// Numbas version: exam_results_page_options
{"name": "Nigel's copy of Basic rates/ratios for nursing", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["volume", "dpml", "ans1", "duration", "dpm", "ans2", "ans3", "minutes", "drops", "ans4", "capacity", "numdrops"], "name": "Nigel's copy of Basic rates/ratios for nursing", "tags": ["conversion", "converting", "ephlth", "rates", "unit", "unitary"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>A certain IV drip&nbsp;delivers {dpml} drops&nbsp;per mL. This is equivalent to [[0]]&nbsp;drops per {volume} mL.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.</em></p>\n<p></p>\n<p>The following are all equivalent ways of writing the same rate:</p>\n<p>{dpml} drops per mL =&nbsp;{dpml} d/mL =&nbsp;{dpml} d / 1 mL = $\\dfrac{\\var{dpml} \\text{ drops}}{1 \\text{ mL}}$.</p>\n<p>We can multiply the top and bottom by any number other than zero and keep the rate the same. Since we are asked about {volume} mL, we multiply the top and bottom by {volume} so the bottom&nbsp;of the fraction is {volume}.</p>\n<p>$\\dfrac{\\var{dpml} \\text{ drops}}{1 \\text{ mL}}\\times\\dfrac{\\var{volume}}{\\var{volume}}=\\dfrac{\\var{ans1} \\text{ drops}}{\\var{volume}\\text{ mL}}$</p>\n<p>In other words the rate is equivalent to {ans1} drops per {volume} mL.</p>\n<hr/>\n<p><em>We can also approach these questions like ratios.</em></p>\n<p></p>\n<p>Think of&nbsp;{dpml} drops&nbsp;per mL as the ratio {dpml} drops : 1 mL.</p>\n<p>We can multiply both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about {volume} mL, we multiply both sides by {volume}.</p>\n<p></p>\n<p>$\\var{dpml} \\text{ drops} \\,:\\, 1 \\text{ mL} = \\var{dpml}\\times \\var{volume}\\text{ drops}\\, :\\, 1 \\times \\var{volume} \\text{ mL} = \\var{ans1} \\text{ drops}\\,:\\, \\var{volume}\\text{ mL}$.</p>\n<p>In other words there are {ans1} drops in {volume} mL.</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>A patient requires {dpm} drops per minute from an IV. How many drops will they need over {duration} minutes?</p>\n<p></p>\n<p>[[0]] drops.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.</em></p>\n<p></p>\n<p>The following are all equivalent ways of writing the same rate:</p>\n<p>{dpm} drops per minute =&nbsp;{dpm} d/min =&nbsp;{dpm} d / 1 min = $\\dfrac{\\var{dpm} \\text{ drops}}{1 \\text{ min}}$.</p>\n<p>We can multiply the top and bottom by any number other than zero and keep the rate the same. Since we are asked about {duration} minutes, we multiply the top and bottom by {duration} so the bottom&nbsp;of the fraction is {duration}.</p>\n<p>$\\dfrac{\\var{dpm} \\text{ drops}}{1 \\text{ min}}\\times\\dfrac{\\var{duration}}{\\var{duration}}=\\dfrac{\\var{ans2} \\text{ drops}}{\\var{duration}\\text{ min}}$</p>\n<p>In other words the rate is equivalent to {ans2} drops per {duration} minutes.</p>\n<hr/>\n<p><em>We can also approach these questions like ratios.</em></p>\n<p></p>\n<p>Think of&nbsp;{dpm} drops&nbsp;per minute as the ratio {dpm} drops : 1 minute.</p>\n<p>We can multiply both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about {duration} minutes, we multiply both sides by {duration}.</p>\n<p>&nbsp;</p>\n<p>$\\var{dpm} \\text{ drops} \\,:\\, 1 \\text{ min} = \\var{dpm}\\times \\var{duration}\\text{ drops}\\, :\\, 1 \\times \\var{duration} \\text{ min} = \\var{ans2} \\text{ drops}\\,:\\, \\var{duration}\\text{ min}$.</p>\n<p>In other words there are {ans2} drops in {duration} minutes.</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>If a&nbsp;patient received {drops} drops over {minutes} minutes, then the patient received [[0]]&nbsp;drops per minute.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.</em></p>\n<p>&nbsp;</p>\n<p>The following are all equivalent ways of writing the same rate:</p>\n<p>{drops} drops per {minutes} minutes =&nbsp;{drops} d/ {minutes} min = $\\dfrac{\\var{drops} \\text{ drops}}{\\var{minutes} \\text{ min}}=\\dfrac{\\var{drops}}{\\var{minutes}} \\text{ drops/min}$.</p>\n<p>&nbsp;So we just need to do the division to determine the rate per minute.