{"id":2559,"date":"2026-09-16T18:47:11","date_gmt":"2026-09-16T18:47:11","guid":{"rendered":"https:\/\/www.jrebsen.dk\/?post_type=aktivitet&p=2559"},"modified":"2026-09-17T06:04:39","modified_gmt":"2026-09-17T06:04:39","slug":"intro-kapitlets-overordnede-emner","status":"publish","type":"aktivitet","link":"https:\/\/www.jrebsen.dk\/?aktivitet=intro-kapitlets-overordnede-emner","title":{"rendered":"Br\u00f8ker"},"content":{"rendered":"\n

Du skal bruge din computer og g\u00e5 ind p\u00e5 SkoleDu.dk f\u00f8r vi g\u00e5r igang<\/strong> <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
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Film – Tal i det uendelige<\/h2>\n\n\n\n
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Episode 1:<\/strong> https:\/\/tv.vg.no\/serier\/jakten-paa-verdens-stoerste-tall\/s1e1\/jakten-paa-verdens-stoerste-tall-episode-1?id=62950<\/a><\/p>\n\n\n\n

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Introopgave ‘Intro – Gange + Div. m. br\u00f8ker’ p\u00e5 SkoleDu.dk<\/h3>\n\n\n\n

https:\/\/app.skoledu.dk\/opgaver\/udskoling\/broeker-og-procent\/forloeb\/regn-med-broeker\/gange-broeker-2?aflevering=990&destination=\/aflevering\/990&assignmentsetType=forlob<\/a><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
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Centrale begreber<\/strong><\/p>\n\n\n\n

