// Numbas version: exam_results_page_options
{"name": "NC NA Write a proportion as a simple fraction using gcd (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NC NA Write a proportion as a simple fraction using gcd (10+)", "tags": ["LANTITE"], "metadata": {"description": "<p>Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number &amp; Algebra strand. Students are given the number of pages read (randomised) and number of pages remaining (randomised), and asked to write the proportion read as a simple fraction.</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<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>{name1} has read {pagesread} pages of a book. There are still {pagesleft} pages yet to read.&nbsp;</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>First, calculate the total number of pages in the book.&nbsp; &nbsp;&nbsp;{pagesread} +&nbsp;{pagesleft} = {pagesread + pagesleft}</p>\n<p>Next write the proportion read as a fraction, with the number of&nbsp;pages read on the top, and the total number of pages on the bottom.&nbsp;</p>\n<p>&nbsp;{name1} has read $ \\frac{\\var{pagesread}} {\\var{pagesread + pagesleft}} $ of the book.</p>\n<p>Finally, simplify this fraction by dividing top (numerator) and bottom (denominator) by the highest common factor, which is {scale_factor}.</p>\n<p>$\\frac{\\var{pagesread} &divide; {\\var{scale_factor}}} {\\var{pagesread + pagesleft} &divide; {\\var{scale_factor}}}$&nbsp;=&nbsp;$\\frac{\\var{numerator}} {\\var{denominator}}$</p>\n<p>{name1} has read $\\frac{\\var{numerator}} {\\var{denominator}}$ of the book, in simplest form.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"den": {"name": "den", "group": "Ungrouped variables", "definition": "num+increment", "description": "<p>This is the denominator of the unsimplified answer. It is forced to be larger than the numerator to ensure a proper fraction by the use of the increment.</p>", "templateType": "anything", "can_override": false}, "scale_factor": {"name": "scale_factor", "group": "Ungrouped variables", "definition": "random(6 .. 24#1)", "description": "<p>The scale factor ensures that the book has enough pages, and that the fraction answer will require simplification.</p>", "templateType": "randrange", "can_override": false}, "denominator": {"name": "denominator", "group": "Ungrouped variables", "definition": "den/hcf", "description": "<p>This is the denominator of the final simplified answer.</p>", "templateType": "anything", "can_override": false}, "pagesleft": {"name": "pagesleft", "group": "Ungrouped variables", "definition": "scale_factor*(denominator-numerator)", "description": "<p>This is given in the question. It is the number of pages already read. It is calculated by multiplying the difference between the&nbsp;denominator and the&nbsp;numerator of the final answer by the scale factor.</p>", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "random(1 .. 6#1)", "description": "<p>This is the numerator of the unsimplified answer. It is the starting point of the fraction answer set-up.</p>", "templateType": "randrange", "can_override": false}, "pagesread": {"name": "pagesread", "group": "Ungrouped variables", "definition": "scale_factor*numerator", "description": "<p>This is given in the question. It is calculated by multiplying the numerator of the final answer by the scale factor.</p>", "templateType": "anything", "can_override": false}, "numerator": {"name": "numerator", "group": "Ungrouped variables", "definition": "num/hcf", "description": "<p>This is the numerator of the final simplified answer.</p>", "templateType": "anything", "can_override": false}, "hcf": {"name": "hcf", "group": "Ungrouped variables", "definition": "gcd(num,den)", "description": "<p>This is the highest common factor of num and den. They are divided by it to give the final simplified answer.</p>", "templateType": "anything", "can_override": false}, "increment": {"name": "increment", "group": "Ungrouped variables", "definition": "random(1..5 except num)", "description": "<p>The increment is added to numerator to force the denominator to be larger than the numerator. This ensures a proper fraction.</p>", "templateType": "anything", "can_override": false}, "NamesIndex": {"name": "NamesIndex", "group": "Ungrouped variables", "definition": "random(0 .. 6#1)", "description": "<p>The random number used to index the list of names.</p>", "templateType": "randrange", "can_override": false}, "Names": {"name": "Names", "group": "Ungrouped variables", "definition": "[ \"Nick\", \"Jessi\", \"Ali\", \"Jo\", \"Lachlan\", \"Ravi\", \"Elisa\" ]", "description": "<p>The lsit of names from which one name is selected.</p>", "templateType": "list of strings", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "Names[NamesIndex]", "description": "<p>The chosen name for the question.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "numerator<denominator", "maxRuns": 100}, "ungrouped_variables": ["pagesread", "pagesleft", "scale_factor", "increment", "denominator", "numerator", "num", "den", "hcf", "Names", "NamesIndex", "name1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "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 book has he read, in simplest form?&nbsp;</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$ \\frac{\\var{pagesread}}{\\var{pagesleft}} $", "$ \\frac{\\var{pagesread}}{\\var{pagesread+pagesleft}} $", "$ \\frac{\\var{numerator}}{\\var{denominator}} $", "$ \\frac{\\var{numerator}}{\\var{denominator-numerator}} $"], "matrix": [0, 0, "1", 0], "distractors": ["How many pages does the book have in total? And is your fraction in simplified form? Click on Reveal Answer and scroll down for Advice regarding this question.", "Is your fraction in simplified form? Click on Reveal Answer and scroll down for Advice regarding this question.", "Well done!", "How many pages does the book have in total? Click on Reveal Answer and scroll down for Advice regarding this question."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}