</p>\n<p>$\\dfrac{\\var{drops}}{\\var{minutes}} \\text{ drops/min}=\\var{ans3} \\text{ drops/min}$</p>\n<p>In other words the rate is equivalent to {ans3} drops per minute.</p>\n<p></p>\n<hr/>\n<p><em>We can also approach these questions like ratios.</em></p>\n<p>&nbsp;</p>\n<p>Think of&nbsp;{drops} drops&nbsp;per {minutes} minutes as the ratio {drops} drops : {minutes}&nbsp;min.</p>\n<p>We can multiply or divide both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about drops per minute, we divide&nbsp;both sides by {minutes}.</p>\n<p>&nbsp;</p>\n<p>$\\var{drops} \\text{ drops} \\,:\\, \\var{minutes}&nbsp;\\text{ min} = \\var{drops}\\div \\var{minutes}\\text{ drops}\\, :\\, \\var{minutes}&nbsp;\\div \\var{minutes} \\text{ min} = \\var{ans3} \\text{ drops}\\,:\\, 1\\text{ min}$.</p>\n<p>In other words there are {ans3} drops per minute.</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>If an IV drip delivers&nbsp;{capacity} mL through {numdrops} drops, then there must be&nbsp;[[0]]&nbsp;drops in each mL.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>We can approach these questions like equivalent fractions by replacing the word 'per' with the operation of division.</em></p>\n<p>&nbsp;</p>\n<p>The following are all equivalent ways of writing the same rate:</p>\n<p>{numdrops} drops per {capacity} mL = {numdrops} drops/{capacity} mL = $\\dfrac{\\var{numdrops} \\text{ drops}}{\\var{capacity} \\text{ mL}}=\\dfrac{\\var{numdrops}}{\\var{capacity}} \\text{ drops/mL}$.</p>\n<p>&nbsp;So we just need to do the division to determine the number of drops per mL.</p>\n<p>$\\dfrac{\\var{numdrops}}{\\var{capacity}} \\text{ drops/mL}=\\var{ans4} \\text{ drops/mL}$</p>\n<p>In other words the rate is equivalent to {ans4} drops per mL.</p>\n<p>&nbsp;</p>\n<hr/>\n<p><em>We can also approach these questions like ratios.</em></p>\n<p>&nbsp;</p>\n<p>Think of {numdrops} drops per&nbsp;{capacity} mL as the ratio {numdrops}&nbsp;drops : {capacity} mL.</p>\n<p>We can multiply or divide both sides of this ratio by any non-zero number to get an equivalent ratio. Since we want to know about drops per mL, we divide&nbsp;both sides by {capacity}.</p>\n<p>&nbsp;</p>\n<p>$\\var{numdrops} \\text{ drops} \\,:\\, \\var{capacity}&nbsp;\\text{ mL} = \\var{numdrops}\\div \\var{capacity}\\text{ drops}\\, :\\, \\var{capacity}&nbsp;\\div \\var{capacity} \\text{ mL} = \\var{ans4} \\text{ drops}\\,:\\, 1\\text{ mL}$.</p>\n<p>In other words there are {ans4} drops per mL.</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"dpml": {"definition": "random(10,15,20,60)", "templateType": "anything", "group": "Ungrouped variables", "name": "dpml", "description": ""}, "capacity": {"definition": "random(5..1000#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "capacity", "description": ""}, "numdrops": {"definition": "ans4*capacity", "templateType": "anything", "group": "Ungrouped variables", "name": "numdrops", "description": ""}, "ans1": {"definition": "dpml*volume", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "duration*dpm", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "random(5..220#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "random(10,15,20,60)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "volume": {"definition": "random(5..1000#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "volume", "description": ""}, "duration": {"definition": "random(5..60#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "duration", "description": ""}, "dpm": {"definition": "random(5..220#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "dpm", "description": ""}, "drops": {"definition": "minutes*ans3", "templateType": "anything", "group": "Ungrouped variables", "name": "drops", "description": ""}, "minutes": {"definition": "random(20..120)", "templateType": "anything", "group": "Ungrouped variables", "name": "minutes", "description": ""}}, "metadata": {"notes": "", "description": "<p>Calculating rates and scaling rates.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}]}], "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}