// Numbas version: exam_results_page_options
{"name": "Ratios and rates", "duration": 0, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["ratio", "Ratios", "ratios", "unitary"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"totaldollars": {"name": "totaldollars", "group": "Ungrouped variables", "definition": "random(50..2000#50)", "description": "", "templateType": "anything", "can_override": false}, "cordialratio": {"name": "cordialratio", "group": "Ungrouped variables", "definition": "random([2,5],[1,3],[1,4],[1,5])", "description": "", "templateType": "anything", "can_override": false}, "totalcordial": {"name": "totalcordial", "group": "Ungrouped variables", "definition": "random(10,20,30,40)", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "twostrokeoil*twostrokefuel", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "requireddistance/onedistance", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "totalcordial*cordialratio[0]/(cordialratio[0]+cordialratio[1])", "description": "", "templateType": "anything", "can_override": false}, "part2": {"name": "part2", "group": "Ungrouped variables", "definition": "random(2..10 except part1)", "description": "", "templateType": "anything", "can_override": false}, "onedistance": {"name": "onedistance", "group": "Ungrouped variables", "definition": "random(list(5..8#0.1))", "description": "", "templateType": "anything", "can_override": false}, "twostrokefuel": {"name": "twostrokefuel", "group": "Ungrouped variables", "definition": "random(16,20,25,30,32,35,37,40,45,50,55,60)", "description": "", "templateType": "anything", "can_override": false}, "part1": {"name": "part1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "requireddistance": {"name": "requireddistance", "group": "Ungrouped variables", "definition": "random(list(10..1000#10))", "description": "", "templateType": "anything", "can_override": false}, "part3": {"name": "part3", "group": "Ungrouped variables", "definition": "random(2..10 except part2)", "description": "", "templateType": "anything", "can_override": false}, "twostrokeoil": {"name": "twostrokeoil", "group": "Ungrouped variables", "definition": "random(list(100..5000#100))", "description": "", "templateType": "anything", "can_override": false}, "totalparts": {"name": "totalparts", "group": "Ungrouped variables", "definition": "part1+part2+part3", "description": "", "templateType": "anything", "can_override": false}, "position": {"name": "position", "group": "Ungrouped variables", "definition": "random(['first',part1],['second',part2],['third',part3])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["twostrokefuel", "twostrokeoil", "ans1", "totalcordial", "cordialratio", "ans3", "onedistance", "requireddistance", "ans2", "totaldollars", "part1", "part2", "part3", "totalparts", "position"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>A two-stroke fuel is mixed using the fuel to oil ratio {twostrokefuel}:1.</p>\n<p>This is equivalent to the ratio &nbsp;[[0]]&nbsp;: {twostrokeoil}.</p>\n<p>&nbsp;</p>", "stepsPenalty": "0", "steps": [{"type": "information", "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>These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, &nbsp;suppose your ratio is $4:5$ and you are asked to find an equivalent ratio that looks like $?:30$. To get from a 5 to a 30 we can multiply by 6, but to keep the ratio equivalent we need to do the same to the other side of the ratio. So we multiply 4 by 6 and get 24 and we can say the ratios $4:5$ and $24:30$ are equivalent.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>As a more complicated example, suppose we need to find an equivalent ratio of $4:5$ in the form $31:?$. We need to get from a 4 to a 31 by multiplying or dividing. The easiest way to do this is probably to divide by 4 and then multiply by 31 (note, this is the same as multiplying by $\\frac{31}{4}$). We need to do the same thing to the other side of the ratio. So we multiply 5 by $\\frac{31}{4}$ and get $\\frac{155}{4}$ and we can say the ratios $4:5$ and $31:\\frac{155}{4}$ are equivalent.</p>\n<p></p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans1}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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>A fixed gear bike is set up in such a way that one revolution of the pedals moves the bike {onedistance} metres. To ride the bike {requireddistance} metres how many revolutions of the pedals are required?