// Numbas version: exam_results_page_options
{"name": "Br\u00f8ker", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Br\u00f8ker", "tags": [], "metadata": {"description": "<p>Add, subtract, multiply and divide numerical fractions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Regn ut og skriv svaret som en br&oslash;k eller et helt tall&nbsp;(ikke desimaltall). Bruk &nbsp;/ som br&oslash;kstrek, f.eks skrives $\\frac{2}{3}$ som 2/3. Pr&oslash;v &aring; forkorte svaret mest mulig.</p>", "advice": "<p>Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.</p>", "rulesets": {}, "extensions": [], "variables": {"g": {"name": "g", "group": "numerical fractions", "definition": "random(2..9 except f)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "numerical fractions", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "numerical fractions", "definition": "random(2..9 except [a,b])", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "numerical fractions", "definition": "random(2..9 except [f,g])", "description": "", "templateType": "anything"}, "j": {"name": "j", "group": "numerical fractions", "definition": "random(2..12 except [f,g,h])", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "numerical fractions", "definition": "random(2..9 except[a,b,c,10])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "numerical fractions", "definition": "random(2..12 except a)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "numerical fractions", "definition": "random(2..9 except d)", "description": "", "templateType": "anything"}, "te": {"name": "te", "group": "numerical fractions", "definition": "shuffle(-3..9 except 0)[0..9]", "description": "", "templateType": "anything"}, "ne": {"name": "ne", "group": "numerical fractions", "definition": "repeat(random(2..9), 9)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "numerical fractions", "variables": ["a", "b", "c", "d", "f", "g", "h", "j", "te", "ne"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>$\\displaystyle\\frac{\\var{a}}{\\var{b}}+\\frac{\\var{c}}{\\var{b}}=$[[0]]</p>\n<p>$\\displaystyle\\frac{\\var{d}}{\\var{c}}-\\frac{\\var{a}}{\\var{c}}=$[[1]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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><em>Legg sammen tellerne, la nevneren st&aring;.</em></p>\n<p></p>\n<p>Disse br&oslash;kene har samme nevner. Det betyr at de h&oslash;rer til samme type oppdeling, og er derfor b&aring;de lett &aring; sammenligne og lett &aring; regne med. Det er f.eks. lett &aring; se att&nbsp;$\\frac{2}{3}$ er mindre enn $\\frac{5}{3}$ , to er jo mindre enn fem.</p>\n<p>Det er ikke like lett &aring; se at f.eks. $\\frac{3}{5}$ er mindre enn $\\frac{2}{3}$, det er ikke s&aring; lett &aring; sammenligne tredeler og femdeler.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Anta at du skal regne sammen&nbsp;$\\frac{2}{3}+\\frac{5}{3}$, alts&aring; 'to tredjedeler plus fem tredjedeler', da har du til sammen syv tredjedeler.Slik skriver vi:</p>\n<p style=\"text-align: center;\">\\[\\frac{2}{3}+\\frac{5}{3}=\\frac{2+5}{3}=\\frac{7}{3}\\]</p>\n<p>Samme gjelder for subtraksjon. Anta at du har syv fjerdedeler og m&aring; gi fra deg tre av dem. Da st&aring;r du igjen med 7-3=4 fjerdedeler, alts&aring; en hel.