// Numbas version: finer_feedback_settings
{"name": "7a. Adding x/n+kx/m", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "7a. Adding x/n+kx/m", "tags": [], "metadata": {"description": "<p>Adding two algebraic fractions with the same variable in the numberators.</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]{{Letter}/{n}+{k}{Letter}/{m}}\\]</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]{{Letter}/{n}+{k}{Letter}/{m}}=\\simplify[basic,unitFactor]{{m}{Letter}/({m}{n})+{n}{k}{Letter}/({n}{m})}\\]</p>\n<p>Finally we add the numerators together and simplify to get</p>\n<p>\\[\\simplify[basic,unitFactor]{{m}{Letter}/({m}{n})+{n}{k}{Letter}/({n}{m})}=\\simplify[basic,unitFactor]{({m}{Letter}+{n}{k}{Letter})/({n}{m})}=\\simplify{({m}{Letter}+{n}{k}{Letter})/({n}{m})}.\\]</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": "", "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}, "Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "expression(random('x','y','a','w','c','z','n'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "m", "k", "Letter"], "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": "{(m+k*n)/(m*n)}{Letter}", "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": "`+-$n*$v/$n `| `+-$v/$n`| `+-$v`| `+-$n*$v", "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/"}]}