&nbsp;</p>\n<p>[[0]] revolutions.</p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": "0", "steps": [{"type": "information", "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>These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, &nbsp;suppose your ratio is $4:5$ and you are asked to find an equivalent ratio that looks like $?:30$. To get from a 5 to a 30 we can multiply by 6, but to keep the ratio equivalent we need to do the same to the other side of the ratio. So we multiply 4 by 6 and get 24 and we can say the ratios $4:5$ and $24:30$ are equivalent.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>As a more complicated example, suppose we need to find an equivalent ratio of $4:5$ in the form $31:?$. We need to get from a 4 to a 31 by multiplying or dividing. The easiest way to do this is probably to divide by 4 and then multiply by 31 (note, this is the same as multiplying by $\\frac{31}{4}$). We need to do the same thing to the other side of the ratio. So we multiply 5 by $\\frac{31}{4}$ and get $\\frac{155}{4}$ and we can say the ratios $4:5$ and $31:\\frac{155}{4}$ are equivalent.</p>\n<p></p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{requireddistance}/{onedistance}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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>A cordial is mixed using the syrup to water ratio {cordialratio[0]}:{cordialratio[1]}. You need to make {totalcordial}&nbsp;litres. How many litres of syrup do you need?</p>\n<p>&nbsp;[[0]]&nbsp;L</p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": "0", "steps": [{"type": "information", "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><em>Determine the total number of parts used in the ratio. Find what one part&nbsp;corresponds to and then multiply by the required number of parts.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose you need to divide 490 kg into the ratio 2:5. The ratio has 7 parts (2+5). One part corresponds to $\\frac{490}{7}=70$ kg. This means 2 parts corresponds to $2\\times 70=140$ kg, and 5 parts corresponds to $5\\times 70=350$ kg. Therefore, 490 kg divided into the ratio 2:5 is 140 <g class=\"gr_ gr_576 gr-alert gr_gramm Punctuation multiReplace\" id=\"576\" data-gr-id=\"576\">kg :</g> 350 kg.&nbsp;</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{totalcordial*cordialratio[0]}/{cordialratio[0]+cordialratio[1]}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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>Three people split \\${totaldollars} amongst themselves in the ratio {part1}:{part2}:{part3}. How much money does the {position[0]} person get?&nbsp;</p>\n<p>\\$&nbsp;[[0]] (to the nearest cent)</p>", "stepsPenalty": "0", "steps": [{"type": "information", "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><em>Determine the total number of parts used in the ratio. Find what one part&nbsp;corresponds to and then multiply by the required number of parts.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose you need to divide 800 kg into the ratio 2:5:1. The ratio has 8&nbsp;parts (2+5+1). One part corresponds to $\\frac{800}{8}=100$ kg. This means 2 parts corresponds to $2\\times 100=200$ kg and 5 parts corresponds to $5\\times 100=500$ kg. Therefore, 800 kg divided into the ratio 2:5:1 is 200 kg : 500 kg : 100 kg.&nbsp;</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{totaldollars}/{totalparts}*{position[1]}", "showPreview": false, "checkingType": "dp", "checkingAccuracy": "2", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Rates", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["conversion", "converting", "rates", "unit", "unitary"], "metadata": {"description": "<p>Unit rates and converting rates.