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{"name": "Simplify a measurement ratio (10+)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simplify a measurement ratio (10+)", "tags": ["LANTITE"], "metadata": {"description": "<p>Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a height in centimetres and another height in metres, and are asked to write the ratio of the two heights in simplest form. There are 16 versions of this question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A class conducted a science experiment to investigate the growth of plants. They planted twenty tomato seedlings, and measured their height once per week, until they were mature tomato plants.</p>\n<p>The average height of the seedlings on the day they were planted was&nbsp; $\\var{s_ht}$ cm, and the mature plants reached an average height of&nbsp; $\\var{m_ht}$ m.&nbsp;</p>", "advice": "<p>Did you estimate what the answer should be and eliminate obviously wrong answers first?</p>\n<p>When writing a ratio, the quantities must be in the same units, then the proportion should be fully simplified.</p>\n<p>The seedling height is given in centimetres while the mature height is given in metres.</p>\n<p>The larger unit should be converted to the smaller unit (to avoid decimals numbers), so convert the measurement in metres (average mature height) to centimetres.</p>\n<p>There are&nbsp; $100$ centimetres in&nbsp; $1$ metre, so we multiply&nbsp; $\\var{m_ht}$ by&nbsp; $100$.</p>\n<p>$\\var{m_ht} \\text{ m} \\times 100 = \\var{m_ht_cm}$ cm.</p>\n<p>So the ratio of average seedling height to average mature height is&nbsp; $\\var{s_ht} : \\var{m_ht_cm}$. Note that we omit the units from the ratio.</p>\n<p>However, this is not in simplest form. The largest number that divides exactly into both of these numbers is&nbsp; $\\var{gcd}$.</p>\n<p>We need to divide both of the measurements by&nbsp; $\\var{gcd}$, to simplify the ratio.</p>\n<p>$\\var{s_ht} \\div \\var{gcd} = \\var{s_ratio}$</p>\n<p>$\\var{m_ht_cm} \\div \\var{gcd} = \\var{m_ratio}$</p>\n<p>The ratio of average seedling height to average mature height is&nbsp; $\\var{s_ratio} : \\var{m_ratio}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"s_ht": {"name": "s_ht", "group": "Ungrouped variables", "definition": "random(5,10,15,20)", "description": "<p>The seedling height in centimetres.</p>", "templateType": "anything", "can_override": false}, "m_ht": {"name": "m_ht", "group": "Ungrouped variables", "definition": "random(1.2,1.3,1.4,1.5)", "description": "<p>The mature plant height in metres.</p>", "templateType": "anything", "can_override": false}, "m_ht_cm": {"name": "m_ht_cm", "group": "Ungrouped variables", "definition": "100*m_ht", "description": "<p>The mature height in centimetres.</p>", "templateType": "anything", "can_override": false}, "gcd": {"name": "gcd", "group": "Ungrouped variables", "definition": "gcd(s_ht,m_ht_cm)", "description": "<p>The greatest common denominator of the seedling height and the mature height.</p>", "templateType": "anything", "can_override": false}, "s_ratio": {"name": "s_ratio", "group": "Ungrouped variables", "definition": "s_ht/gcd", "description": "<p>The simplified ratio component for&nbsp;seedling height.</p>", "templateType": "anything", "can_override": false}, "m_ratio": {"name": "m_ratio", "group": "Ungrouped variables", "definition": "m_ht_cm/gcd", "description": "<p>The simplified ratio component for mature height.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["s_ht", "m_ht", "m_ht_cm", "gcd", "s_ratio", "m_ratio"], "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 is the simplest ratio of the average seedling height to the average mature plant height?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["$\\var{s_ratio} : \\var{m_ratio}$", "$\\var{s_ht} : \\var{m_ht_cm}$", "$\\var{s_ht} : \\var{m_ht}$", "$\\var{s_ratio} : \\var{m_ratio*10}$"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done - you are correct!", "Have you simplified this ratio?", "Have you converted to the same units, then simplified?", "Check how many centimetres there are in a metre."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}