    \n
  • t\u00e6ller og n\u00e6vner<\/li>\n\n\n\n
  • br\u00f8kstreg<\/li>\n\n\n\n
  • \u00e6kvivalente br\u00f8ker<\/li>\n\n\n\n
  • forl\u00e6ngelse og forkortelse<\/li>\n\n\n\n
  • f\u00e6llesn\u00e6vner<\/li>\n\n\n\n
  • blandet tal<\/li>\n\n\n\n
  • u\u00e6gte br\u00f8k<\/li>\n\n\n\n
  • stambr\u00f8k<\/li>\n\n\n\n
  • br\u00f8k som division<\/li>\n\n\n\n
  • br\u00f8k som forhold<\/li>\n\n\n\n
  • rationelt tal.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n
    Regel<\/th>Med ord<\/th>Formel<\/th>Eksempel <\/th><\/tr><\/thead>
    Forkorte<\/strong><\/td>Divider t\u00e6ller og n\u00e6vner med det samme tal.<\/td>a<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi>\u2217<\/mo>c<\/mi><\/mrow><\/mfrac>=<\/mo>a<\/mi>b<\/mi><\/mfrac><\/mrow>\\frac{a*c}{b*c}=\\frac{a}{b}<\/annotation><\/semantics><\/math><\/td>12<\/mn>18<\/mn><\/mfrac>=<\/mo>12<\/mn>:<\/mo>6<\/mn><\/mrow>18<\/mn>:<\/mo>6<\/mn><\/mrow><\/mfrac>=<\/mo>2<\/mn>3<\/mn><\/mfrac><\/mrow>\\frac{12}{18}=\\frac{12:6}{18:6}=\\frac23<\/annotation><\/semantics><\/math><\/td><\/tr>
    Forl\u00e6nge<\/strong><\/td>Gang t\u00e6ller og n\u00e6vner med det samme tal.<\/td>a<\/mi>b<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi>\u2217<\/mo>c<\/mi><\/mrow><\/mfrac><\/mrow>\\frac{a}{b}=\\frac{a*c}{b*c}<\/annotation><\/semantics><\/math><\/td>2<\/mn>3<\/mn><\/mfrac>=<\/mo>2<\/mn>\u2217<\/mo>4<\/mn><\/mrow>3<\/mn>\u2217<\/mo>4<\/mn><\/mrow><\/mfrac>=<\/mo>8<\/mn>12<\/mn><\/mfrac><\/mrow>\\frac23=\\frac{2*4}{3*4}=\\frac8{12}<\/annotation><\/semantics><\/math><\/td><\/tr>
    Addition \u2013 samme n\u00e6vner<\/strong><\/td>L\u00e6g t\u00e6llerne sammen, og behold n\u00e6vneren.<\/td>a<\/mi>c<\/mi><\/mfrac>+<\/mo>b<\/mi>c<\/mi><\/mfrac>=<\/mo>a<\/mi>+<\/mo>b<\/mi><\/mrow>c<\/mi><\/mfrac><\/mrow>\\frac{a}{c}+\\frac{b}{c}=\\frac{a+b}{c}<\/annotation><\/semantics><\/math><\/td>2<\/mn>5<\/mn><\/mfrac>+<\/mo>1<\/mn>5<\/mn><\/mfrac>=<\/mo>2<\/mn>+<\/mo>1<\/mn><\/mrow>5<\/mn><\/mfrac>=<\/mo>3<\/mn>5<\/mn><\/mfrac><\/mrow>\\frac25+\\frac15=\\frac{2+1}{5}=\\frac35<\/annotation><\/semantics><\/math><\/td><\/tr>
    Addition \u2013 forskellig n\u00e6vner<\/strong><\/td>Find f\u00f8rst en f\u00e6lles n\u00e6vner. L\u00e6g derefter t\u00e6llerne sammen.