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{"name": "Welche Bruchzahl ist verschieden von allen anderen? (Kleine Nenner)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Welche Bruchzahl ist verschieden von allen anderen? (Kleine Nenner)", "tags": [], "metadata": {"description": "<p>Suche von den f&uuml;nf gegebenen Bruchzahlen diejenige aus, die nicht denselben Wert hat wie alle anderen.</p>\n<p>Quelle: Angepasste und &uuml;bersetzte Version von https://numbas.mathcentre.ac.uk/question/23233/select-the-fraction-not-equivalent-to-the-others-small-denominators/ von Christian Lawson-Perfect.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Eine kleine &Uuml;bung zum Vergleichen von Bruchzahlen.</p>", "advice": "<p>Um die gesuchte Zahl zu finden, k&uuml;rzen wir alle Br&uuml;che.</p>\n<p>\\begin{align}<br/>\\frac{\\var{mone}}{\\var{none}} &amp;= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{one}}{\\var{one}} = \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\\\[0.5em]<br/>\\frac{\\var{mtwo}}{\\var{ntwo}} &amp;= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{two}}{\\var{two}} = \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\\\[0.5em]<br/>\\frac{\\var{mthree}}{\\var{nthree}} &amp;= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{three}}{\\var{three}} = \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\\\[0.5em]<br/>\\frac{\\var{mfour}}{\\var{nfour}} &amp;= \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\times\\frac{\\var{four}}{\\var{four}} = \\frac{\\var{m_coprime}}{\\var{n_coprime}}\\\\[0.5em]<br/>\\frac{\\var{mfive}}{\\var{nfive}} &amp;= \\frac{\\var{mfive/gcd(mfive,nfive)}}{\\var{nfive/gcd(mfive,nfive)}} \\times \\frac{\\var{gcd(mfive,nfive)}}{\\var{gcd(mfive,nfive)}} = \\frac{\\var{mfive/gcd(mfive,nfive)}}{\\var{nfive/gcd(mfive,nfive)}}<br/>\\end{align}</p>\n<p>In allen F&auml;llen bis auf einen erhalten wir den Wert $\\displaystyle\\frac{\\var{m_coprime}}{\\var{n_coprime}}$.</p>\n<p>Der Ausnahmebruch ist $\\displaystyle\\frac{\\var{mfive}}{\\var{nfive}}$.</p>", "rulesets": {}, "extensions": [], "variables": {"five": {"name": "five", "group": "Ungrouped variables", "definition": "random(1..7 except one except two except three except four)", "description": "", "templateType": "anything"}, "m_coprime": {"name": "m_coprime", "group": "Ungrouped variables", "definition": "m/gcd_mn", "description": "", "templateType": "anything"}, "mthree": {"name": "mthree", "group": "Ungrouped variables", "definition": "m_coprime*three", "description": "", "templateType": "anything"}, "ntwo": {"name": "ntwo", "group": "Ungrouped variables", "definition": "n_coprime*two", "description": "", "templateType": "anything"}, "mfive": {"name": "mfive", "group": "Ungrouped variables", "definition": "m_coprime*five+random(-4..4 except 0)", "description": "", "templateType": "anything"}, "mtwo": {"name": "mtwo", "group": "Ungrouped variables", "definition": "m_coprime*two", "description": "", "templateType": "anything"}, "four": {"name": "four", "group": "Ungrouped variables", "definition": "random(5..20 except one except two except three)", "description": "", "templateType": "anything"}, "none": {"name": "none", "group": "Ungrouped variables", "definition": "n_coprime*one", "description": "", "templateType": "anything"}, "nthree": {"name": "nthree", "group": "Ungrouped variables", "definition": "n_coprime*three", "description": "", "templateType": "anything"}, "two": {"name": "two", "group": "Ungrouped variables", "definition": "random(2..15 except one)", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(1..7)", "description": "<p>Random number between 1 and 10</p>", "templateType": "anything"}, "nfive": {"name": "nfive", "group": "Ungrouped variables", "definition": "n_coprime*five", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(7..15 except m)", "description": "", "templateType": "anything"}, "one": {"name": "one", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", 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"marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>W&auml;hlen Sie von den gegebenen Zahlen diejenige aus, die nicht denselben Wert hat wie alle anderen.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$\\displaystyle\\frac{\\var{mone}}{\\var{none}}$</p>", "<p>$\\displaystyle\\frac{\\var{mtwo}}{\\var{ntwo}}$</p>", "<p>$\\displaystyle\\frac{\\var{mthree}}{\\var{nthree}}$</p>", "<p>$\\displaystyle\\frac{\\var{mfour}}{\\var{nfour}}$</p>", "<p>$\\displaystyle\\frac{\\var{mfive}}{\\var{nfive}}$</p>"], "matrix": [0, 0, "0", 0, "1"], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Ulrich G\u00f6rtz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7603/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Ulrich G\u00f6rtz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7603/"}]}