// Numbas version: finer_feedback_settings
{"name": "NC NA Fraction addition - sausage sizzle leftovers (9)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NC NA Fraction addition - sausage sizzle leftovers (9)", "tags": ["LANTITE"], "metadata": {"description": "<p>Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number &amp; Algebra strand. Students need to add two fractions with different denominators, then subtract the answer from 1. There are 9 different versions of this question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Northam&nbsp;High School&nbsp;held a sausage sizzle at their athletics carnival.</p>\n<p>Three Year 11 students, {name1},&nbsp;{name2} and {name3} volunteered to cook the sausages.</p>\n<p>{name1} cooked {frac1name} of the sausages, and {name2} cooked&nbsp;{frac2name} of the sausages.</p>", "advice": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>{name1}&nbsp;cooked {frac1name} of the sausages,&nbsp;and {name2}&nbsp;cooked {frac2name} of the sausages.&nbsp;</p>\n<p>We need to&nbsp;add these&nbsp;fractions.&nbsp;</p>\n<p>$ \\frac{\\var{frac1num}}{\\var{frac1denom}} +&nbsp;\\frac{\\var{frac2num}}{\\var{frac2denom}} $</p>\n<p>=&nbsp;$ \\frac{\\var{frac1num*frac2denom}}{\\var{frac1denom*frac2denom}} +&nbsp;\\frac{\\var{frac2num*frac1denom}}{\\var{frac2denom*frac1denom}} $</p>\n<p>=$ \\frac{\\var{frac1num*frac2denom+frac2num*frac1denom}}{\\var{frac1denom*frac2denom}} $</p>\n<p>Then we subtract this answer from one whole to find the fraction of sausages remaining for {name3} to cook.</p>\n<p>1 -&nbsp;$ \\frac{\\var{frac1num*frac2denom+frac2num*frac1denom}}{\\var{frac1denom*frac2denom}} $</p>\n<p>=&nbsp;$ \\frac {\\var{frac1denom*frac2denom-(frac1num*frac2denom+frac2num*frac1denom)}}{\\var{frac1denom*frac2denom}} $</p>\n<div data-jme-visible=\"gcd(frac1denom*frac2denom - (frac1num*frac2denom+frac2num*frac1denom),frac1denom*frac2denom)=1\">\n<p>This fraction cannot be simplified.</p>\n<p>So {name3}&nbsp;cooked the remaining $ \\frac {\\var{answernumerator}} {\\var{answerdenominator}} $ of the sausages.</p>\n</div>\n<p></p>\n<div data-jme-visible=\"gcd(frac1denom*frac2denom - (frac1num*frac2denom+frac2num*frac1denom),frac1denom*frac2denom)&gt;1\">\n<p>This fraction needs to be simplified. Divide both numerator and denominator by&nbsp;{gcd(frac1denom*frac2denom-(frac1num*frac2denom+frac2num*frac1denom),frac1denom*frac2denom)}.</p>\n<p>$ \\frac&nbsp; {\\var {frac1denom*frac2denom-(frac1num*frac2denom+frac2num*frac1denom)}}{\\var{frac1denom*frac2denom}} $ = $ \\frac {\\var{answernumerator}} {\\var{answerdenominator}}$</p>\n<p>So {name3}&nbsp;cooked the remaining $ \\frac {\\var{answernumerator}} {\\var{answerdenominator}} $ of the sausages.</p>\n</div>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"frac1name": {"name": "frac1name", "group": "Ungrouped variables", "definition": "frac1[\"name\"]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The randomly selected fraction for the first student -&nbsp;&nbsp;in word form.</p>", "templateType": "anything", "can_override": false}, "fractionnotcooked": {"name": "fractionnotcooked", "group": "Ungrouped variables", "definition": "rational_approximation(decimalnotcooked)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The&nbsp;proportion of sausages not cooked by students 1 and 2 together, as a fraction.</p>", "templateType": "anything", "can_override": false}, "answernumerator": {"name": "answernumerator", "group": "Ungrouped variables", "definition": "fractionnotcooked[0]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The numerator of the proportion&nbsp;of sausages not cooked by students 1 and 2 together (fraction not yet simplified)</p>", "templateType": "anything", "can_override": false}, "decimalnotcooked": {"name": "decimalnotcooked", "group": "Ungrouped variables", "definition": "1-((frac1num/frac1denom)+(frac2num/frac2denom))", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The&nbsp;proportion of sausages not cooked by students 1 and 2 together.</p>", "templateType": "anything", "can_override": false}, "frac2": {"name": "frac2", "group": "Ungrouped variables", "definition": "random(frac2options)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The randomly selected fraction for the&nbsp;second student - in both word and numerical form.</p>", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random(\"Sue\",\"Edwin\",\"Matt\",\"Jake\",\"Madi\",\"Julia\")", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>A randomly selected name from the list for the first person.