Multiplikation er en matematisk operation, der kan repræsenteres som en sum af identiske led.

Indhold

Generelt princip for multiplikation

For eksempel a ⋅ b (læses som "a gange b") betyder, at vi summerer vilkårene a, hvis antal er lig med b. Resultatet af en multiplikation kaldes et produkt.

Sådan lærer du hurtigt og nemt multiplikationstabellen

eksempler:

  • 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

    (seks gange to)

  • 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

    (fire gange fem)

  • 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24

    (otte gange tre)

Som vi ved, fra permutationen af ​​faktorernes steder, ændres produktet ikke. For eksemplerne ovenfor viser det sig:

  • 6 ⋅ 2 = 6 + 6 = 12

    (to gange seks)

  • 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

    (fem gange fire)

  • 8 ⋅ 3 = 8 + 8 + 8 = 24

    (tre gange otte)

Praktiske fordele

Takket være multiplikation kan du markant reducere antallet af det samlede antal genstande af samme type osv. Hvis vi for eksempel har 7 pakker, som hver indeholder 5 kuglepenne, så findes det samlede antal kuglepenne ved at gange disse to tal:

5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35

(fem penne syv gange)

Multiplicer med 0

Resultatet er altid nul.

  • 0 ⋅ 0 = 0
  • 1 ⋅ 0 = 0 ⋅ 1 = 0
  • 2 ⋅ 0 = 0 ⋅ 2 = 0 + 0 = 0
  • 3 ⋅ 0 = 0 ⋅ 3 = 0 + 0 + 0 = 0
  • 4 ⋅ 0 = 0 ⋅ 4 = 0 + 0 + 0 + 0 = 0
  • 5 ⋅ 0 = 0 ⋅ 5 = 0 + 0 + 0 + 0 + 0 = 0
  • 6 ⋅ 0 = 0 ⋅ 6 = 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 7 ⋅ 0 = 0 ⋅ 7 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 8 ⋅ 0 = 0 ⋅ 8 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 9 ⋅ 0 = 0 ⋅ 9 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 10 ⋅ 0 = 0 ⋅ 10 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0

Multiplicer med 1

Produktet er lig med en anden multiplikator end én.

  • 1 ⋅ 1 = 1
  • 2 ⋅ 1 = 2 ⋅ 1 = 2
  • 3 ⋅ 1 = 3 ⋅ 1 = 3
  • 4 ⋅ 1 = 4 ⋅ 1 = 4
  • 5 ⋅ 1 = 5 ⋅ 1 = 5
  • 6 ⋅ 1 = 6 ⋅ 1 = 6
  • 7 ⋅ 1 = 7 ⋅ 1 = 7
  • 8 ⋅ 1 = 8 ⋅ 1 = 8
  • 9 ⋅ 1 = 9 ⋅ 1 = 9
  • 10 ⋅ 1 = 10 ⋅ 1 = 10

Multiplicer med 2

Tilføj den første faktor til sig selv.

  • 1 ⋅ 2 = 1 + 1 = 2
  • 2 ⋅ 2 = 2 + 2 = 4
  • 3 ⋅ 2 = 3 + 3 = 6
  • 4 ⋅ 2 = 4 + 4 = 8
  • 5 ⋅ 2 = 5 + 5 = 10
  • 6 ⋅ 2 = 6 + 6 = 12
  • 7 ⋅ 2 = 7 + 7 = 14
  • 8 ⋅ 2 = 8 + 8 = 16
  • 9 ⋅ 2 = 9 + 9 = 18
  • 10 ⋅ 2 = 10 + 10 = 20

Multiplicer med 3

Vi multiplicerer den første faktor med 2 og lægger den derefter til resultatet.

