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Vermenigvuldiging is 'n wiskundige bewerking wat voorgestel kan word as 'n som van identiese terme.
Algemene beginsel van vermenigvuldiging
Byvoorbeeld, die a ⋅ b (gelees as "a maal b") beteken dat ons die terme som a, waarvan die getal gelyk is aan b. Die resultaat van 'n vermenigvuldiging word 'n produk genoem.
voorbeelde:
- 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12
(ses keer twee)
- 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20
(vier keer vyf)
- 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
(agt keer drie)
Soos ons weet, van die permutasie van die plekke van die faktore, verander die produk nie. Vir die voorbeelde hierbo blyk dit:
- 6 ⋅ 2 = 6 + 6 = 12
(twee keer ses)
- 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20
(vyf maal vier)
- 8 ⋅ 3 = 8 + 8 + 8 = 24
(drie keer agt)
Praktiese voordele
Danksy vermenigvuldiging kan jy die telling van die totale aantal items van dieselfde tipe aansienlik verminder, ens. Byvoorbeeld, as ons 7 pakkies het wat elk 5 penne bevat, dan word die totale aantal penne gevind deur hierdie te vermenigvuldig twee nommers:
5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
(vyf penne sewe keer)
Vermenigvuldig met 0
Die resultaat is altyd 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
Die produk is gelyk aan 'n ander vermenigvuldiger anders as een.
- 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 die eerste faktor by homself.
- 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
Ons vermenigvuldig die eerste faktor met 2 en tel dit dan by die 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
Ons voeg dieselfde hoeveelheid by die verdubbelde eerste 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
Vermenigvuldig met 5
As die ander vermenigvuldiger 'n ewe getal is, sal die resultaat in nul eindig, indien onewe, in die 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
Ons vermenigvuldig die eerste faktor met 5 en tel dan die resultaat daarby.
- 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
Daar is geen vereenvoudigde algoritme om met 7 te vermenigvuldig nie, daarom gebruik ons metodes wat van toepassing is op ander faktore.
- 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
Ons vermenigvuldig die eerste faktor met 4 en tel dan dieselfde hoeveelheid by die 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
Ons vermenigvuldig die eerste faktor met 10 en trek dit dan af van die resultaat wat verkry is.
- 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
Tel nul by die einde van die ander 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