// Numbas version: finer_feedback_settings
{"name": "Express given fractions with different denominators", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"q": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5,7,11,13,17)", "description": "", "name": "q"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..29 except a)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2*p2", "description": "", "name": "c"}, "t2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..11 except t)", "description": "", "name": "t2"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..7 except s)", "description": "", "name": "s2"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "p*q", "description": "", "name": "k"}, "p2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5,7,11,13,17)", "description": "", "name": "p2"}, "l": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2*p2*q2", "description": "", "name": "l"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "b*q2", "description": "", "name": "n"}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..7)", "description": "", "name": "s"}, "q2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5,7,11,13,17)", "description": "", "name": "q2"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..29)", "description": "", "name": "a"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5,7,11,13,17)", "description": "", "name": "p"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..11)", "description": "", "name": "t"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a*q", "description": "", "name": "m"}}, "ungrouped_variables": ["a", "p2", "c", "b", "s2", "k", "m", "l", "n", "q", "p", "s", "q2", "t", "t2"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Express given fractions with different denominators", "functions": {}, "showQuestionGroupNames": false, "parts": [{"prompt": "<p>$\\dfrac{\\var{a}}{\\var{p}}$</p>\n      <p>If expressed with denominator $\\var{k}$, the numerator is [[0]].</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{m}", "minValue": "{m}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{s*t}}{\\var{t*k}}$</p>\n      <p>If expressed with denominator $\\var{k}$, the numerator is [[0]].</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{s}", "minValue": "{s}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{b}}{\\var{2*p2}}$</p>\n      <p>If expressed with denominator $\\var{l}$, the numerator is [[0]].</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{n}", "minValue": "{n}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"prompt": "<p>$\\dfrac{\\var{t2*s2}}{\\var{t2*l}}$</p>\n      <p>If expressed with denominator $\\var{l}$, the numerator is [[0]].</p>", "scripts": {}, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "allowFractions": false, "type": "numberentry", "maxValue": "{s2}", "minValue": "{s2}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "statement": "<p>Express each the following fractions as a fraction with the given denominator. Write the numerator in the given box.</p>", "tags": ["checked2015", "Fractions", "fractions", "SFY0001"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Questions testing understanding of numerators and denominators of numerical fractions.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>a) Observe that $\\var{k} \\div \\var{p} =\\var{q}$, so we multiply top and bottom by $\\var{q}$ to get $\\dfrac{\\var{a*q}}{\\var{p*q}}$.</p>\n<p>The numerator is then the number on the top, i.e., $\\var{a*q}$.</p>\n<p>b) Observe that $\\var{t*k} =\\var{t} \\times \\var{k}$, so we divide top and bottom by $\\var{t}$ to get $\\dfrac{\\var{s}}{\\var{k}}$.</p>\n<p>The numerator is then the number on the top, i.e., $\\var{s}$.</p>\n<p>c) Observe that $\\var{l} \\div \\var{2*p2} =\\var{q2}$, so we multiply top and bottom by $\\var{q2}$ to get $\\dfrac{\\var{b*q2}}{\\var{2*p2*q2}}$.</p>\n<p>The numerator is then the number on the top, i.e., $\\var{b*q2}$.</p>\n<p>d) Observe that $\\var{t2*l} =\\var{t2} \\times \\var{l}$, so we divide top and bottom by $\\var{t2}$ to get $\\dfrac{\\var{s2}}{\\var{l}}$.</p>\n<p>The numerator is then the number on the top, i.e., $\\var{s2}$.</p>\n<p></p>\n<p></p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}