{"id":2656,"date":"2026-09-29T19:31:23","date_gmt":"2026-09-29T19:31:23","guid":{"rendered":"https:\/\/www.jrebsen.dk\/?post_type=aktivitet&#038;p=2656"},"modified":"2026-09-29T19:40:44","modified_gmt":"2026-09-29T19:40:44","slug":"broeker-dianostiske-opgaver","status":"publish","type":"aktivitet","link":"https:\/\/www.jrebsen.dk\/?aktivitet=broeker-dianostiske-opgaver","title":{"rendered":"Br\u00f8ker &#8211; diagnostiske opgaver"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">1. Br\u00f8ken som en del af en helhed<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> En pizza er delt i \\(8\\) lige store stykker. Du spiser \\(3\\) stykker. Skriv som en br\u00f8k, hvor stor en del af pizzaen du har spist.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> En figur er delt i \\(12\\) lige store felter, og \\(5\\) af dem er farvede. Skriv den farvede del som en br\u00f8k.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. T\u00e6ller og n\u00e6vner<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> I br\u00f8ken \\(\\frac{4}{7}\\): Hvad fort\u00e6ller tallet \\(4\\), og hvad fort\u00e6ller tallet \\(7\\)?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Skriv en br\u00f8k, hvor n\u00e6vneren er \\(9\\), og hvor \\(5\\) af delene er valgt. Forklar betydningen af b\u00e5de t\u00e6ller og n\u00e6vner.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Br\u00f8ken som et tal<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Plac\u00e9r \\(\\frac{3}{4}\\) p\u00e5 en tallinje fra \\(0\\) til \\(1\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Plac\u00e9r \\(\\frac{5}{4}\\) p\u00e5 en tallinje fra \\(0\\) til \\(2\\), og forklar hvorfor br\u00f8ken er st\u00f8rre end \\(1\\).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u00c6kvivalente br\u00f8ker<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Udfyld det manglende tal:\\[ \\frac{2}{3}=\\frac{\\square}{12} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Er\\[ \\frac{6}{8}=\\frac{3}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Forklar, hvordan du kan afg\u00f8re det.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">5. Forkorte og forl\u00e6nge br\u00f8ker<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Forkort br\u00f8ken mest muligt:\\[ \\frac{18}{24} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Forl\u00e6ng\\[ \\frac{3}{5} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">s\u00e5 n\u00e6vneren bliver \\(30\\).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">6. Sammenligne br\u00f8ker<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Hvilken br\u00f8k er st\u00f8rst?\\[ \\frac{3}{5}\\qquad \\frac{2}{3} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Begrund dit svar.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> S\u00e6t \\(&lt;\\), \\(&gt;\\) eller \\(=\\):\\[ \\frac{7}{8}\\ \\square\\ \\frac{5}{6} \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">7. Br\u00f8k som division<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Skriv divisionen som en br\u00f8k:\\[ 5:8 \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Beregn\\[ \\frac{3}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ved at opfatte br\u00f8ken som en division.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">8. Br\u00f8k, decimaltal og procent<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Skriv\\[ \\frac{3}{5} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">som decimaltal og procent.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Skriv\\[ 0,25 \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">som procent og som en forkortet br\u00f8k.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">9. Addition og subtraktion med samme n\u00e6vner<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Beregn:\\[ \\frac{3}{8}+\\frac{2}{8} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Beregn:\\[ \\frac{11}{15}-\\frac{4}{15} \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">10. F\u00e6lles n\u00e6vner<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Find en f\u00e6lles n\u00e6vner for\\[ \\frac{1}{3}\\qquad \\text{og}\\qquad \\frac{1}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">og omskriv begge br\u00f8ker.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Forklar, hvorfor man ikke bare kan regne\\[ \\frac{1}{2}+\\frac{1}{3}=\\frac{2}{5}. \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">11. Addition og subtraktion med forskellige n\u00e6vnere<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Beregn:\\[ \\frac{2}{3}+\\frac{1}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Beregn:\\[ \\frac{5}{6}-\\frac{1}{4} \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">12. U\u00e6gte br\u00f8ker og blandede tal<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Omskriv til blandet tal:\\[ \\frac{11}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Omskriv til u\u00e6gte br\u00f8k:\\[ 3\\frac{2}{5} \\]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">13. Multiplikation med en br\u00f8k<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Beregn:\\[ \\frac{3}{4}\\cdot 20 \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">og forklar, hvad beregningen betyder.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> En klasse har \\(28\\) elever. \\(\\frac{3}{7}\\) af eleverne cykler i skole. Hvor mange elever er det?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">14. Multiplikation af to br\u00f8ker<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Beregn og forkort:\\[ \\frac{2}{3}\\cdot\\frac{3}{5} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Beregn:\\[ \\frac{3}{4}\\cdot\\frac{2}{7} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">og forklar resultatet som &#8220;en del af en del&#8221;.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">15. Division med en br\u00f8k<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> Hvor mange \\(\\frac{1}{4}\\) er der i \\(3\\)?\\[ 3:\\frac{1}{4} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> Beregn:\\[ \\frac{3}{4}:\\frac{1}{8} \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">og forklar, hvad resultatet fort\u00e6ller.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">16. Regning med br\u00f8ker i problemer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> En beholder kan rumme \\(12\\,\\mathrm{L}\\). Den er fyldt \\(\\frac{3}{4}\\). Hvor mange liter vand er der i beholderen?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> En rute er \\(18\\,\\mathrm{km}\\) lang. Anna har g\u00e5et \\(\\frac{5}{6}\\) af ruten. Hvor mange kilometer har hun g\u00e5et, og hvor mange kilometer mangler hun?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">17. Br\u00f8ker i algebra<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 1:<\/strong> L\u00f8s ligningen:\\[ \\frac{x}{4}=7 \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Opgave 2:<\/strong> L\u00f8s ligningen:\\[ \\frac{3}{5}x=18 \\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Br\u00f8ken som en del af en helhed Opgave 1: En pizza er delt i \\(8\\) lige store stykker. Du spiser \\(3\\) stykker. Skriv som en br\u00f8k, hvor stor en del af pizzaen du har spist. Opgave 2: En figur er delt i \\(12\\) lige store felter, og \\(5\\) af dem er farvede. Skriv den [&hellip;]<\/p>\n","protected":false},"featured_media":0,"menu_order":0,"template":"","meta":[],"categories":[],"tags":[],"aktivitetstype":[],"elementrolle":[],"fag":[90],"fagomraade":[],"produkt":[],"class_list":["post-2656","aktivitet","type-aktivitet","status-publish","hentry","fag-matematik"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=\/wp\/v2\/aktivitet\/2656","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=2656"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2656"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2656"},{"taxonomy":"aktivitetstype","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Faktivitetstype&post=2656"},{"taxonomy":"elementrolle","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Felementrolle&post=2656"},{"taxonomy":"fag","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ffag&post=2656"},{"taxonomy":"fagomraade","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ffagomraade&post=2656"},{"taxonomy":"produkt","embeddable":true,"href":"https:\/\/www.jrebsen.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fprodukt&post=2656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}