&nbsp;</p>\n<p>Vi skriver:</p>\n<p style=\"text-align: center;\">\\[\\frac{7}{4}-\\frac{3}{4}=\\frac{7-3}{4}=\\frac{4}{4}=1\\]</p>\n<p></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": "(a+c)/b", "maxValue": "(a+c)/b", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"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": "(d-a)/c", "maxValue": "(d-a)/c", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>$\\displaystyle\\simplify{{f}/{g}+{h}/{j}}=$[[0]]</p>\n<p>$\\displaystyle\\simplify{{h}/{f}-{j}/{g}}=$[[1]]</p>\n<p>$\\displaystyle \\frac{\\var{a}}{\\var{d}}+\\var{f}=$[[2]]</p>", "stepsPenalty": "2", "steps": [{"type": "information", "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><em>Finn fellesnevner f&oslash;r du adderer eller subtraherer.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Eksempel: Hvis vi skal regne ut&nbsp;$\\frac{5}{4}+\\frac{3}{8}$ kan vi utvide den f&oslash;rste br&oslash;ken til $\\frac{10}{8}$ ved &aring; multiplisere teller og nevner med 2. Da vil begge br&oslash;kene ha felles faktor 8, og vi kan regne sammen.</p>\n<p>Vi skriver slik:</p>\n<p style=\"text-align: center;\">\\[\\frac{5}{4}+\\frac{3}{8}=\\frac{5\\cdot 2}{4\\cdot 2}+\\frac{3}{8}=\\frac{10}{8}+\\frac{3}{8}=\\frac{13}{8}\\]</p>\n<p style=\"text-align: left;\"></p>\n<p></p>\n<hr/>\n<p></p>\n<p style=\"text-align: left;\">Ofte m&aring; begge br&oslash;kene skrives om, f.eks. i regnestykket $\\frac{5}{4}-\\frac{2}{3}$. Her kan vi multiplisere den f&oslash;rste br&oslash;ken med 3 over og under br&oslash;kstrek, og den andre med 4 over og under br&oslash;kstrek, slik at begge f&aring;r 12 som nevner. S&aring; kan vi subtrahere:</p>\n<p style=\"text-align: center;\">\\[\\frac{5}{4}-\\frac{2}{3}=\\frac{5\\cdot 3}{4\\cdot 3}-\\frac{2\\cdot 4}{3\\cdot 4}=\\frac{15}{12}-\\frac{8}{12}=\\frac{7}{12}\\]</p>\n<p style=\"text-align: left;\"></p>\n<p></p>\n<hr/>\n<p></p>\n<p style=\"text-align: left;\">Husk ogs&aring; at vi kan gj&oslash;re hele tall om til br&oslash;ker for &aring; lettere bruke reglene. F. eks er &nbsp;$3=\\frac{3}{1}$.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(f*j+h*g)/(g*j)", "maxValue": "(f*j+h*g)/(g*j)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(h*g-j*f)/(f*g)", "maxValue": "(h*g-j*f)/(f*g)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(a+f*d)/(d)", "maxValue": "(a+f*d)/(d)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>$\\displaystyle\\frac{\\var{a}}{\\var{b}}\\cdot \\frac{\\var{c}}{\\var{d}}=$[[0]]</p>\n<p>$\\displaystyle -\\frac{\\var{f}}{\\var{j}}\\cdot \\var{d}=$[[1]]</p>\n<p></p>\n<p></p>\n<p></p>", "stepsPenalty": "1", "steps": [{"type": "information", "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><em>Multipliser teller med teller og nevner med nevner.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Eksempel:&nbsp;</p>\n<p style=\"text-align: center;\">\\[\\frac{4}{5}\\cdot \\frac{2}{3}=\\frac{4\\cdot 2}{5 \\cdot 3}=\\frac{8}{15}\\]</p>\n<p style=\"text-align: center;\"></p>\n<p></p>\n<hr/>\n<p></p>\n<p style=\"text-align: left;\">Husk ogs&aring; at et helt tall er det samme som en br&oslash;k med nevner 1, f.eks er&nbsp;$7=\\frac{7}{1}$.</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": "(a*c)/(b*d)", "maxValue": "(a*c)/(b*d)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "-f*d/j", "maxValue": "-f*d/j", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>$\\displaystyle&nbsp;\\frac{\\var{f}}{\\var{h}}: \\frac{\\var{g}}{\\var{j}}=$[[0]]</p>\n<p>$\\displaystyle \\frac{\\var{b}}{\\var{c}}: \\var{d}=$[[1]]</p>\n<p>$\\displaystyle \\var{j}: \\left(\\frac{\\var{-d}}{\\var{f}}\\right)=$[[2]]</p>\n<p></p>", "stepsPenalty": "2", "steps": [{"type": "information", "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><em>N&aring;r vi dividerer to br&oslash;ker, kan vi regne ut ved &aring; i stedet multiplisere med den omvendte br&oslash;ken.