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Modul 5: Division af brøker med brøker
Matematik
6. klasse
Regning med rationelle tal
Division af brøker med brøker
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Gennemgang af division af brøker

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Gennemgå det grundlæggende med division af brøker og løs nogle opgaver.

Division af brøker

Man dividerer brøker ved at gange med den omvendte, eller reciprokke, brøk.
For eksempel:
start fraction, 3, divided by, 4, end fraction, start color #e07d10, colon, end color #e07d10, start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 3, end color #1fab54, end fractionequals, start fraction, 3, divided by, 4, end fraction, start color #e07d10, dot, end color #e07d10, start fraction, start color #1fab54, 3, end color #1fab54, divided by, start color #11accd, 2, end color #11accd, end fraction
Når vi ganger to brøker, ganger vi tæller med tæller og nævner med nævner.
Eksempel 1: Brøker
start fraction, 3, divided by, 2, end fraction, colon, start fraction, 8, divided by, 3, end fraction, equals, question mark
Den omvendte brøk af start fraction, 8, divided by, 3, end fraction er start fraction, 3, divided by, 8, end fraction.
Derfor:
start fraction, 3, divided by, 2, end fraction, colon, start fraction, 8, divided by, 3, end fraction, equals, start fraction, 3, divided by, 2, end fraction, dot, start fraction, 3, divided by, 8, end fraction
empty space, equals, start fraction, 3, dot, 3, divided by, 2, dot, 8, end fraction
empty space, equals, start fraction, 9, divided by, 16, end fraction
Eksempel 2: Blandede tal
3, start fraction, 1, divided by, 2, end fraction, colon, 1, start fraction, 1, divided by, 4, end fraction, equals
Lad os starte med at omskrive de blandede tal til uægte brøker.
empty space, 3, start fraction, 1, divided by, 2, end fraction, colon, 1, start fraction, 1, divided by, 4, end fraction
equals, start fraction, 7, divided by, 2, end fraction, colon, start fraction, 5, divided by, 4, end fraction
equals, start fraction, 7, divided by, 2, end fraction, dot, start fraction, 4, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, G, a, n, g, space, m, e, d, space, d, e, n, space, o, m, v, e, n, d, t, e, space, b, r, ø, k, point, end text
equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, start cancel, 2, end cancel, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, start cancel, 4, end cancel, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, R, e, d, u, c, e, r, point, end text
equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, divided by, 5, end fraction
equals, start fraction, 14, divided by, 5, end fraction, start text, space, e, l, l, e, r, space, end text, 2, start fraction, 4, divided by, 5, end fraction
Vil du lære mere om division af brøker? Tjek denne video.
Vil du gennemgå multiplikation af brøker? Tjek denne artikel.

Øvelsesopgaver

Opgave 1
  • Nuværende
start fraction, 3, divided by, 5, end fraction, colon, start fraction, 1, divided by, 9, end fraction, equals, question mark
  • Dit svar skal være
  • et heltal, som f.eks. 6
  • en reduceret, ægte brøk, som eksempelvis 3, slash, 5
  • en reduceret, uægte brøk, som eksempelvis 7, slash, 4
  • et blandet tal, som eksempelvis 1, space, 3, slash, 4
  • et eksakt decimaltal, som eksempelvis 0, comma, 75
  • et multiplum af pi, som f.eks. 12, space, start text, p, i, end text eller 2, slash, 3, space, start text, p, i, end text

Vil du prøve flere opgaver i samme stil? Tjek denne øvelse.

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