// Numbas version: exam_results_page_options {"name": "Keeping track of units (dimension analysis) 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Keeping track of units (dimension analysis) 1", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Nursing question. Determine the units of an answer given the units and operations used."}, "extensions": [], "preamble": {"js": "", "css": ""}, "statement": "

Evaluate the following without using a calculator.

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If you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "variable_groups": [], "functions": {}, "variables": {"units": {"name": "units", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "shuffle(fulllist)[0..3]"}, "fulllist": {"name": "fulllist", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "['mL','mg','hr','drops','min','kg','mcg','units']"}, "seed": {"name": "seed", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(0,1)"}}, "tags": [], "parts": [{"variableReplacements": [], "gaps": [{"variableReplacements": [], "displayAnswer": "{units[1]}/{units[2]}", "type": "patternmatch", "useCustomName": false, "matchMode": "regex", "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "answer": "{units[1]}/{units[2]}", "showCorrectAnswer": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": 1}], "type": "gapfill", "useCustomName": false, "prompt": "

Suppose you calculate something using the following units and operations.

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\$\\frac{\\var{units[1]}/\\var{units[0]}\\times \\var{units[0]}}{\\var{units[2]}}\$ \$\\frac{\\var{units[0]}\\times \\var{units[1]}/\\var{units[0]}}{\\var{units[2]}}\$

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What units would the final answer have?

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", "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "

In our situation

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\$\\frac{\\var{units[1]}/\\var{units[0]}\\times \\var{units[0]}}{\\var{units[2]}}\$ \$\\frac{\\var{units[0]}\\times \\var{units[1]}/\\var{units[0]}}{\\var{units[2]}}\$

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the {units[0]} 'cancel', leaving $\\displaystyle\\frac{\\var{units[1]}}{\\var{units[2]}}$, which as units we write as {units[1]}/{units[2]}.

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So why do the {units[0]} cancel? Well, on the top of the fraction we have a '{units[0]}'  but we also have a 'divide by {units[0]}', and if you divide something by itself you get $1$, which doesn't affect the units.

", "rulesets": {}, "ungrouped_variables": ["fulllist", "units", "seed"], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}