// Numbas version: finer_feedback_settings
{"name": "BODMAS: Percentages", "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", "mint", "chocolate", "sweets", "num", "den", "n", "d", "per", "marks", "increase", "new_mark", "decimal", "gcd_per100", "numerator", "denominator", "marks_increased", "p", "dec"], "name": "BODMAS: Percentages", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Questions of the form \"find $\\var{a}\\%$ of $\\var{b}$\".&nbsp;</strong></p>\n<p>In order to answer this you multiply the number, $\\var{b}$, by the percentage over 100, $\\dfrac{\\var{a}}{100}$</p>\n<p>$\\var{b} \\times \\dfrac{\\var{a}}{100} = \\simplify{{a}*{b}/100}$</p>\n<p><strong>Remember:</strong>&nbsp;Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"if a mixed bag of $\\var{sweets}$ sweets contains $\\var{mint}$ mints and $\\var{chocolate}$ chocolates. What percentage of the contents&nbsp;is chocolate\"</strong></p>\n<p>To calculate the percentage of chocolate sweets in the bag you must divide the number of chocolates by the total number of sweets and then multiply by $100%$.</p>\n<p>$\\dfrac{\\var{chocolate}}{\\var{sweets}}\\times 100 = \\simplify{100*{chocolate}/{sweets}}.</p>\n<p><strong>Remember:</strong>&nbsp;Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"convert $\\dfrac{\\var{num}}{\\var{den}}$ into a percentage\"</strong></p>\n<p>This question is very similar to part b). We already have the number in fractional form if we covert this into a decimal and multiply by $100\\%$ we obtain the percentage</p>\n<p>$\\dfrac{\\var{num}}{\\var{den}} = \\var{deciamal}\\times 100\\% = \\simplify{{decimal}*100}\\%$</p>\n<p><strong>Remember:</strong> Give you answer to 2 decimal places.</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"convert $\\var{per}\\%$ into a fraction\"</strong></p>\n<p>To do this you simply divide by $100$.</p>\n<p>$\\var{per}\\% = \\dfrac{\\var{per}}{100} = \\dfrac{\\var{numerator}}{\\var{denominator}}$&nbsp;</p>\n<p></p>\n<p></p>\n<p><strong>Questions of the form \"Last year the average mark in an exam was $\\var{marks}$. They have now increased by $\\var{increase}$ percent. What is the current average mark?\"</strong></p>\n<p>We start by finding $\\var{increase}$ % of $\\var{marks}$.</p>\n<p>$\\var{marks}\\times\\dfrac{\\var{increase}}{100} = \\var{marks_increased}$</p>\n<p>We then add this onto last years average marks to find this years</p>\n<p>$\\var{marks} + \\var{marks_increased} = \\var{new_mark}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find $\\var{a}\\%$ of $\\var{b}$</p>\n<p>Answer: &nbsp; [[0]] &nbsp;(2.d.p)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct number of decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(a/100)*b", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(a/100)*b", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>If a mixed bag of $\\var{sweets}$ sweets contains $\\var{mint}$ mints and $\\var{chocolate}$ chocolates. What percentage of the contents&nbsp;is chocolate?</p>\n<p></p>\n<p>Answer: &nbsp;[[0]] %(2.dp)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(chocolate/sweets)*100", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(chocolate/sweets)*100", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Convert $\\dfrac{\\var{num}}{\\var{den}}$ into a percentage.</p>\n<p>Answer: [[0]] % (2dp)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct number of decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "(num/den)*100", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "(num/den)*100", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Convert $\\var{per}\\%$ into a fraction. Fraction must be in it's simplest form.</p>\n<p>Answer: [[0]]&nbsp;/[[1]]</p>", "marks": 0, "gaps": [{"allowFractions": false, "marks": 1, "maxValue": "numerator", "minValue": "numerator", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "marks": 1, "maxValue": "denominator", "minValue": "denominator", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Last year the average mark in an exam was $\\var{marks}$. They have now increased by $\\var{increase}$ percent. What is the current average mark?</p>\n<p>Answer: [[0]]</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "new_mark", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "new_mark", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p>Write $\\var{p}$ as a decimal?</p>\n<p>Answer: &nbsp;[[0]] (2 d.p.)</p>", "marks": 0, "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision. Please give your answer to 2 decimal places.</p>", "allowFractions": false, "marks": 1, "precision": "2", "maxValue": "dec", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "minValue": "dec", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "<p>Answer the following questions on percentages.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..20)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(1..30)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(n+1..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "p": {"definition": "random(1..99)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "marks_increased": {"definition": "marks*increase/100", "templateType": "anything", "group": "Ungrouped variables", "name": "marks_increased", "description": ""}, "new_mark": {"definition": "marks*(1+(increase/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "new_mark", "description": ""}, "denominator": {"definition": "100/gcd_per100", "templateType": "anything", "group": "Ungrouped variables", "name": "denominator", "description": ""}, "numerator": {"definition": "per/gcd_per100", "templateType": "anything", "group": "Ungrouped variables", "name": "numerator", "description": ""}, "per": {"definition": "precround(100*n/d,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "per", "description": ""}, "chocolate": {"definition": "sweets - mint", "templateType": "anything", "group": "Ungrouped variables", "name": "chocolate", "description": ""}, "increase": {"definition": "random(1..40)", "templateType": "anything", "group": "Ungrouped variables", "name": "increase", "description": ""}, "sweets": {"definition": "random(1..4)*10", "templateType": "anything", "group": "Ungrouped variables", "name": "sweets", "description": ""}, "num": {"definition": "random(1..90)", "templateType": "anything", "group": "Ungrouped variables", "name": "num", "description": ""}, "gcd_per100": {"definition": "gcd(per,100)", "templateType": "anything", "group": "Ungrouped variables", "name": "gcd_per100", "description": ""}, "den": {"definition": "random(num..99 except num)", "templateType": "anything", "group": "Ungrouped variables", "name": "den", "description": ""}, "marks": {"definition": "random(40..100)", "templateType": "anything", "group": "Ungrouped variables", "name": "marks", "description": ""}, "n": {"definition": "random(1..18)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "dec": {"definition": "p/100", "templateType": "anything", "group": "Ungrouped variables", "name": "dec", "description": ""}, "mint": {"definition": "random(1..sweets)", "templateType": "anything", "group": "Ungrouped variables", "name": "mint", "description": ""}, "decimal": {"definition": "num/den", "templateType": "anything", "group": "Ungrouped variables", "name": "decimal", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}]}], "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}