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"firstunit": {"name": "firstunit", "group": "part c", "definition": "if(seed[0]='cap',random([\"millilitre\",\"kilolitre\",1000000],[\"millilitre\",\"megalitre\",1000000000]),\nif(seed[0]='mass',random([\"gram\",\"tonne\",1000000],[\"milligram\",\"tonne\",1000000000],[\"milligram\",\"kilogram\",1000000]),\nif(seed[0]='time',random([\"millisecond\",\"hour\",3600000],[\"minute\",\"day\",1440],[\"second\",\"day\",86400],[\"millisecond\",\"day\",24*3600000]),\nif(seed[0]='distance',random([\"millimetre\",\"kilometre\", 1000000], [\"centimetre\", \"kilometre\",100000],[\"millimetre\",\"metre\",1000]),'error'))))", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "part c", "definition": "random(5..45)", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "part c", "definition": "random(5..45 except num1)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "fuel", "definition": "if(vehicle='car',random(400..650),if(vehicle='motorbike',random(210..375),'error'))", "description": "", "templateType": "anything", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(2..100)", "description": "", "templateType": "anything", "can_override": false}, "thing": {"name": "thing", "group": "Ungrouped variables", "definition": "random([['eats','eating','watermelons'],['eats','eating','pies'],['eats','eating','apples'],['eats','eating','grapes'],['eats','eating','sultanas'],['eats','eating','pickles'],['eats','eating','berries'],['serves', 'serving','tennis balls'],['bowls', 'bowling','cricket balls'],['mows', 'mowing','lawns'],['runs', 'running','kilometres'],['rides', 'riding','kilometres'],['writes', 'writing','lines of code'],['reads', 'reading','pages'],['reads', 'reading','books'],['buys','buying','unnecessary things off the internet'],['buys','buying','collectables'],['buys','buying','star wars figurines'],['buys','buying','movies'],['throws out','throwing out','pieces of scribble paper'],['plays','playing','games of football'],['plays','playing','games of quidditch']])", "description": "<p>plural, singular, object</p>", "templateType": "anything", "can_override": false}, "amount": {"name": "amount", "group": "fuel", "definition": "if(vehicle='car',random(35..60),if(vehicle='motorbike',random(11..20),'error'))", "description": "", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "Random(['Aaron', 'Alex', 'Ben', 'Claire', 'Charlotte',  'Daniel', 'Deb', 'Ethan', 'Elizabeth', 'Grace', 'Hunter', 'Julia', 'Isaac', 'Xavier', 'Victoria', 'Sophie', 'Abbey', 'Annie', 'Noah'])", "description": "", "templateType": "anything", "can_override": false}, "niceamount": {"name": "niceamount", "group": "fuel", "definition": "random(list(10..50#5) except amount)", "description": "", "templateType": "anything", "can_override": false}, "nicedistance": {"name": "nicedistance", "group": "fuel", "definition": "random(list(50..200#10))", "description": "", "templateType": "anything", "can_override": false}, "vehicle": {"name": "vehicle", "group": "fuel", "definition": "random(['car','motorbike'])", "description": "", "templateType": "anything", "can_override": false}, "integer": {"name": "integer", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "secondunit": {"name": "secondunit", "group": "part c", "definition": "if(seed[1]='cap',random([\"millilitre\",\"kilolitre\",1000000],[\"millilitre\",\"megalitre\",1000000000]),\nif(seed[1]='mass',random([\"gram\",\"tonne\",1000000],[\"milligram\",\"tonne\",1000000000],[\"milligram\",\"kilogram\",1000000]),\nif(seed[1]='time',random([\"millisecond\",\"hour\",3600000],[\"minute\",\"day\",1440],[\"second\",\"day\",86400],[\"millisecond\",\"day\",24*3600000]),\nif(seed[1]='distance',random([\"millimetre\",\"kilometre\", 1000000], [\"centimetre\", \"kilometre\",100000],[\"millimetre\",\"metre\",1000]),'error'))))", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "part c", "definition": "shuffle(['cap','time','mass','distance'])[0..2]", "description": "", "templateType": "anything", "can_override": false}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random(['hour', 'minute', 'day', 'month'])", "description": "", "templateType": "anything", "can_override": false}, "temp": {"name": "temp", "group": "part c", "definition": "num1*secondunit[2]/(num2*firstunit[2])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["person", "number", "integer", "unit", "thing"], "variable_groups": [{"name": "fuel", "variables": ["vehicle", "distance", "amount", "nicedistance", "niceamount"]}, {"name": "part c", "variables": ["firstunit", "seed", "secondunit", "num1", "num2", "temp"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>{person} {thing[0]} {number} {thing[2]} per {integer} {unit}s. This is equivalent to {thing[1]} [[0]]&nbsp;{thing[2]} per {unit}.</p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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><em>The word 'per' can be replaced with the operation of division.