// Numbas version: exam_results_page_options {"name": "Keeping track of units (dimension analysis) 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"preventleave": false, "allowregen": true, "showfrontpage": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["fulllist", "units", "seed"], "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."}, "name": "Keeping track of units (dimension analysis) 1", "statement": "

Evaluate the following without using a calculator.

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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.

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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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