// Numbas version: exam_results_page_options
{"name": "Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["percent", "nicelist", "factorsofhun", "amount2", "percent2", "ans2", "amount3", "percent3", "ans3", "b", "a", "mult", "mult2", "c", "d", "number", "dec1", "dec2", "dec3"], "name": "Percentages", "tags": ["converting", "decimals", "Fractions", "fractions", "percentages"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1.5", "prompt": "<p>{percent}% means {percent} out of&nbsp;[[0]].</p>\n<p>This&nbsp;means we can write {percent}% as the fraction [[1]]&nbsp;.</p>\n<p>And so we can write {percent}% as the decimal&nbsp;[[2]].</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "100", "minValue": "100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{percent}/100", "minValue": "{percent}/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{percent/100}", "minValue": "{percent/100}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>'Percent' means 'out of 100'. So we can write 34% as $\\frac{34}{100}$. Since this is the same as&nbsp;$34\\div 100$ we can write this as a decimal by moving the decimal point two places (the number of zeroes in 100). So 34 (which has a decimal point after the 4) becomes 0.34. In summary:</p>\n<p>\\[34\\%=\\frac{34}{100}=0.34\\]</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>Writing a percentage as a fraction or a decimal can be&nbsp;useful&nbsp;in the following type of questions:</p>\n<p>{percent2}% of {amount2} is&nbsp;[[0]]</p>\n<p>{percent3}% of {amount3} is&nbsp;[[1]]</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}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>Write the percentage as a fraction or decimal and replace the word 'of' with '$\\times$'. </em></p>\n<p>This question requires you know how to multiply fractions and/or decimals. If using a fraction, it will&nbsp;help to simplify&nbsp;it.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, 40% of 55 is $40\\%\\times 55=\\frac{40}{100}\\times 55$, which equals $\\frac{2}{5}\\times 55$ by simplifying the fraction, next&nbsp;there is a factor of 5 which can be cancelled to give $2\\times 11=22$. So we have 40% of 55 is 22.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "2", "prompt": "<p>{a} out of {b} as a fraction is [[0]]. What is this equal to as a percentage?&nbsp;[[1]]% &nbsp;</p>\n<p>{c} out of {d} as a fraction is [[2]]. What is this equal to as a percentage?&nbsp;[[3]]% &nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{a}/{b}", "minValue": "{a}/{b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a/b*100}", "minValue": "{a/b*100}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{c/d}", "minValue": "{c/d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{c/d*100}", "minValue": "{c/d*100}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Recall that $\\frac{2}{3}$ means '2&nbsp;out of 3', and so going the other way, expressions like '4 out of 5' are equivalent to $\\frac{4}{5}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>To convert a fraction into a percentage, make an equivalent fraction with a denominator of 100, then the numerator will be the percentage. For example, given $\\frac{4}{5}$ we can multiply the top and bottom by 20 to get it over 100 (we could have multiplied&nbsp;by 2 and then 10 as well since this is the same thing). Our working could look like this:</p>\n<p>\\[\\frac{4}{5}=\\frac{4\\times 20}{5\\times 20}=\\frac{80}{100}=80\\%\\]&nbsp;</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "2.5", "prompt": "<p>It is often useful to determine 1% of an amount and 10% of an amount so you can combine them to get other percentages. For example</p>\n<p></p>\n<p>10% of {number} is&nbsp;[[0]]</p>\n<p>1% of {number} is&nbsp;[[1]]</p>\n<p>therefore 11% of {number} is &nbsp;[[2]], 9% of {number} is&nbsp;[[3]]&nbsp;and&nbsp;20% of {number} is [[4]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{number/10}", "minValue": "{number/10}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{number/100}", "minValue": "{number/100}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{0.11*number}", "minValue": "{0.11*number}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{0.09*number}", "minValue": "{0.09*number}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{0.2*number}", "minValue": "{0.2*number}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>Move the decimal point once to the left to get 10%, move it one more time to the left to get 1%. Add and subtract multiples of these as required.