<\/td>a<\/mi>b<\/mi><\/mfrac>+<\/mo>c<\/mi>d<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>d<\/mi>+<\/mo>b<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi>\u2217<\/mo>d<\/mi><\/mrow><\/mfrac><\/mrow>\\frac ab+\\frac cd=\\frac{a*d+b*c}{b*d}<\/annotation><\/semantics><\/math><\/td>1<\/mn>2<\/mn><\/mfrac>+<\/mo>1<\/mn>3<\/mn><\/mfrac>=<\/mo>1<\/mn>\u2217<\/mo>3<\/mn>+<\/mo>1<\/mn>\u2217<\/mo>2<\/mn><\/mrow>2<\/mn>\u2217<\/mo>3<\/mn><\/mrow><\/mfrac>=<\/mo>3<\/mn>+<\/mo>2<\/mn><\/mrow>6<\/mn><\/mfrac>=<\/mo>5<\/mn>6<\/mn><\/mfrac><\/mrow>\\frac12+\\frac13=\\frac{1*3+1*2}{2*3}=\\frac{3+2}{6}=\\frac56<\/annotation><\/semantics><\/math><\/td><\/tr>
    Subtraktion<\/strong><\/td>Find f\u00f8rst en f\u00e6lles n\u00e6vner. Tr\u00e6k derefter t\u00e6llerne fra hinanden.<\/td>a<\/mi>b<\/mi><\/mfrac>\u2212<\/mo>c<\/mi>d<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>d<\/mi>\u2212<\/mo>b<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi>\u2217<\/mo>d<\/mi><\/mrow><\/mfrac><\/mrow>\\frac ab-\\frac cd=\\frac{a*d-b*c}{b*d}<\/annotation><\/semantics><\/math><\/td>3<\/mn>4<\/mn><\/mfrac>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac>=<\/mo>3<\/mn>\u2217<\/mo>2<\/mn>\u2212<\/mo>1<\/mn>\u2217<\/mo>4<\/mn><\/mrow>4<\/mn>\u2217<\/mo>2<\/mn><\/mrow><\/mfrac>=<\/mo>6<\/mn>\u2212<\/mo>4<\/mn><\/mrow>8<\/mn><\/mfrac>=<\/mo>2<\/mn>8<\/mn><\/mfrac>=<\/mo>1<\/mn>4<\/mn><\/mfrac><\/mrow>\\frac34-\\frac12=\\frac{3*2-1*4}{4*2}=\\frac{6-4}{8}=\\frac28=\\frac14<\/annotation><\/semantics><\/math><\/td><\/tr>
    Multiplikation<\/strong><\/td>Gang t\u00e6ller med t\u00e6ller og n\u00e6vner med n\u00e6vner.<\/td>a<\/mi>b<\/mi><\/mfrac>\u2217<\/mo>c<\/mi>d<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi>\u2217<\/mo>d<\/mi><\/mrow><\/mfrac><\/mrow>\\frac ab*\\frac cd=\\frac{a*c}{b*d}<\/annotation><\/semantics><\/math><\/td>2<\/mn>3<\/mn><\/mfrac>\u2217<\/mo>4<\/mn>5<\/mn><\/mfrac>=<\/mo>2<\/mn>\u2217<\/mo>4<\/mn><\/mrow>3<\/mn>\u2217<\/mo>5<\/mn><\/mrow><\/mfrac>=<\/mo>8<\/mn>15<\/mn><\/mfrac><\/mrow>\\frac23*\\frac45=\\frac{2*4}{3*5}=\\frac8{15}<\/annotation><\/semantics><\/math><\/td><\/tr>
    Division<\/strong><\/td>Vend den br\u00f8k, du dividerer med, og gang derefter.<\/td>a<\/mi>b<\/mi><\/mfrac>:<\/mo>c<\/mi>d<\/mi><\/mfrac>=<\/mo>a<\/mi>b<\/mi><\/mfrac>\u2217<\/mo>d<\/mi>c<\/mi><\/mfrac><\/mrow>\\frac ab:\\frac cd=\\frac ab*\\frac dc<\/annotation><\/semantics><\/math><\/td>2<\/mn>3<\/mn><\/mfrac>:<\/mo>4<\/mn>5<\/mn><\/mfrac>=<\/mo>2<\/mn>3<\/mn><\/mfrac>\u2217<\/mo>5<\/mn>4<\/mn><\/mfrac>=<\/mo>2<\/mn>\u2217<\/mo>5<\/mn><\/mrow>3<\/mn>\u2217<\/mo>4<\/mn><\/mrow><\/mfrac>=<\/mo>10<\/mn>12<\/mn><\/mfrac>=<\/mo>5<\/mn>6<\/mn><\/mfrac><\/mrow>\\frac23:\\frac45=\\frac23*\\frac54=\\frac{2*5}{3*4}=\\frac{10}{12}=\\frac56<\/annotation><\/semantics><\/math><\/td><\/tr>
