exec(op(\"^\"),[L1,-c])]),\n      if(b<0 && c<0,\n        exec(op(\"*\"),[m,exec(op(\"*\"),[exec(op(\"^\"),[L1,-c]),exec(op(\"^\"),[L2,-b])])]),\n1))))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "m", "k", "p", "L1", "L2", "a", "b", "c", "Frac1", "Frac2", "letter", "Numerator1", "Denominator1", "Numerator2", "Denominator2"], "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": "({Numerator1}{Denominator2}+{Numerator2}{Denominator1})/({Denominator1}{Denominator2})", "answerSimplification": "all", "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": "?/?", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}