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{"name": "Fractions: improper and mixed numerals [L5]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"prompt": "<p>Convert the following improper fractions to mixed numerals (also known as mixed numbers):</p>\n<p><em>Note: Write the whole number part in the first box&nbsp;and the fraction&nbsp;part&nbsp;in the second&nbsp;</em></p>\n<p>$\\displaystyle\\frac{\\var{a1*c1+b1}}{\\var{c1}}=$[[0]][[1]]</p>\n<p>$\\displaystyle\\frac{\\var{a2*c2+b2}}{\\var{c2}}=$[[2]][[3]]</p>", "gaps": [{"minValue": "a1", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "maxValue": "a1", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5", "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}, {"minValue": "b1/c1", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "maxValue": "b1/c1", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5", "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": true, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}, {"minValue": "a2", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "maxValue": "a2", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5", "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}, {"minValue": "b2/c2", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "maxValue": "b2/c2", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": "0.5", "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": true, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "sortAnswers": false, "stepsPenalty": "1", "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Do the division and write your remainder over the original denominator. Simplify the fraction if possible.</em>&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example,&nbsp;converting&nbsp;$\\frac{21}{9}$ into a mixed numeral, you ask yourself \"how many times does 9&nbsp;go into 21?\", it goes in twice&nbsp;(since $2\\times 9=18$ but $3\\times 9=27$), with a remainder of 3&nbsp;(since $21-18=3$). So we can write our answer as $2\\frac{3}{9}$ (which actually means $2+\\frac{3}{9}$). But notice we can simplify the fraction, so we should rewrite our answer as $2\\frac{1}{3}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note: we could have cancelled common factors at the beginning.&nbsp;</p>", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "type": "information"}]}, {"prompt": "<p>Convert the following mixed numerals to improper fractions:</p>\n<p>$\\var{a3}\\frac{\\var{b3}}{\\var{c3}}=$[[0]]</p>\n<p>$\\var{a4}\\frac{\\var{b4}}{\\var{c4}}=$[[1]]</p>", "gaps": [{"minValue": "ans3", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "maxValue": "ans3", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": true, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}, {"minValue": "ans4", "allowFractions": true, "extendBaseMarkingAlgorithm": true, "maxValue": "ans4", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "marks": 1, "showFeedbackIcon": true, "type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "correctAnswerFraction": true, "variableReplacements": [], "mustBeReduced": false, "unitTests": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "sortAnswers": false, "stepsPenalty": "1", "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Multiply the whole number and the denominator, add the numerator, and put it all over the denominator.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example $2\\frac{3}{4}$ can be written as $\\frac{2\\times 4+3}{4}$ that is, $\\frac{11}{4}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>To understand why, realise that $2\\frac{3}{4}$ is shorthand for $2+\\frac{3}{4}$&nbsp;and&nbsp;if we want to add these numbers we need to&nbsp;have a common denominator (recall the denominator of a whole number is 1). Our working could look like this:</p>\n<p>\\[2\\tfrac{3}{4}=2+\\frac{3}{4}=\\frac{2\\times 4}{4}+\\frac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]</p>\n<p>but in practice we normally don't write anything more than \\[2\\tfrac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]</p>", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "type": "information"}]}], "preamble": {"js": "", "css": ""}, "advice": "", "ungrouped_variables": ["a1", "b1", "c1", "a2", "b2", "c2", "a3", "b3", "c3", "ans3", "a4", "b4", "c4", "ans4"], "functions": {}, "name": "Fractions: improper and mixed numerals [L5]", "variable_groups": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "variables": {"c1": {"definition": "b1+random(1..6)", "description": "", "group": "Ungrouped variables", "name": "c1", "templateType": "anything"}, "a1": {"definition": "random(1..4)", "description": "", "group": "Ungrouped variables", "name": "a1", "templateType": "anything"}, "a3": {"definition": "random(1..5)", "description": "", "group": "Ungrouped variables", "name": "a3", "templateType": "anything"}, "c2": {"definition": "b2+random(1..6)", "description": "", "group": "Ungrouped variables", "name": "c2", "templateType": "anything"}, "ans3": {"definition": "(a3*c3+b3)/c3", "description": "", "group": "Ungrouped variables", "name": "ans3", "templateType": "anything"}, "a2": {"definition": "random(1..4)", "description": "", "group": "Ungrouped variables", "name": "a2", "templateType": "anything"}, "c3": {"definition": "b3+random(1..7)", "description": "", "group": "Ungrouped variables", "name": "c3", "templateType": "anything"}, "c4": {"definition": "b4+random(1..6)", "description": "", "group": "Ungrouped variables", "name": "c4", "templateType": "anything"}, "b3": {"definition": "random(1..5)", "description": "", "group": "Ungrouped variables", "name": "b3", "templateType": "anything"}, "a4": {"definition": "random(1..12)", "description": "", "group": "Ungrouped variables", "name": "a4", "templateType": "anything"}, "b4": {"definition": "random(1..6)", "description": "", "group": "Ungrouped variables", "name": "b4", "templateType": "anything"}, "b2": {"definition": "random(1..11)", "description": "", "group": "Ungrouped variables", "name": "b2", "templateType": "anything"}, "ans4": {"definition": "(a4*c4+b4)/c4", "description": "", "group": "Ungrouped variables", "name": "ans4", "templateType": "anything"}, "b1": {"definition": "random(1..11)", "description": "", "group": "Ungrouped variables", "name": "b1", "templateType": "anything"}}, "tags": ["L5"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "", "type": "question", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}]}