    Helt tal \u00d7 br\u00f8k<\/strong><\/td>Gang det hele tal med t\u00e6lleren, og behold n\u00e6vneren.<\/td>a<\/mi>\u2217<\/mo>b<\/mi>c<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>b<\/mi><\/mrow>c<\/mi><\/mfrac><\/mrow>a*\\frac bc=\\frac{a*b}{c}<\/annotation><\/semantics><\/math><\/td>3<\/mn>\u2217<\/mo>2<\/mn>5<\/mn><\/mfrac>=<\/mo>3<\/mn>\u2217<\/mo>2<\/mn><\/mrow>5<\/mn><\/mfrac>=<\/mo>6<\/mn>5<\/mn><\/mfrac><\/mrow>3*\\frac25=\\frac{3*2}{5}=\\frac65<\/annotation><\/semantics><\/math><\/td><\/tr>
    Helt tal som br\u00f8k<\/strong><\/td>Skriv det hele tal over 1.<\/td>a<\/mi>=<\/mo>a<\/mi>1<\/mn><\/mfrac><\/mrow>a=\\frac a1<\/annotation><\/semantics><\/math><\/td>4<\/mn>=<\/mo>4<\/mn>1<\/mn><\/mfrac><\/mrow>4=\\frac41<\/annotation><\/semantics><\/math><\/td><\/tr>
    Br\u00f8k af et tal<\/strong><\/td>Gang tallet med br\u00f8ken.<\/td>a<\/mi>b<\/mi><\/mfrac>\u2217<\/mo>c<\/mi>=<\/mo>a<\/mi>\u2217<\/mo>c<\/mi><\/mrow>b<\/mi><\/mfrac><\/mrow>\\frac ab*c=\\frac{a*c}{b}<\/annotation><\/semantics><\/math><\/td>3<\/mn>4<\/mn><\/mfrac>\u2217<\/mo>20<\/mn>=<\/mo>3<\/mn>\u2217<\/mo>20<\/mn><\/mrow>4<\/mn><\/mfrac>=<\/mo>60<\/mn>4<\/mn><\/mfrac>=<\/mo>15<\/mn><\/mrow>\\frac34*20=\\frac{3*20}{4}=\\frac{60}{4}=15<\/annotation><\/semantics><\/math><\/td><\/tr>
    Blandet tal \u2192 u\u00e6gte br\u00f8k<\/strong><\/td>Gang det hele tal med n\u00e6vneren, l\u00e6g t\u00e6lleren til, og behold n\u00e6vneren.<\/td>a<\/mi>b<\/mi>c<\/mi><\/mfrac>=<\/mo>a<\/mi>\u2217<\/mo>c<\/mi>+<\/mo>b<\/mi><\/mrow>c<\/mi><\/mfrac><\/mrow>a\\frac bc=\\frac{a*c+b}{c}<\/annotation><\/semantics><\/math><\/td>2<\/mn>1<\/mn>3<\/mn><\/mfrac>=<\/mo>2<\/mn>\u2217<\/mo>3<\/mn>+<\/mo>1<\/mn><\/mrow>3<\/mn><\/mfrac>=<\/mo>7<\/mn>3<\/mn><\/mfrac><\/mrow>2\\frac13=\\frac{2*3+1}{3}=\\frac73<\/annotation><\/semantics><\/math><\/td><\/tr>
    U\u00e6gte br\u00f8k \u2192 blandet tal<\/strong><\/td>Divider t\u00e6lleren med n\u00e6vneren. Kvotienten bliver det hele tal, og resten bliver t\u00e6lleren i br\u00f8kdelen.<\/td>a<\/mi>b<\/mi><\/mfrac>=<\/mo>q<\/mi>+<\/mo>r<\/mi>b<\/mi><\/mfrac><\/mrow>\\frac ab=q+\\frac rb<\/annotation><\/semantics><\/math><\/td>11<\/mn>4<\/mn><\/mfrac>=<\/mo>2<\/mn>+<\/mo>3<\/mn>4<\/mn><\/mfrac>=<\/mo>2<\/mn>3<\/mn>4<\/mn><\/mfrac><\/mrow>\\frac{11}{4}=2+\\frac34=2\\frac34<\/annotation><\/semantics><\/math><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
    \n\n\n\n

