// Numbas version: exam_results_page_options {"name": "Merryn's copy of Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Merryn's copy of Percentages", "tags": ["converting", "decimals", "Fractions", "fractions", "percentages"], "metadata": {"description": "

Basics, percentage of an amount, converting to fractions and decimals.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..b-1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "mult*random(1..mult2-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random([50,4,25,5,20])", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "mult*mult2", "description": "", "templateType": "anything", "can_override": false}, "nicelist": {"name": "nicelist", "group": "Ungrouped variables", "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", "description": "", "templateType": "anything", "can_override": false}, "factorsofhun": {"name": "factorsofhun", "group": "Ungrouped variables", "definition": "shuffle([[2,50],[4,25],[5,20]])", "description": "", "templateType": "anything", "can_override": false}, "amount2": {"name": "amount2", "group": "Ungrouped variables", "definition": "random(2..12)*factorsofhun[0][1]", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "percent2*amount2/100", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "percent3*amount3/100", "description": "", "templateType": "anything", "can_override": false}, "percent": {"name": "percent", "group": "Ungrouped variables", "definition": "random(1..99 except list(0..100#5))", "description": "", "templateType": "anything", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(12..78)", "description": "", "templateType": "anything", "can_override": false}, "amount3": {"name": "amount3", "group": "Ungrouped variables", "definition": "random(2..12)*factorsofhun[2][1]", "description": "", "templateType": "anything", "can_override": false}, "mult": {"name": "mult", "group": "Ungrouped variables", "definition": "random(3,7,9,11)", "description": "", "templateType": "anything", "can_override": false}, "mult2": {"name": "mult2", "group": "Ungrouped variables", "definition": "random(4,5)", "description": "", "templateType": "anything", "can_override": false}, "percent3": {"name": "percent3", "group": "Ungrouped variables", "definition": "random(2..19)*factorsofhun[2][0]", "description": "", "templateType": "anything", "can_override": false}, "percent2": {"name": "percent2", "group": "Ungrouped variables", "definition": "random(2..19)*factorsofhun[0][0]", "description": "", "templateType": "anything", "can_override": false}, "dec1": {"name": "dec1", "group": "Ungrouped variables", "definition": "random(0.1..0.9#0.01)", "description": "", "templateType": "anything", "can_override": false}, "dec2": {"name": "dec2", "group": "Ungrouped variables", "definition": "random(0.1..0.9#0.001 except list(0.1..0.9#0.01))", "description": "", "templateType": "anything", "can_override": false}, "dec3": {"name": "dec3", "group": "Ungrouped variables", "definition": "random(1..5#0.01)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["percent", "nicelist", "factorsofhun", "amount2", "percent2", "ans2", "amount3", "percent3", "ans3", "b", "a", "mult", "mult2", "c", "d", "number", "dec1", "dec2", "dec3"], "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": "

{percent}% means {percent} out of [[0]].

This means we can write {percent}% as the fraction [[1]] .

And so we can write {percent}% as the decimal [[2]].

", "stepsPenalty": "1.5", "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": "

'Percent' means 'out of 100'. So we can write 34% as $\\frac{34}{100}$. Since this is the same as $34\\div 100$ 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:

\\[34\\%=\\frac{34}{100}=0.34\\]

Writing a percentage as a fraction or a decimal can be useful in the following type of questions:

{percent2}% of {amount2} is [[0]]

{percent3}% of {amount3} is [[1]]

", "stepsPenalty": "1", "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": "

Write the percentage as a fraction or decimal and replace the word 'of' with '$\\times$'.

This question requires you know how to multiply fractions and/or decimals. If using a fraction, it will help to simplify it.

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 there is a factor of 5 which can be cancelled to give $2\\times 11=22$. So we have 40% of 55 is 22.

{a} out of {b} as a fraction is [[0]]. What is this equal to as a percentage? [[1]]%

{c} out of {d} as a fraction is [[2]]. What is this equal to as a percentage? [[3]]%

", "stepsPenalty": "2", "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": "

Recall that $\\frac{2}{3}$ means '2 out of 3', and so going the other way, expressions like '4 out of 5' are equivalent to $\\frac{4}{5}$.

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 by 2 and then 10 as well since this is the same thing). Our working could look like this:

\\[\\frac{4}{5}=\\frac{4\\times 20}{5\\times 20}=\\frac{80}{100}=80\\%\\]

"}], "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": "{a}/{b}", "maxValue": "{a}/{b}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{a/b*100}", "maxValue": "{a/b*100}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{c/d}", "maxValue": "{c/d}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{c/d*100}", "maxValue": "{c/d*100}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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": "

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

10% of {number} is [[0]]

1% of {number} is [[1]]

therefore 11% of {number} is [[2]], 9% of {number} is [[3]] and 20% of {number} is [[4]].

", "stepsPenalty": "2.5", "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": "

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.

Notice

\\[10\\%=\\frac{10}{100}=\\frac{1}{10}=1\\div 10 = 0.1\\]

and

\\[1\\%=\\frac{1}{100}=1\\div 100 = 0.01\\]

This means that 10% of 12 is 1.2 and 1% of 12 is 0.12. From this we can calculate many simple percentages:

11% by adding 10% and 1%, that is $1.2+0.12=1.32$
9% by doing 10% minus 1%, that is $1.2-0.12=1.08$
30% by doing 3 times 10%, that is $3\\times 1.2=3.6$
99% by doing 100% minus 1%, that is $12-0.12=11.88$

"}], "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/10}", "maxValue": "{number/10}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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/100}", "maxValue": "{number/100}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{0.11*number}", "maxValue": "{0.11*number}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{0.09*number}", "maxValue": "{0.09*number}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "{0.2*number}", "maxValue": "{0.2*number}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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": "

Rewrite the following decimals as percentages:

{dec1} = [[0]]%

{dec2} = [[1]]%

{dec3} = [[2]]%

Move the decimal point to the right two places.

To get from a percentage to a decimal we ultimately moved the decimal place twice to the left. Recall

\\[34\\%=\\frac{34}{100}=34\\div 100=0.34\\]

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

\\[0.34=34\\div 100=\\frac{34}{100}=34\\%\\]

Often it is useful to remember that 1 represents 100%, this can help you to check if your answer makes sense.