</em></p>\n<p>These questions are very similar to equivalent fractions.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Suppose you are told 'Daniel eats 61 berries per 3 hours'. The following three methods are equivalent but might appear different.</p>\n<ol>\n<li>We are given 61 berries / 3 hours. Divide both sides of the rate by 3 (so that we are dealing with 'per hour' not 'per 3 hours'). This gives 61/3 berries/hour.</li>\n<li><br/>\\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61}{3}\\frac{\\text{berries}}{\\text{hour}}=\\frac{61}{3} \\,\\text{berries/hour}.\\]</li>\n<li><br/>\\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61\\text{ berries }\\div 3}{3 \\text{ hours }\\div 3}=\\frac{61\\div 3\\text{ berries }}{1 \\text{ hour }}=\\frac{61}{3} \\,\\text{berries/hour}.\\]</li>\n</ol>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{number}/{integer}", "maxValue": "{number}/{integer}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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>A {vehicle} travels {distance} km per {amount} L of petrol. &nbsp;</p>\n<p></p>\n<p>How many kilometres can be travelled by using {niceamount} L?&nbsp;[[1]] km</p>\n<p>How many litres of petrol are needed to travel {nicedistance} km?&nbsp;[[0]] L</p>\n<p><strong></strong></p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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><em>Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Suppose you have 'a motorbike travels 245 km per 13 L of petrol'. Note, this can be&nbsp;written as 245 km / 13 L.</p>\n<p>To determine kilometres per 20 L, first determine how many kilometres per 1 L, and then multiply by 20. That is,&nbsp;</p>\n<p style=\"text-align: center;\">245 km / 13 &nbsp;L &nbsp;= $\\frac{345}{13}$ km/L = &nbsp;$\\frac{345}{13}\\times 20$ km / 20 L.</p>\n<p>To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,</p>\n<p style=\"text-align: center;\">245 km / 13 L = 1 km / $\\frac{13}{245}$ L = 50 km / $\\frac{13}{245}\\times 50$ L.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note,&nbsp;245 km per 13 L could also be written as 13 L / 245 km.&nbsp;It might be simpler to do the second question this way:</p>\n<p>&nbsp;To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,</p>\n<p style=\"text-align: center;\">13 L / 245 km = $\\frac{13}{245}$ L / km =&nbsp;$\\frac{13}{245}\\times 50$ L / 50 km.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{amount}*{nicedistance}/{distance}", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{distance}/{amount}*{niceamount}", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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>A&nbsp;rate of {num1} {firstunit[0]}s / {num2} {secondunit[0]}s is equivalent to [[0]]&nbsp;{firstunit[1]}s / {secondunit[1]}.</p>\n<p></p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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><strong></strong><em>Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).&nbsp;</em><em>Do one thing at a time to avoid making a mistake.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose we need to convert 24 milliseconds / 4 litres into an equivalent rate in minutes / kilolitre. We need to do the following steps:</p>\n<ol>\n<li>convert milliseconds to minutes,</li>\n<li>convert litres to kilolitres,</li>\n<li>make it per kilolitre.&nbsp;</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<ol>\n<li>There are 60,000 milliseconds in a minute so to convert from millisecond to minutes we divide the milliseconds by 60,000. We now have 0.0004 minutes / 4 litres.</li>\n<li>There are 1,000 litres in a kilolitre so to convert from litres to kilolitres, you need to divide the litres by 1,000. We now have&nbsp;0.0004 minutes / 0.004 litres.&nbsp;</li>\n<li>To make it per litre we recall that 0.0004 minutes / 0.004 litres <g class=\"gr_ gr_1763 gr-alert gr_gramm Grammar multiReplace\" id=\"1763\" data-gr-id=\"1763\">is</g> equivalent to&nbsp;0.0004/0.004 minutes / litre (this is the same as dividing both sides by 0.004).&nbsp;</li>\n</ol>\n<p>So our final answer is 0.1 minutes / litre.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{num1}*{secondunit[2]}/({num2}*{firstunit[2]})", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "extensions": [], "custom_part_types": [], "resources": []}