// Numbas version: exam_results_page_options
{"name": "Subtract two fractions with different denominators", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This question tests a student's ability to subtract one fraction from another with different denominators.</p>"}, "variables": {"a": {"definition": "random(1..99)", "templateType": "anything", "description": "<p>Numerator of the first fraction.</p>", "group": "Ungrouped variables", "name": "a"}, "b": {"definition": "random(2..99)", "templateType": "anything", "description": "<p>This is the denominator of the first fraction.</p>", "group": "Ungrouped variables", "name": "b"}, "d": {"definition": "random(2..99)", "templateType": "anything", "description": "<p>This is the denominator of the second fraction.</p>", "group": "Ungrouped variables", "name": "d"}, "c": {"definition": "random(1..99)", "templateType": "anything", "description": "<p>This is the numerator of the second fraction.</p>", "group": "Ungrouped variables", "name": "c"}}, "variablesTest": {"condition": "(a<>1 or b<>2 or c<>3 or d<>4) and gcd(a,b)=1 and gcd(c,d)=1 and b<>d", "maxRuns": 100}, "extensions": [], "rulesets": {"std": ["all"]}, "variable_groups": [], "preamble": {"js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');", "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"}, "tags": [], "advice": "<p>The correct calculation is $\\dfrac{\\var{a}}{\\var{b}}-\\dfrac{\\var{c}}{\\var{d}}=\\frac{\\boxed{\\var{a*d}}-\\boxed{\\var{b*c}}}{\\boxed{\\var{b*d}}}=\\frac{\\boxed{\\var{a*d-b*c}}}{\\boxed{\\var{b*d}}}$.</p>", "functions": {}, "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p><fraction><numerator>{a}</numerator><denominator>{b}</denominator></fraction> $\\ -\\ $ <fraction><numerator>{c}</numerator><denominator>{d}</denominator></fraction> $\\ =\\ $ <fraction><numerator>[[0]] $\\ -\\ $ [[1]]</numerator><denominator> [[2]]</denominator></fraction> $\\ =\\ $ <fraction><numerator>[[3]]</numerator><denominator>[[4]]</denominator></fraction>.</p>", "gaps": [{"mustBeReducedPC": 0, "minValue": "a*d", "correctAnswerFraction": false, "maxValue": "a*d", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": 1, "correctAnswerStyle": "plain", "type": "numberentry"}, {"mustBeReducedPC": 0, "minValue": "b*c", "correctAnswerFraction": false, "maxValue": "b*c", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": 1, "correctAnswerStyle": "plain", "type": "numberentry"}, {"mustBeReducedPC": 0, "minValue": "b*d", "correctAnswerFraction": false, "maxValue": "b*d", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": "1", "correctAnswerStyle": "plain", "type": "numberentry"}, {"mustBeReducedPC": 0, "minValue": "a*d-b*c", "correctAnswerFraction": false, "maxValue": "a*d-b*c", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": 1, "correctAnswerStyle": "plain", "type": "numberentry"}, {"mustBeReducedPC": 0, "minValue": "b*d", "correctAnswerFraction": false, "maxValue": "b*d", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "allowFractions": false, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "marks": 1, "correctAnswerStyle": "plain", "type": "numberentry"}], "type": "gapfill"}], "ungrouped_variables": ["a", "b", "c", "d"], "statement": "<p>Subtract one fraction from another using the formula $\\dfrac{a}{b}-\\dfrac{c}{d}=\\frac{\\boxed{ad}-\\boxed{bc}}{\\boxed{bd}}=\\frac{\\boxed{ad-bc}}{\\boxed{bd}}$.</p>\n<p>An example of a correct calculation would be $\\dfrac{1}{2}-\\dfrac{3}{4}=\\frac{\\boxed{4}-\\boxed{6}}{\\boxed{8}}=\\frac{\\boxed{-2}}{\\boxed{8}}$.</p>\n<p>Note that in the intermediate stage, you have to use the denominator $bd$ to be marked correct, you should not use a smaller common denominator (if one exists). Also note the final fraction should be left as it is and should not be entered in lowest form (if this is different).</p>", "name": "Subtract two fractions with different denominators", "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/"}]}