Hvordan raskt og enkelt lære multiplikasjonstabellen

Multiplikasjon er en matematisk operasjon som kan representeres som en sum av identiske ledd.

Generelt prinsipp for multiplikasjon

For eksempel a ⋅ b (lest som "a ganger b") betyr at vi summerer begrepene a, hvor antallet er lik b. Resultatet av en multiplikasjon kalles et produkt.

eksempler:

• 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

  (seks ganger to)

• 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

  (fire ganger fem)

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

  (åtte ganger tre)

Som vi vet, fra permutasjonen av stedene til faktorene, endres ikke produktet. For eksemplene ovenfor viser det seg:

• 6 ⋅ 2 = 6 + 6 = 12

  (to ganger seks)

• 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

  (fem ganger fire)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (tre ganger åtte)

Praktiske fordeler

Takket være multiplikasjon kan du redusere antallet totalt antall varer av samme type betraktelig osv. Hvis vi for eksempel har 7 pakker som hver inneholder 5 penner, så finner man det totale antallet penner ved å multiplisere disse to tall:

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

(fem penner syv ganger)

Multipliser med 0

Resultatet er alltid null.

• 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

Multipliser med 1

Produktet er lik en annen multiplikator enn 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

Multipliser med 2

Legg den første faktoren til seg 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

Multipliser med 3

Vi multipliserer den første faktoren med 2, og legger den så 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

Multipliser med 4

Vi legger til samme mengde til den doblede første faktoren.

• 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

Multipliser med 5

Hvis den andre multiplikatoren er et partall, vil resultatet ende på null, hvis oddetall, 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

Multipliser med 6

Vi multipliserer den første faktoren med 5, og legger deretter 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

Multipliser med 7

Det finnes ingen forenklet algoritme for å multiplisere med 7, så vi bruker metoder som gjelder 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

Multipliser med 8

Vi multipliserer den første faktoren med 4, og legger deretter samme mengde 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

Multipliser med 9

Vi multipliserer den første faktoren med 10, og trekker den fra det oppnådde resultatet.

• 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

Multipliser med 10

Legg til null på slutten av den andre multiplikatoren.

• 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