// Numbas version: exam_results_page_options {"name": "INLEIDING: Twee breuken optellen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "INLEIDING: Twee breuken optellen", "tags": [], "metadata": {"description": "
Oefeningen:
\nBASIS: Maak een extra \"part\" aan, waar om het product van de twee breuken gevraagd wordt.
\nBASIS: Zoek uit waar typische_fout
voor dient (bij de variabelen) en hoe die typische fout dan effectief gesignaleerd wordt.
GEMIDDELD: Zorg dat geen/enkel (jouw keuze) noemers voorkomen die geen gemeenschappelijke deler hebben. (Hint: gcd(a,b)
kan een hulp zijn, met een for-loop.)
Je hebt twee breuken: \\(\\frac{\\var{a}}{\\var{b}}\\) en \\(\\frac{\\var{c}}{\\var{d}}\\)
\n\nOm twee breuken op te tellen, gebruiken we de volgende regel:
\n\\[\\frac{a}{b} + \\frac{c}{d} = \\frac{ad+bc}{bd}\\]
\nIn dit specifieke geval, geeft dat dus
\n\\[\\frac{\\var{a}}{\\var{b}} + \\frac{\\var{c}}{\\var{d}} =
\\frac{\\var{a}\\times\\var{d}+\\var{b}\\times\\var{c}}{\\var{b}\\times\\var{d}} =
\\frac{\\var{a*d}+\\var{b*c}}{\\var{b*d}} =
\\frac{\\var{a*d+b*c}}{\\var{b*d}}\\]
De vereenvoudigde breuk is dan \\(\\var[fractionNumbers]{juiste_som}\\).
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(mogelijke_getallen)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(mogelijke_getallen)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(mogelijke_getallen)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(mogelijke_getallen)", "description": "", "templateType": "anything", "can_override": false}, "juiste_som": {"name": "juiste_som", "group": "Ungrouped variables", "definition": "a/b+c/d", "description": "Merk op: het systeem van NUMBAS berekent zelf de correcte breuk. Ik hoef niets te doen om op gelijke noemer te zetten.
", "templateType": "anything", "can_override": false}, "typische_fout": {"name": "typische_fout", "group": "Ungrouped variables", "definition": "(a+c)/(b+d)", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Indien je priemgetallen wil gebruiken", "definition": "x for: x of: 1..100 where: length(divisors(x))=2", "description": "", "templateType": "anything", "can_override": false}, "mogelijke_getallen": {"name": "mogelijke_getallen", "group": "Ungrouped variables", "definition": "2..10#1", "description": "Getallen van 2 tot 10 (inclusief) in stapjes van 1
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "aWat is de som van deze twee breuken?", "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "typische_fout_mogelijkheid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Je telde tellers en noemers apart op, maar zo tel je breuken niet op.
\nIn dat geval zou namelijk $\\frac{1}{2}+\\frac{1}{2}$ gelijk zijn aan $\\frac{1+1}{2+2}=\\frac{2}{4}=\\frac{1}{2}$ dus weer een halfje...
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