    Talm\u00e6ngder<\/h3>\n\n\n\n

    Du kan inddele tal i forskellige grupper. Tallene har de samme egenskaber. M\u00e6ngderne med tal kan l\u00e6gges \u2019inde i hinanden\u2019, som det er illustreret p\u00e5 figuren.<\/p>\n\n\n\n

    \"et<\/p>\n\n\n\n

    N<\/strong> – De naturlige tal<\/strong> er alle positive hele tal, alts\u00e5 1, 2, 3… Ogs\u00e5 kaldet t\u00e6lletallene.<\/p>\n\n\n\n

    Z<\/strong> – De hele tal<\/strong> inkluderer b\u00e5de positive og negative heltal samt 0, alts\u00e5 fx \u2026 -3, -2, -1, 0, 1,2, 3…<\/p>\n\n\n\n

    Q<\/strong> – De rationale tal<\/strong> er alle hele tal, samt tal der kan skrives som et endeligt eller et periodisk decimaltal, og de tal, der kan skrives som br\u00f8ker.<\/p>\n\n\n\n

    R<\/strong> – De reelle tal <\/strong>best\u00e5r af alle rationale og alle irrationale tal. Irrationale tal<\/strong> er tal, der ikke kan skrives som endelige eller periodiske decimaltal (fx \u03c0 og 2<\/mn><\/msqrt><\/mrow><\/semantics><\/math>2\u200b).<\/p>\n\n\n\n
    \n\n\n\n

    Regn selv <\/h3>\n\n\n\n

    KonteXt+9 <\/strong><\/p>\n\n\n\n

      \n
    • s.32 Opg. 1-7<\/li>\n<\/ul>\n\n\n\n

      SkoleDu.dk<\/strong><\/p>\n\n\n\n

        \n
      • ‘Br\u00f8ker 1’<\/li>\n\n\n\n
      • ‘Br\u00f8ker 2’<\/li>\n<\/ul>\n\n\n\n

        Aftal med l\u00e6reren hvor du arbejder inden du forlader din plads<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Milep\u00e6le for det selvst\u00e6ndige arbejde<\/strong>:<\/p>\n\n\n\n

          \n
        • Start:<\/strong> Skriv, hvilke opgaver du vil n\u00e5.<\/li>\n\n\n\n
        • Undervejs:<\/strong> Vis og forklar mindst \u00e9n l\u00f8st opgave.<\/li>\n\n\n\n
        • Afslutning:<\/strong> Not\u00e9r, hvor langt du n\u00e5ede, og hvilken opgave du starter med n\u00e6ste gang.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          Problem- og f\u00e6rdighedsregning<\/strong><\/h3>\n\n\n\n

          FP9 December 2023<\/p>\n\n\n\n

          Aflevering torsdag d. 8. oktober<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Du skal bruge din computer og g\u00e5 ind p\u00e5 SkoleDu.dk f\u00f8r vi g\u00e5r igang Film – Tal i det uendelige Episode 1: https:\/\/tv.vg.no\/serier\/jakten-paa-verdens-stoerste-tall\/s1e1\/jakten-paa-verdens-stoerste-tall-episode-1?id=62950 Introopgave ‘Intro – Gange + Div. m. br\u00f8ker’ p\u00e5 SkoleDu.dk https:\/\/app.skoledu.dk\/opgaver\/udskoling\/broeker-og-procent\/forloeb\/regn-med-broeker\/gange-broeker-2?aflevering=990&destination=\/aflevering\/990&assignmentsetType=forlob Centrale begreber Regel Med ord Formel Eksempel Forkorte Divider t\u00e6ller og n\u00e6vner med det samme tal. a\u2217cb\u2217c=ab\\frac{a*c}{b*c}=\\frac{a}{b} 1218=12:618:6=23\\frac{12}{18}=\\frac{12:6}{18:6}=\\frac23 Forl\u00e6nge Gang t\u00e6ller […]<\/p>\n","protected":false},"featured_media":0,"menu_order":0,"template":"","meta":[],"categories":[],"tags":[],"aktivitetstype":[],"elementrolle":[],"fag":[],"fagomraade":[],"produkt":[],"class_list":["post-2559","aktivitet","type-aktivitet","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=\/wp\/v2\/aktivitet\/2559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=\/wp\/v2\/aktivitet"}],"about":[{"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=\/wp\/v2\/types\/aktivitet"}],"wp:attachment":[{"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2559"},{"taxonomy":"aktivitetstype","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Faktivitetstype&post=2559"},{"taxonomy":"elementrolle","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Felementrolle&post=2559"},{"taxonomy":"fag","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ffag&post=2559"},{"taxonomy":"fagomraade","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ffagomraade&post=2559"},{"taxonomy":"produkt","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fprodukt&post=2559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}