// Numbas version: finer_feedback_settings
{"name": "Percentages - One Amount as a Percentage of Another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "name": "Percentages - One Amount as a Percentage of Another", "tags": [], "advice": "<p>Write it as a fraction - the small amount over the larger amount.</p>\n<p>If the denominator is not a factor of 100 then cancel the fraction down till it is a factor of 100.</p>\n<p>Once the denominator is a factor of 100 multiply the fraction up so that the denominator is 100.</p>\n<p>The percentage is the value of the numerator.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{a}$ is $\\var{b}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "b/a", "minValue": "b/a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(b/a)*((100/a)/(100/a))", "minValue": "(b/a)*((100/a)/(100/a))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{c}$ is $\\var{d}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d/c", "minValue": "d/c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(d/c)*((100/c)/(100/c))", "minValue": "(d/c)*((100/c)/(100/c))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{j}$ is what percengage of $\\var{h}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "j/h", "minValue": "j/h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(j/h)*((100/h)/(100/h))", "minValue": "(j/h)*((100/h)/(100/h))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{f}$ is what percentage of $\\var{g}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f/4)/(g/4)", "minValue": "(f/4)/(g/4)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f*(100/g))/(g*(100/g))", "minValue": "(f*(100/g))/(g*(100/g))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{k}$ is what percentage of $\\var{l}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "k/l", "minValue": "k/l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k/3)/(l/3)", "minValue": "(k/3)/(l/3)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k*(100/l))/(l*(100/l))", "minValue": "(k*(100/l))/(l*(100/l))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{m}$ is what percentage of $\\var{n}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "m/n", "minValue": "m/n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m/7)/(n/7)", "minValue": "(m/7)/(n/7)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m*(100/n))/(m*(100/n))", "minValue": "(m*(100/n))/(n*(100/n))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>For each of the following questions work out one value as a percentage of the other. You are&nbsp;expected to do this without the help of a calculator.</p>\n<p>You can click reveal steps to show you how to solve each question. You will lose marks for revealing steps.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..a-1) //random number that is less than the value of a", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..c-1) //random number that is less than the value of c", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(20,40,80) //random number from list", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(4..g-1#4) // a random number less than f that is divisible by 4", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random([5,10,20,25,50,100,200]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(3..l-1#3)  //random number less than l that is divisible by 3", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(1..h-1) //random number that is less than the value of h", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(7..n-1#7)  //random number that is divisble by 7 and less than n", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(15,30,60,75,150)  //a random number that divides by 3 to give a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(35,70,140,175,350)  //random number that when divided by 7 gives a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "<p>This question asks you to work out one value as a percentage of another. &nbsp;You are expected to do these without the help of a calculator.</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": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}]}]}], "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}]}