// Numbas version: exam_results_page_options
{"name": "1.4.3.1 Add two algebraic fractions version 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.4.3.1 Add two algebraic fractions version 1", "tags": [], "metadata": {"description": "<p>Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify, if possible, $\\displaystyle{\\var{te[0]}\\var{sgnl}\\var{te[1]}}$</p>", "advice": "<p>Given $\\displaystyle{\\var{te[0]}\\var{sgnl}\\var{te[1]}}$</p>\n<p><span data-jme-visible=\"te[0]&lt;&gt;te_red[0]\">$\\displaystyle{\\var{te[0]}}$ can be simplified to $\\displaystyle{\\var{te_red[0]}}$</span></p>\n<p><span data-jme-visible=\"te[1]&lt;&gt;te_red[1]\">$\\displaystyle{\\var{te[1]}}$ can be simplified to $\\displaystyle{\\var{te_red[1]}}$</span></p>\n<p><span data-jme-visible=\"te[0]&lt;&gt;te_red[0] or te[1]&lt;&gt;te_red[1]\">so $\\displaystyle{\\var{te[0]}\\var{sgnl}\\var{te[1]} = \\var{te_red[0]} \\var{sgnl} \\var{te_red[1]}}$</span></p>\n<p>The terms have a common factor of $\\var{ve}$.</p>\n<p>So $\\displaystyle{\\var{te_red[0]}\\var{sgnl}\\var{te_red[1]} = \\var{ve}\\left(\\var{fre[0]}\\var{sgnl}\\var{fre[1]} \\right)&nbsp; }$</p>\n<p>The lowest common multiple of $\\var{den_red[0]}$ and $\\var{den_red[1]}$ is $\\var{lcm}$.</p>\n<p>So: \\[\\begin{align*}\\var{te_red[0]} \\var{sgnl} \\var{te_red[1]} &amp;= \\var{ve} \\left( \\frac{\\var{mult[0]}}{\\var{mult[0]}}\\times\\var{fre[0]} \\var{sgnl} \\frac{\\var{mult[1]}}{\\var{mult[1]}}\\times \\var{fre[1]}\\right)\\\\&amp;=\\var{ve}\\left(\\frac{\\var{mult[0]}\\times\\var{num_red[0]} \\var{sgnl} \\var{mult[1]}\\times\\var{num_red[1]}}{\\var{lcm}}\\right)\\\\&amp;=\\var{ans}\\end{align*}\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"letter": {"name": "letter", "group": "Ungrouped variables", "definition": "random(\"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}, "dens": {"name": "dens", "group": "Ungrouped variables", "definition": "shuffle(4..9)", "description": "<p>list of possible denominators</p>", "templateType": "anything", "can_override": false}, "nums": {"name": "nums", "group": "Ungrouped variables", "definition": "[random(1,shuffle(1..dens[0]-1)[0]),\n  random(1,shuffle(1..dens[1]-1)[0])]", "description": "<p>The numerators</p>", "templateType": "anything", "can_override": false}, "ts": {"name": "ts", "group": "Ungrouped variables", "definition": "[\"(\"+nums[0]+\"*\"+letter+\")/\"+dens[0],\n  \"(\"+nums[1]+\"*\"+letter+\")/\"+dens[1]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "te_red": {"name": "te_red", "group": "Ungrouped variables", "definition": "[simplify(expression(ts[0]),\"all\"),simplify(expression(ts[1]),\"all\")]", "description": "<p>The two tems as reduced expressions. Used in the advice.</p>", "templateType": "anything", "can_override": false}, "te": {"name": "te", "group": "Ungrouped variables", "definition": "[simplify(expression(ts[0]),[\"basic\",\"unitFactor\"]),\n  simplify(expression(ts[1]),[\"basic\",\"unitFactor\"])]", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "simplify(expression(letter+\"*\"+(frsum)),\"all\")", "description": "<p>the final answer</p>", "templateType": "anything", "can_override": false}, "fr": {"name": "fr", "group": "Ungrouped variables", "definition": "[rational(nums[0]/dens[0]),\n  rational(nums[1]/dens[1])\n  ]", "description": "<p>The fractions without the variable</p>", "templateType": "anything", "can_override": false}, "lcm": {"name": "lcm", "group": "Ungrouped variables", "definition": "den_red[0]*den_red[1]/gcd(den_red[0],den_red[1])", "description": "<p>lowest common multiple of the reduced denominators</p>", "templateType": "anything", "can_override": false}, "mult": {"name": "mult", "group": "Ungrouped variables", "definition": "[lcm/den_red[0],lcm/den_red[1]]", "description": "<p>What each term needs to be multipled by to put it over a common fraction. Used in the advice display.</p>", "templateType": "anything", "can_override": false}, "den_red": {"name": "den_red", "group": "Ungrouped variables", "definition": "[int(decimal(split(string(fr[0]),\"/\")[1])),\n  int(decimal(split(string(fr[1]),\"/\")[1]))\n  ]", "description": "<p>the denominators of the reduced fractions</p>", "templateType": "anything", "can_override": false}, "ve": {"name": "ve", "group": "Ungrouped variables", "definition": "expression(letter)", "description": "<p>for display in the advice</p>", "templateType": "anything", "can_override": false}, "fre": {"name": "fre", "group": "Ungrouped variables", "definition": "[expression(string(fr[0])),\n  expression(string(fr[1]))]", "description": "<p>the fractions as strings, for display</p>", "templateType": "anything", "can_override": false}, "sgn": {"name": "sgn", "group": "Ungrouped variables", "definition": "random(\"+\",\"-\")", "description": "", "templateType": "anything", "can_override": false}, "sgnl": {"name": "sgnl", "group": "Ungrouped variables", "definition": "latex(sgn)", "description": "<p>display version of the sign.</p>", "templateType": "anything", "can_override": false}, "frsum": {"name": "frsum", "group": "Ungrouped variables", "definition": "eval(expression(fr[0] + sgn + fr[1]))", "description": "", "templateType": "anything", "can_override": false}, "num_red": {"name": "num_red", "group": "Ungrouped variables", "definition": "[int(decimal(split(string(fr[0]),\"/\")[0])),\n  int(decimal(split(string(fr[1]),\"/\")[0]))\n  ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["letter", "dens", "den_red", "nums", "num_red", "ts", "fr", "frsum", "te", "te_red", "ans", "lcm", "mult", "ve", "fre", "sgn", "sgnl"], "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": "{ans}", "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`?", "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/"}]}