// Numbas version: exam_results_page_options
{"name": "Divide two fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "(a<>2 or b<>3) and (c<>4 or d<>5) and gcd(a,b)=1 and gcd(c,d)=1", "maxRuns": 100}, "variable_groups": [], "statement": "<p>Divide the following fractions using the formula $\\dfrac{a}{b}\\div\\dfrac{c}{d}=\\dfrac{a}{b}\\times\\dfrac{d}{c}=\\frac{\\boxed{\\vphantom{d}a}\\times \\boxed{d}}{\\boxed{b}\\times \\boxed{\\vphantom{b}c}}=\\frac{\\boxed{a\\times d}}{\\boxed{b\\times c}}$.</p>\n<p>An example of a correct calculation would be $\\dfrac{2}{3}\\div\\dfrac{4}{5}=\\dfrac{2}{3}\\times\\dfrac{5}{4}=\\frac{\\boxed{2}\\times\\boxed{5}}{\\boxed{3}\\times\\boxed{4}}=\\frac{\\boxed{10}}{\\boxed{12}}$.</p>\n<p>Note the final fraction should be left as it is and should not be entered in lowest form (if this is different).</p>", "functions": {}, "name": "Divide two fractions", "ungrouped_variables": ["a", "b", "c", "d"], "parts": [{"type": "gapfill", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "prompt": "<p><fraction><numerator>{a}</numerator><denominator>{b}</denominator></fraction> $\\ \\div \\ $ <fraction><numerator>{c}</numerator><denominator>{d}</denominator></fraction> $\\ =\\ $<fraction><numerator>[[0]]</numerator><denominator>[[1]]</denominator></fraction> $\\ \\times \\ $ <fraction><numerator>[[2]]</numerator><denominator>[[3]]</denominator></fraction> $\\ =\\ $ <fraction><numerator>[[4]] $\\ \\times\\ $ [[5]]</numerator><denominator> [[6]] $\\ \\times \\ $ [[7]]</denominator></fraction> $\\ =\\ $ <fraction><numerator>[[8]]</numerator><denominator>[[9]]</denominator></fraction>.</p>", "showCorrectAnswer": true, "scripts": {}, "gaps": [{"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "a", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "b", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "d", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": "1", "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "c", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "a", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "d", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "b", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "c", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "a*d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "a*d", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "minValue": "b*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "b*c", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "type": "numberentry", "allowFractions": false, "marks": 1, "mustBeReducedPC": 0}], "variableReplacementStrategy": "originalfirst"}], "rulesets": {"std": ["all"]}, "advice": "<p>The correct calculation is $\\dfrac{\\var{a}}{\\var{b}}\\div\\dfrac{\\var{c}}{\\var{d}}=\\dfrac{\\boxed{\\var{a}}}{\\boxed{\\var{b}}}\\times\\dfrac{\\boxed{\\var{d}}}{\\boxed{\\var{c}}}=\\frac{\\boxed{\\var{a}}\\times\\boxed{\\var{d}}}{\\boxed{\\var{b}}\\times\\boxed{\\var{c}}}=\\frac{\\boxed{\\var{a*d}}}{\\boxed{\\var{b*c}}}$.</p>", "tags": [], "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This question tests a student's ability to divide one fraction by another.</p>"}, "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "variables": {"d": {"templateType": "anything", "definition": "random(2..99)", "description": "<p>Denominator of the second fraction.</p>", "name": "d", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(2..99)", "description": "<p>Numerator of the first fraction.</p>", "name": "a", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "random(2..99)", "description": "<p>Numerator of the second fraction.</p>", "name": "c", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "random(2..99)", "description": "<p>Denomnator of the first fraction.</p>", "name": "b", "group": "Ungrouped variables"}}, "type": "question", "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}]}], "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}