// Numbas version: exam_results_page_options
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Z&auml;hler und Nenner haben keinen gemeinsamen Teiler.</p>\n<p>(b) Es gilt</p>\n<p>\\[ \\simplify[std]{ ({a2} + {b2}/{c2})/({d2}/{e2} + {f2}/{g2}) } = \\simplify[std]{ {a2*c2+b2}/{c2}} / \\simplify[std]{({d2*g2+e2*f2}/{e2*g2}) } = \\simplify[std]{{a2*c2+b2}/{c2}} \\cdot \\simplify[std]{ {e2*g2}/{d2*g2+e2*f2} }= \\simplify[std]{ {(a2*c2+b2)*e2*g2}/{c2*(d2*g2+e2*f2)} }\\]</p>\n<p>(c) Es gilt</p>\n<p>\\[ \\simplify[std]{ ({b3}/{c3} + {a3})/({d3}/{e3} + {f3}/{g3}) } = \\simplify[std]{ {a3*c3+b3}/{c3}} / \\simplify[std]{({d3*g3+e3*f3}/{e3*g3}) } = \\simplify[std]{{a3*c3+b3}/{c3}} \\cdot \\simplify[std]{ {e3*g3}/{d3*g3+e3*f3} }= \\simplify[std]{ {(a3*c3+b3)*e3*g3}/{c3*(d3*g3+e3*f3)} }\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "extensions": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "if(abs(a*f+s*b*g)=1,-s,s)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..7)", "description": "", "templateType": "anything"}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "switch(g=2,random(3..7#2),g=3,random(2,4,5),g=4,random(3,5),g=5, random(2,3,4),g=6,random(5,7),g=7,random(2,3,4),g=8,random(3,5,7),g=9,random(2,4,5),g=10,random(3,7),g=11,random(2..5))", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "switch(f=2,1,f=3,random(1,2),f=4,random(1,3),f=5, random(1..4),f=6,random(1,5),f=7,random(1..5),f=8,random(1,3,5),f=9,random(1,2,4,5),f=10,random(1,3),f=11,random(1..5))", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "switch(a=1, random(2..7),a=2,random(3..7#2),a=3,random(4,5,7),a=4,random(5,7),a=5, random(6,7,8),a=6,random(7,11),a=7,random(8,9))", 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\[\\simplify{{g} / ({a} + {s1} * ({b * g} / {f}))}\\]<br/>Ergebnis: [[0]]</p>\n<p>Das Ergebnis muss in der Form a/b mit ganzen Zahlen a und b angegeben werden (keine Dezimalzahlen, keine Klammern, ...).</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{result}", "maxValue": "{result}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": [], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, 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null, "minValue": "{result2}", "maxValue": "{result2}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\[ \\simplify{ ({b3}/{c3} + {a3})/({d3}/{e3} + {f3}/{g3}) } \\]</p>\n<p>Ergebnis: [[0]]</p>\n<p>Das Ergebnis muss in der Form a/b mit ganzen Zahlen a und b angegeben werden (keine Dezimalzahlen, keine Klammern, ...).</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", 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