  • 1 ⋅ 3 = (1 ⋅ 2) + 1 = 2 + 1 = 3
  • 2 ⋅ 3 = (2 ⋅ 2) + 2 = 4 + 2 = 6
  • 3 ⋅ 3 = (3 ⋅ 2) + 3 = 6 + 3 = 9
  • 4 ⋅ 3 = (4 ⋅ 2) + 4 = 8 + 4 = 12
  • 5 ⋅ 3 = (5 ⋅ 2) + 5 = 10 + 5 = 15
  • 6 ⋅ 3 = (6 ⋅ 2) + 6 = 12 + 6 = 18
  • 7 ⋅ 3 = (7 ⋅ 2) + 7 = 14 + 7 = 21
  • 8 ⋅ 3 = (8 ⋅ 2) + 8 = 16 + 8 = 24
  • 9 ⋅ 3 = (9 ⋅ 2) + 9 = 18 + 9 = 27
  • 10 ⋅ 3 = (10 ⋅ 2) + 10 = 20 + 10 = 30

Multiplicer med 4

Vi tilføjer den samme mængde til den fordoblede første faktor.

  • 1 ⋅ 4 = (1 ⋅ 2) + (1 ⋅ 2) = 2 + 2 = 4
  • 2 ⋅ 4 = (2 ⋅ 2) + (2 ⋅ 2) = 4 + 4 = 8
  • 3 ⋅ 4 = (3 ⋅ 2) + (3 ⋅ 2) = 6 + 6 = 12
  • 4 ⋅ 4 = (4 ⋅ 2) + (4 ⋅ 2) = 8 + 8 = 16
  • 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 10 + 10 = 20
  • 6 ⋅ 4 = (6 ⋅ 2) + (6 ⋅ 2) = 12 + 12 = 24
  • 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 14 + 14 = 28
  • 8 ⋅ 4 = (8 ⋅ 2) + (8 ⋅ 2) = 16 + 16 = 32
  • 9 ⋅ 4 = (9 ⋅ 2) + (9 ⋅ 2) = 18 + 18 = 36
  • 10 ⋅ 4 = (10 ⋅ 2) + (10 ⋅ 2) = 20 + 20 = 40

Multiplicer med 5

Hvis den anden multiplikator er et lige tal, ender resultatet på nul, hvis ulige, i tallet 5.

  • 1 ⋅ 5 = 5 ⋅ 1 = 5
  • 2 ⋅ 5 = 5 ⋅ 2 = 5 + 5 = 10
  • 3 ⋅ 5 = 5 ⋅ 3 = (5 ⋅ 2) + 5 = 15
  • 4 ⋅ 5 = 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 20
  • 5 ⋅ 5 = 5 + 5 + 5 + 5 + 5 = 25
  • 6 ⋅ 5 = 5 ⋅ 6 = (5 ⋅ 5) + 5 = 30
  • 7 ⋅ 5 = 5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
  • 8 ⋅ 5 = 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
  • 9 ⋅ 5 = 5 ⋅ 9 = (5 ⋅ 10) – 5 = 45
  • 10 ⋅ 5 = 5 ⋅ 10 = 50

Multiplicer med 6

Vi multiplicerer den første faktor med 5, og lægger derefter resultatet til den.

  • 1 ⋅ 6 = (1 ⋅ 5) + 1 = 5 + 1 = 6
  • 2 ⋅ 6 = (2 ⋅ 5) + 2 = 10 + 2 = 12
  • 3 ⋅ 6 = (3 ⋅ 5) + 3 = 15 + 3 = 18
  • 4 ⋅ 6 = (4 ⋅ 5) + 4 = 20 + 4 = 24
  • 5 ⋅ 6 = (5 ⋅ 5) + 5 = 25 + 5 = 30
  • 6 ⋅ 6 = (6 ⋅ 5) + 6 = 30 + 6 = 36
  • 7 ⋅ 6 = (7 ⋅ 5) + 7 = 35 + 7 = 42
  • 8 ⋅ 6 = (8 ⋅ 5) + 8 = 40 + 8 = 48
  • 9 ⋅ 6 = (9 ⋅ 5) + 9 = 45 + 9 = 54
  • 10 ⋅ 6 = (10 ⋅ 5) + 10 = 50 + 10 = 60

Multiplicer med 7

Der er ingen forenklet algoritme til at gange med 7, så vi bruger metoder, der kan anvendes til andre faktorer.

