// Numbas version: exam_results_page_options {"name": "Br\u00f8kregning 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Br\u00f8kregning 1", "tags": ["br\u00f8k", "fellesnevner"], "preamble": {"css": "", "js": ""}, "advice": "
Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.
", "rulesets": {}, "parts": [{"stepsPenalty": "0", "prompt": "$\\displaystyle\\frac{\\var{a}}{\\var{b}}+\\frac{\\var{c}}{\\var{b}}=$[[0]]
\n$\\displaystyle\\frac{\\var{d}}{\\var{c}}-\\frac{\\var{a}}{\\var{c}}=$[[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Legg sammen tellerne, behold nevner.
\nDisse brøkene har felles nevner, og kan enkelt legges sammen. La oss illustrere det med eksempler (som ikke er like oppgaven):
\n\\[\\frac{2}{3}+\\frac{5}{3}=\\frac{2+5}{3}=\\frac{7}{3}\\]
\nDen samme fremgangsmåten kan brukes for subtraksjon:
\n\\[\\frac{7}{4}-\\frac{3}{4}=\\frac{7-3}{4}=\\frac{4}{4}=1\\]
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "(a+c)/b", "minValue": "(a+c)/b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(d-a)/c", "minValue": "(d-a)/c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "Regn ut
\n$\\displaystyle\\simplify{{h}/{f}-{j}/{g}}=$ [[0]]
\n$\\displaystyle \\frac{\\var{a}}{\\var{d}}+\\var{f}=$ [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Utvid brøkene slik at de får en felles nevner. Deretter kan du addere eller subtrahere slik som i forrige oppgave.
\nHvis oppgaven var $\\frac{5}{4}+\\frac{3}{8}$ kunne vi utvidet den første brøken til $\\frac{10}{8}$ (ved å multiplisere med 2 i teller og nevner), slik at begge brøkene fikk nevner lik 8. Deretter kunne vi addert brøkene:
\n\\[\\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}\\]
\nSom regel må vi utvide begge brøkene for å få en felles nevner, for eksempel når vi skal regne ut $\\frac{5}{4}-\\frac{2}{3}$. Her kan 12 være en felles nevner, og utregningen kan se slik ut:
\n\\[\\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}\\]
\nEt godt valg for fellesnevneren er minste felles multiplum til de to nevnerne.
\nNB! Husk at hele tall kan skrives som en brøk med nevner lik 1, for eksempel $3=\\frac{3}{1}$.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "(h*g-j*f)/(f*g)", "minValue": "(h*g-j*f)/(f*g)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(a+f*d)/(d)", "minValue": "(a+f*d)/(d)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "Regn ut og oppgi svaret ditt som en brøk eller et helt tall (ikke desimaltall). Bruk / som brøkstrek, for eksempel skal $\\frac{2}{3}$ skrives som 2/3.
", "variable_groups": [{"variables": ["a", "b", "c", "d", "f", "g", "h", "j"], "name": "numerical fractions"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..12)", "templateType": "anything", "group": "numerical fractions", "name": "a", "description": ""}, "c": {"definition": "random(2..12 except [a,b])", "templateType": "anything", "group": "numerical fractions", "name": "c", "description": ""}, "b": {"definition": "random(2..8 except a)", "templateType": "anything", "group": "numerical fractions", "name": "b", "description": ""}, "d": {"definition": "random(2..8 except[a,b,c,10])", "templateType": "anything", "group": "numerical fractions", "name": "d", "description": ""}, "g": {"definition": "random(2..9 except f)", "templateType": "anything", "group": "numerical fractions", "name": "g", "description": ""}, "f": {"definition": "random(2..9 except d)", "templateType": "anything", "group": "numerical fractions", "name": "f", "description": ""}, "h": {"definition": "random(3..5 except [f,g])", "templateType": "anything", "group": "numerical fractions", "name": "h", "description": ""}, "j": {"definition": "random(2..9 except [f,g,h])", "templateType": "anything", "group": "numerical fractions", "name": "j", "description": ""}}, "metadata": {"description": "Add, subtract, multiply and divide numerical fractions.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Morten Brekke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/478/"}]}]}], "contributors": [{"name": "Morten Brekke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/478/"}]}