</p>", "templateType": "anything", "can_override": false}, "frac1denom": {"name": "frac1denom", "group": "Ungrouped variables", "definition": "frac1[\"denom\"]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The denominator of the randomly selected fraction for the first student.</p>", "templateType": "anything", "can_override": false}, "frac2denom": {"name": "frac2denom", "group": "Ungrouped variables", "definition": "frac2[\"denom\"]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The denominator of the randomly selected fraction for the&nbsp;second student.</p>", "templateType": "anything", "can_override": false}, "frac2options": {"name": "frac2options", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n    {\\n        \\\"name\\\": \\\"one fifth\\\",\\n        \\\"num\\\": 1,\\n        \\\"denom\\\": 5\\n    },\\n    {\\n        \\\"name\\\": \\\"one sixth\\\",\\n        \\\"num\\\": 1,\\n        \\\"denom\\\": 6\\n    },\\n    {\\n        \\\"name\\\": \\\"two fifths\\\",\\n        \\\"num\\\": 2,\\n        \\\"denom\\\": 5\\n    }\\n]\"))", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>List of three possible scenarios for the proportion of sausages cooked by the&nbsp;second student.</p>", "templateType": "json", "can_override": false}, "frac2name": {"name": "frac2name", "group": "Ungrouped variables", "definition": "frac2[\"name\"]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The randomly selected fraction for the&nbsp;second student -&nbsp;&nbsp;in word form.</p>", "templateType": "anything", "can_override": false}, "frac1options": {"name": "frac1options", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n    {\\n        \\\"name\\\": \\\"half\\\",\\n        \\\"num\\\": 1,\\n        \\\"denom\\\": 2\\n    },\\n    {\\n        \\\"name\\\": \\\"one third\\\",\\n        \\\"num\\\": 1,\\n        \\\"denom\\\": 3\\n    },\\n    {\\n        \\\"name\\\": \\\"one quarter\\\",\\n        \\\"num\\\": 1,\\n        \\\"denom\\\": 4\\n    }\\n]\"))", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>List of three possible scenarios for the proportion of sausages cooked by the first student.</p>", "templateType": "json", "can_override": false}, "answerdenominator": {"name": "answerdenominator", "group": "Ungrouped variables", "definition": "fractionnotcooked[1]", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The&nbsp;denominator of the proportion&nbsp;of sausages not cooked by students 1 and 2 together (fraction not yet simplified)</p>", "templateType": "anything", "can_override": false}, "frac1": {"name": "frac1", "group": "Ungrouped variables", "definition": "random(frac1options)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>The randomly selected fraction for the first student - in both word and numerical form.</p>", "templateType": "anything", "can_override": false}, "name2": {"name": "name2", "group": "Ungrouped variables", "definition": "random(\"Lisa\",\"Shelley\",\"Liz\",\"Mike\",\"Jack\",\"Andrew\")", "description": "<p>A randomly selected name from the list for the&nbsp;second person.</p>", "templateType": "anything", "can_override": false}, "name3": {"name": "name3", "group": "Ungrouped variables", "definition": "random(\"Amber\",\"Becky\",\"Yuhan\",\"Shani\",\"Ravi\",\"Jim\")", "description": "<p>A randomly selected name from the list for the&nbsp;third person.</p>", "templateType": "anything", "can_override": false}, "frac1num": {"name": "frac1num", "group": "Ungrouped variables", "definition": "frac1[\"num\"]", "description": "<p>The numerator of the randomly selected fraction for the first student.</p>", "templateType": "anything", "can_override": false}, "frac2num": {"name": "frac2num", "group": "Ungrouped variables", "definition": "frac2[\"num\"]", "description": "<p>The numerator of the randomly selected fraction for the&nbsp;second student.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["name1", "name2", "name3", "frac1options", "frac1", "frac1name", "frac1num", "frac1denom", "frac2options", "frac2", "frac2name", "frac2num", "frac2denom", "decimalnotcooked", "fractionnotcooked", "answernumerator", "answerdenominator"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What fraction of the sausages was left for {name3} to cook?&nbsp;</p>\n<p>Use the&nbsp; /&nbsp; key to enter your answer as a fraction in simplest form.</p>", "minValue": "decimalnotcooked", "maxValue": "decimalnotcooked", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}