Hoe u snel en gemakkelijk de tafel van vermenigvuldiging leert

Vermenigvuldiging is een wiskundige bewerking die kan worden weergegeven als een som van identieke termen.

Algemeen principe van vermenigvuldiging

Bijvoorbeeld, de een b (lees als "a maal b") betekent dat we de termen optellen a, waarvan het aantal gelijk is aan b. Het resultaat van een vermenigvuldiging wordt een product genoemd.

voorbeelden:

• 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

  (zes keer twee)

• 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

  (vier keer vijf)

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

  (acht keer drie)

Zoals we weten, verandert het product niet door de permutatie van de plaatsen van de factoren. Voor de bovenstaande voorbeelden blijkt:

• 6 ⋅ 2 = 6 + 6 = 12

  (twee keer zes)

• 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

  (vijf keer vier)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (drie keer acht)

Praktische voordelen

Dankzij vermenigvuldiging kunt u de telling van het totale aantal items van hetzelfde type aanzienlijk verminderen, enz. Als we bijvoorbeeld 7 pakketten hebben, die elk 5 pennen bevatten, dan wordt het totale aantal pennen gevonden door deze te vermenigvuldigen twee cijfers:

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

(vijf pennen zeven keer)

Vermenigvuldig met 0

Het resultaat is altijd 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

Vermenigvuldig met 1

Het product is gelijk aan een andere vermenigvuldiger dan één.

• 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

Vermenigvuldig met 2

Voeg de eerste factor toe aan zichzelf.

• 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

Vermenigvuldig met 3

We vermenigvuldigen de eerste factor met 2 en voegen deze toe aan het resultaat.

• 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

Vermenigvuldig met 4

We voegen hetzelfde bedrag toe aan de verdubbelde eerste factor.

• 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

Vermenigvuldig met 5

Als de andere vermenigvuldiger een even getal is, eindigt het resultaat op nul, als het oneven is, op het getal 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

Vermenigvuldig met 6

We vermenigvuldigen de eerste factor met 5 en voegen het resultaat eraan toe.

• 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

Vermenigvuldig met 7

Er is geen vereenvoudigd algoritme om met 7 te vermenigvuldigen, dus gebruiken we methoden die van toepassing zijn op andere factoren.

• 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

Vermenigvuldig met 8

We vermenigvuldigen de eerste factor met 4 en voegen vervolgens hetzelfde bedrag toe aan het resultaat.

• 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

Vermenigvuldig met 9

We vermenigvuldigen de eerste factor met 10 en trekken deze vervolgens af van het verkregen resultaat.

• 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

Vermenigvuldig met 10

Voeg nul toe aan het einde van de andere vermenigvuldiger.

• 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