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>N&aring;r vi skal dele p&aring; et helt tall, multipliserer vi med det omvendte tallet. Da skriver vi heltallet som en br&oslash;k med 1 i nevner, f.eks. er $6=\\frac{6}{1}$, og det omvendte tallet til 6 blir da $\\frac{1}{6}$</p>\n<p>Hvordan finner man f.eks halvparten av en br&oslash;k? Man kan \"dele p&aring; to\", eller man kan multiplisere med det omvendte tallet, nemlig $\\frac{1}{2}$.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Anta at du skal regne ut $\\frac{3}{7}\\div\\frac{5}{4}$. Det er ikke s&aring; lett &aring; se for seg hvor mange \"$\\frac{5}{4}$\" man kan dele $\\frac{3}{7}$\" opp i! Da er det lettere &aring; multiplisere med $\\frac{4}{5}$.</p>\n<p>Vi kan skrive slik:</p>\n<p>\\[\\frac{3}{7}:\\frac{5}{4}=\\frac{3}{7}\\cdot\\frac{4}{5}=\\frac{3\\cdot 4}{7\\cdot 5}=\\frac{12}{35}\\]</p>\n<p>&nbsp;</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(f*j)/(h*g)", "maxValue": "(f*j)/(h*g)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b/(c*d)", "maxValue": "b/(c*d)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "j*f/(-d)", "maxValue": "j*f/(-d)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>$\\displaystyle \\frac{\\frac{\\var{b}}{\\var{c}}}{ \\frac{\\var{a}}{\\var{d}}}=$[[0]]</p>\n<p></p>\n<p>$\\displaystyle \\frac{\\frac{\\var{d}}{\\var{g}}}{\\var{f}}=$[[1]]</p>\n<p></p>\n<p>$\\displaystyle \\frac{\\var{j}}{\\frac{\\var{h}}{\\var{c}}}=$[[2]]</p>\n<p></p>", "stepsPenalty": "2", "steps": [{"type": "information", "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>Husk at br&oslash;kstreken er det samme som et delingstegn.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Br&oslash;ken $\\frac{2}{3}$ betyr \"2 delt p&aring; 3\". S&aring; brudne br&oslash;ker er egentlig delingsstykker. &nbsp;&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Noen eksempler:</p>\n<p>\\[\\frac{7}{\\frac{5}{6}}=7:\\frac{5}{6} =7\\cdot\\frac{6}{5}=\\frac{42}{5}\\]</p>\n<p>\\[\\frac{\\frac{7}{5}}{6}=\\frac{7}{5}: 6=\\frac{7}{5}\\cdot \\frac{1}{6}=\\frac{7}{30}\\]</p>\n<p>\\[\\frac{\\frac{9}{11}}{\\frac{5}{3}}=\\frac{9}{11}:\\frac{5}{3}=\\frac{9}{11}\\cdot \\frac{3}{5}=\\frac{27}{55}\\]</p>\n<hr/>\n<p>Vi kan ogs&aring; bruke f&oslash;lgende metode:</p>\n<ol>\n<li>Finn fellesnevner for begge sm&aring;br&oslash;kene</li>\n<li>Multipliser begge sm&aring;br&oslash;kene med denne fellesnevneren</li>\n<li>Forkort og regn ut.</li>\n</ol>\n<hr/>\n<p>Eksempler p&aring; denne m&aring;ten: $\\require{cancel}$</p>\n<p>\\[\\frac{7}{\\frac{5}{6}}=\\frac{\\:\\frac{7}{1}\\:}{\\:\\frac{5}{6}\\:}=\\frac{\\:\\frac{7}{1}\\cdot 6\\:}{\\:\\frac{5}{\\cancel{6}}\\cdot \\cancel{6}\\:}=\\frac{42}{5}\\]</p>\n<p>\\[\\frac{\\frac{9}{11}}{\\frac{5}{3}}=\\frac{\\frac{9}{\\cancel{11}}\\cdot \\overset{3}{\\cancel{33}}}{\\frac{5}{\\cancel{3}}\\cdot \\overset{11}{\\cancel{33}}}=\\frac{9\\cdot 3}{5\\cdot 11}=\\frac{27}{55}\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(b*d)/(a*c)", "maxValue": "(b*d)/(a*c)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", 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"minValue": "j*c/h", "maxValue": "j*c/h", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>$\\simplify{{te[0]} / {ne[0]}}\\cdot\\left(\\simplify[!collectNumbers]{{te[1]} / {ne[1]}+{te[2]}/{ne[2]}}\\right)=$[[0]]</p>\n<p>$\\simplify{{te[3]} / {ne[3]}}\\cdot\\left(\\simplify[!collectNumbers]{{te[4]} / {ne[4]}+{te[5]}/{ne[5]}}\\right)=$&nbsp;[[1]]</p>\n<p>$\\simplify{{te[6]} / 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