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Notice</p>\n<p>\\[10\\%=\\frac{10}{100}=\\frac{1}{10}=1\\div 10 = 0.1\\]</p>\n<p>and&nbsp;</p>\n<p>\\[1\\%=\\frac{1}{100}=1\\div 100 = 0.01\\]</p>\n<p>This means that 10% of 12 is 1.2 and 1% of 12 is 0.12. From this we can calculate many simple percentages:</p>\n<ul>\n<li>11% by adding&nbsp;10% and 1%, that is $1.2+0.12=1.32$</li>\n<li>9% by doing 10% minus 1%, that is $1.2-0.12=1.08$</li>\n<li>30% by doing 3 times 10%, that is $3\\times 1.2=3.6$</li>\n<li>99% by doing 100% minus&nbsp;1%, that is $12-0.12=11.88$</li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1.5", "prompt": "<p>Rewrite the following decimals as percentages:</p>\n<p>{dec1}&nbsp;=&nbsp;[[0]]%</p>\n<p>{dec2} =&nbsp;[[1]]%</p>\n<p>{dec3} =&nbsp;[[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "dec1*100", "minValue": "dec1*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "dec2*100", "minValue": "dec2*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "dec3*100", "minValue": "dec3*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p><em>Move the decimal point to the right two places.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>To get from a percentage to a <g class=\"gr_ gr_12 gr-alert gr_gramm Punctuation only-ins replaceWithoutSep\" id=\"12\" data-gr-id=\"12\">decimal</g> we ultimately moved the decimal place twice to the left.&nbsp;Recall&nbsp;</p>\n<p>\\[34\\%=\\frac{34}{100}=34\\div 100=0.34\\]</p>\n<p>That means to go the other way (from a decimal to a percentage) we need to move the decimal place twice to the right, in other words</p>\n<p>\\[0.34=34\\div 100=\\frac{34}{100}=34\\%\\]</p>\n<p>Often it is useful to remember that 1 represents 100%, this can help&nbsp;you to check if your answer makes sense.</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": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..b-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "mult*random(1..mult2-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random([50,4,25,5,20])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "mult*mult2", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "nicelist": {"definition": "shuffle(map(2^a*5^b,[a,b],[[0,1],[0,2],[1,0],[2,0],[3,0],[4,0],[5,0],[6,0],[1,1],[2,1],[3,1],[4,1],[1,2]]))\n", "templateType": "anything", "group": "Ungrouped variables", "name": "nicelist", "description": ""}, "factorsofhun": {"definition": "shuffle([[2,50],[4,25],[5,20]])", "templateType": "anything", "group": "Ungrouped variables", "name": "factorsofhun", "description": ""}, "amount2": {"definition": "random(2..12)*factorsofhun[0][1]", "templateType": "anything", "group": "Ungrouped variables", "name": "amount2", "description": ""}, "ans2": {"definition": "percent2*amount2/100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "percent3*amount3/100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "percent": {"definition": "random(1..99 except list(0..100#5))", "templateType": "anything", "group": "Ungrouped variables", "name": "percent", "description": ""}, "number": {"definition": "random(12..78)", "templateType": "anything", "group": "Ungrouped variables", "name": "number", "description": ""}, "amount3": {"definition": "random(2..12)*factorsofhun[2][1]", "templateType": "anything", "group": "Ungrouped variables", "name": "amount3", "description": ""}, "mult": {"definition": "random(3,7,9,11)", "templateType": "anything", "group": "Ungrouped variables", "name": "mult", "description": ""}, "mult2": {"definition": "random(4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "mult2", "description": ""}, "percent3": {"definition": "random(2..19)*factorsofhun[2][0]", "templateType": "anything", "group": "Ungrouped variables", "name": "percent3", "description": ""}, "percent2": {"definition": "random(2..19)*factorsofhun[0][0]", "templateType": "anything", "group": "Ungrouped variables", "name": "percent2", "description": ""}, "dec1": {"definition": "random(0.1..0.9#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "dec1", "description": ""}, "dec2": {"definition": "random(0.1..0.9#0.001 except list(0.1..0.9#0.01))", "templateType": "anything", "group": "Ungrouped variables", "name": "dec2", "description": ""}, "dec3": {"definition": "random(1..5#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "dec3", "description": ""}}, "metadata": {"notes": "<p>Need to write questions on decimals to fractions and fractions to decimals.</p>", "description": "<p>&nbsp;Basics, percentage of an amount, converting to fractions and decimals.</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": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}