// Numbas version: finer_feedback_settings
{"name": "Percentages by Cancelling", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["denom1", "Factor1", "bigDenom1", "num1", "bigNum1", "perc1", "denom2", "Factor2", "bigDenom2", "num2", "bigNum2", "perc2", "multiplier"], "name": "Percentages by Cancelling", "tags": [], "advice": "<p>See the step for part a.</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{bigNum1}</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnumNoBtm \">[[0]]%</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{bigDenom1}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<pre></pre>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "perc1", "minValue": "perc1", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>In these sorts of questions our aim is to find an equivalent fraction with 100 as the denominator (bottom number). The numerator (top number) of this new equivalent fraction will be the percentage.</p>\n<p>The easiest way to do this is in stages &ndash; the first stage is to find an equivalent fraction with a denominator of either 5, 10, 20, 25 or 50.</p>\n<p>(If the fraction <em><strong>already</strong></em> has 20 (or 25) as the denominator, you can just multiply top and bottom by 5 (or 4) to get a denominator of 100.&nbsp; Then the new numerator will be the percentage.)</p>\n<p>In this example we can divide the top and bottom of the fraction by the same number to find an equivalent fraction with a denominator of $\\var{denom1}$.</p>\n<p>The next stage is to multiply the top and bottom of our new fraction by a number that will give us an equivalent fraction with a denominator of 100.</p>\n<p>In this example, we will need to multiply by $\\var{multiplier}$.</p>\n<p>The number that we get on the top of this fraction is the percentage.</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<div class=\"fractiontable\">\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">{bigNum2}</td>\n<td class=\"tdeq\">=</td>\n<td class=\"tdnumNoBtm \">[[0]]%</td>\n</tr>\n<tr>\n<td class=\"tddenom\">{bigDenom2}</td>\n</tr>\n</tbody>\n</table>\n</div>\n<pre></pre>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "perc2", "minValue": "perc2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>In the QTS test, it's often quicker to convert a fraction to a percentage by cancelling so you have 5, 10, 20, 25 or 50 as the denominator (bottom number).&nbsp; Then you can multiply top and bottom of the fraction so you've got 100 as the denominator: the numerator will be the percentage you want.</p>", "variable_groups": [], "variablesTest": {"maxRuns": "62", "condition": "bigDenom1 <> 100 &&bigDenom1 <> 200 && bigDenom2 <> 100 && bigDenom2 <> 200 "}, "preamble": {"css": ".fractiontable table {\n  width: 20%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdnumNoBtm \n{\n  width: 15%; \n  border-bottom: 0px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size: x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n", "js": ""}, "variables": {"denom1": {"definition": "random(5,10,20,25)", "templateType": "anything", "group": "Ungrouped variables", "name": "denom1", "description": ""}, "denom2": {"definition": "random([5,10,20,25]  except [denom1])", "templateType": "anything", "group": "Ungrouped variables", "name": "denom2", "description": ""}, "Factor1": {"definition": "random(4..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "Factor1", "description": ""}, "Factor2": {"definition": "random(3..8 except Factor1)", "templateType": "anything", "group": "Ungrouped variables", "name": "Factor2", "description": ""}, "num2": {"definition": "denom2-random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "bigNum1": {"definition": "num1*Factor1\n", "templateType": "anything", "group": "Ungrouped variables", "name": "bigNum1", "description": ""}, "bigNum2": {"definition": "num2*Factor2", "templateType": "anything", "group": "Ungrouped variables", "name": "bigNum2", "description": ""}, "multiplier": {"definition": "100/denom1", "templateType": "anything", "group": "Ungrouped variables", "name": "multiplier", "description": ""}, "perc1": {"definition": "num1/denom1*100", "templateType": "anything", "group": "Ungrouped variables", "name": "perc1", "description": ""}, "bigDenom1": {"definition": "denom1*Factor1", "templateType": "anything", "group": "Ungrouped variables", "name": "bigDenom1", "description": ""}, "bigDenom2": {"definition": "denom2*Factor2", "templateType": "anything", "group": "Ungrouped variables", "name": "bigDenom2", "description": ""}, "perc2": {"definition": "num2/denom2*100", "templateType": "anything", "group": "Ungrouped variables", "name": "perc2", "description": ""}, "num1": {"definition": "denom1-random(2..4)\n ", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}}, "metadata": {"description": "<p>8/9/15</p>\n<p>Practice of cancelling a fraction, where the denominator will reduce to either 5,10, 20, 25, or 50 and then multiplying numerator and denominator by either 20, 10, 5, 4 or 2 respectively, to represent the fraction as a percentage.&nbsp; A helpful strategy in the QTS test...</p>\n<p>Tweaked the variables to avoid duplicate fractions in the 2 parts &amp; make the second slightly more tricky, on average.&nbsp; Used the Testing facility to prevent 100 or 200 appearing in the denominators.</p>\n<p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}]}]}], "contributors": [{"name": "Rob Cade", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/70/"}]}