// Numbas version: exam_results_page_options {"name": "Percentages/decimals of an amount", "metadata": {"description": "

A quick practice set of problems for education students to take in preparation for their numeracy test.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "Percentages: Percentage of an amount ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "

Percentage of an amount

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following question down on paper and evaluate it without using a calculator.

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q": {"name": "q", "group": "Ungrouped variables", "definition": "random(9,11,20,90,99)", "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}, "amount2": {"name": "amount2", "group": "Ungrouped variables", "definition": "random(2..12)*factorsofhun[0][1]", "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}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "percent2*amount2/100", "description": "", "templateType": "anything", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(12..78)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["factorsofhun", "amount2", "percent2", "ans2", "number", "q"], "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": "

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

$\\var{percent2}\\%$ of $\\var{amount2}$ is [[0]]

", "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 to know how to multiply fractions (multiply the tops and multiply the bottoms) and divide by $100$ (move the decimal place twice to make the number smaller).

In particular, \\begin{align}\\var{percent2}\\% \\text{ of } \\var{amount2} &= \\frac{\\var{percent2}}{100}\\times \\var{amount2} \\\\[2mm]&=\\frac{\\var{percent2}}{100}\\times \\frac{\\var{amount2}}{1}\\\\[2mm]&= \\frac{\\var{percent2}\\times \\var{amount2}}{100}\\\\[2mm]&=\\frac{\\var{percent2*amount2}}{100}\\\\[2mm]&=\\var{ans2}\\end{align}

It is often useful to determine $10\\%$ and $1\\%$ of an amount so you can combine them to get other percentages. For example,

$10\\%$ of $\\var{number}$ is [[0]],

$1\\%$ of $\\var{number}$ is [[1]],

and by using the above we can say $\\var{q}\\%$ of $\\var{number}$ is [[2]].

", "stepsPenalty": "3", "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 $\\var{number}$ is $\\var{number/10}$,

$1\\%$ of $\\var{number}$ is $\\var{number/100}$,

and from this we can calculate $\\var{q}\\%$ of $\\var{number}$ since

$9\\%=10\\%-1\\%=\\var{number/10}-\\var{number/100}=\\var{q*number/100}$. $11\\%=10\\%+1\\%=\\var{number/10}+\\var{number/100}=\\var{q*number/100}$. $20\\%=10\\%+10\\%=\\var{number/10}+\\var{number/10}=\\var{q*number/100}$. $90\\%=100\\%-10\\%=\\var{number}-\\var{number/10}=\\var{q*number/100}$. $99\\%=100\\%-1\\%=\\var{number}-\\var{number/100}=\\var{q*number/100}$.

"}], "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": "{q*number}/100", "maxValue": "{q*number}/100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decimals of an amount", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["converting", "Decimals", "decimals", "Fractions", "fractions", "percentages"], "metadata": {"description": "

Decimals of an amount, including a non-calculator technique.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"factorsofhun": {"name": "factorsofhun", "group": "Ungrouped variables", "definition": "shuffle([[2,50],[4,25],[5,20]])", "description": "", "templateType": "anything", "can_override": true}, "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", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "percent3*amount3", "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}, "percent3": {"name": "percent3", "group": "Ungrouped variables", "definition": "decimal(random(2..19)*factorsofhun[2][0]/100)", "description": "", "templateType": "anything", "can_override": false}, "percent2": {"name": "percent2", "group": "Ungrouped variables", "definition": "decimal(random(2..19)*factorsofhun[0][0]/100)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(0.09,0.11,0.20,0.90,0.99)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["factorsofhun", "amount2", "percent2", "ans2", "amount3", "percent3", "ans3", "number", "q"], "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": "

Fill in the following:

$\\var{percent2}$ of $\\var{amount2}$ is [[0]]

Replace the word 'of' with '$\\times$'.

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

In particular, \\begin{align}\\var{percent2} \\text{ of } \\var{amount2} &= \\frac{\\var{percent2*100}}{100}\\times \\var{amount2} \\\\[2mm]&=\\frac{\\var{percent2*100}}{100}\\times \\frac{\\var{amount2}}{1}\\\\[2mm]&= \\frac{\\var{percent2*100}\\times \\var{amount2}}{100}\\\\[2mm]&=\\frac{\\var{percent2*100*amount2}}{100}\\\\[2mm]&=\\var{ans2}\\end{align}

It is often useful to determine $0.01$ of an amount and $0.1$ of an amount so you can combine them to get other proportions of the amount. For example

$0.1$ of $\\var{number}$ is [[0]]

$0.01$ of $\\var{number}$ is [[1]]

therefore $\\var{q}$ of $\\var{number}$ is [[2]].

Move the decimal point once to the left to get 0.1 (or 10%) of the amount, move it one more time to the left to get 0.01 (or 1%) of the amount. 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

$0.1$ of $\\var{number}$ is $\\var{number/10}$,

$0.01$ of $\\var{number}$ is $\\var{number/100}$,

and from this we can calculate $\\var{q}$ of $\\var{number}$ since

$0.09 \\text{ of }\\var{number}=0.10\\text{ of }\\var{number}-0.01\\text{ of }\\var{number}=\\var{number/10}-\\var{number/100}=\\var{q*number}$. $0.11\\text{ of }\\var{number}=0.10\\text{ of }\\var{number}+0.01\\text{ of }\\var{number}=\\var{number/10}+\\var{number/100}=\\var{q*number}$. $0.20\\text{ of }\\var{number}=0.10\\text{ of }\\var{number}+0.10\\text{ of }\\var{number}=\\var{number/10}+\\var{number/10}=\\var{q*number}$. $0.90\\text{ of }\\var{number}=1.00\\text{ of }\\var{number}-0.10\\text{ of }\\var{number}=\\var{number}-\\var{number/10}=\\var{q*number}$. $0.99\\text{ of }\\var{number}=1.00\\text{ of }\\var{number}-0.01\\text{ of }\\var{number}=\\var{number}-\\var{number/100}=\\var{q*number}$.

"}], "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": "{q*number}", "maxValue": "{q*number}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "extensions": [], "custom_part_types": [], "resources": []}