  • 1 ⋅ 7 = 7 ⋅ 1 = 7
  • 2 ⋅ 7 = 7 ⋅ 2 = 7 + 7 = 14
  • 3 ⋅ 7 = 7 ⋅ 3 = (7 ⋅ 2) + 7 = 21
  • 4 ⋅ 7 = 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 28
  • 5 ⋅ 7 = 7 ⋅ 5 = 7 + 7 + 7 + 7 + 7 = 35
  • 6 ⋅ 7 = 7 ⋅ 6 = (7 ⋅ 5) + 7 = 42
  • 7 ⋅ 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
  • 8 ⋅ 7 = 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
  • 9 ⋅ 7 = 7 ⋅ 9 = (7 ⋅ 10) – 7 = 63
  • 10 ⋅ 7 = 70

Multiplicer med 8

Vi multiplicerer den første faktor med 4 og lægger derefter samme mængde til resultatet.

  • 1 ⋅ 8 = (1 ⋅ 4) + (1 ⋅ 4) = 8
  • 2 ⋅ 8 = (2 ⋅ 4) + (2 ⋅ 4) = 16
  • 3 ⋅ 8 = (3 ⋅ 4) + (3 ⋅ 4) = 24
  • 4 ⋅ 8 = (4 ⋅ 4) + (4 ⋅ 4) = 32
  • 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
  • 6 ⋅ 8 = (6 ⋅ 4) + (6 ⋅ 4) = 48
  • 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
  • 8 ⋅ 8 = (8 ⋅ 4) + (8 ⋅ 4) = 64
  • 9 ⋅ 8 = (9 ⋅ 4) + (9 ⋅ 4) = 72
  • 10 ⋅ 8 = (10 ⋅ 4) + (10 ⋅ 4) = 80

Multiplicer med 9

Vi multiplicerer den første faktor med 10 og trækker den fra det opnåede resultat.

  • 1 ⋅ 9 = (1 ⋅ 10) – 1 = 10 – 1 = 9
  • 2 ⋅ 9 = (2 ⋅ 10) – 2 = 20 – 2 = 18
  • 3 ⋅ 9 = (3 ⋅ 10) – 3 = 30 – 3 = 27
  • 4 ⋅ 9 = (4 ⋅ 10) – 4 = 40 – 4 = 36
  • 5 ⋅ 9 = (5 ⋅ 10) – 5 = 50 – 5 = 45
  • 6 ⋅ 9 = (6 ⋅ 10) – 6 = 60 – 6 = 54
  • 7 ⋅ 9 = (7 ⋅ 10) – 7 = 70 – 7 = 63
  • 8 ⋅ 9 = (8 ⋅ 10) – 8 = 80 – 8 = 72
  • 9 ⋅ 9 = (9 ⋅ 10) – 9 = 90 – 9 = 81
  • 10 ⋅ 9 = (10 ⋅ 10) – 10 = 100 – 10 = 90

Multiplicer med 10

Tilføj nul til slutningen af ​​den anden multiplikator.

  • 1 ⋅ 10 = 10 ⋅ 1 = 10
  • 2 ⋅ 10 = 10 ⋅ 2 = 20
  • 3 ⋅ 10 = 10 ⋅ 3 = 30
  • 4 ⋅ 10 = 10 ⋅ 4 = 40
  • 5 ⋅ 10 = 10 ⋅ 5 = 50
  • 6 ⋅ 10 = 10 ⋅ 6 = 60
  • 7 ⋅ 10 = 10 ⋅ 7 = 70
  • 8 ⋅ 10 = 10 ⋅ 8 = 80
  • 9 ⋅ 10 = 10 ⋅ 9 = 90
  • 10 ⋅ 10 = 10 ⋅ 10 = 100

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