Summary
Summary Gr 8 Wiskunde Kwartaal 1 en 2
Telgetalle, Heelgetalle, Eksponente, Numeriese en Meetkundige Patrone, Funksies en verwantskappe, Algebraise Uitdrukkings, Gewone Breuke, Desimale Breuke
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TelgetalleKommutatief
a+b=b+a axb=bxa
Assosiatief
Wanneer meer as 2 getalle opgetel of gemaal word, mag enige getalle saam gegroepeer
word.
4+2+3
=2+3+4 Kommutatief
= 2 + (3 + 4) Assosiatief
=2+7
=9
Distributief
n Maal oor n hakkie wat plus of minus
2 x (3 + 5) 2 x (5 – 2)
=(2 x 3) + (2 x 5) = (2 x 5) – (2 x 2)
= 6 + 10 = 10 – 4
= 16 =6
Volgorde van bewerking: Inverse Bewerkings:
Hakkies + en – is mekaar se inverse
Ander (Eksponente en wortels) x en ÷ is mekaar se inverse
Deling
Vermenigvuldiging
• Natuurlike getalle (N): 1; 2; 3; 4; 5; 6; 7; …
Optel
• Telgetalle (N0): 0; 1; 2; 3; 4; 5; 6; …
Aftrek
• Heelgetalle (ℤ) sluit telgetalle in wat beide positief
en negatief is, asook nul.
ℤ = { . . . −3, −2, −1, 0, 1, 2, 3 . . . }
NB!
• 0 word genoem die identiteitselement vir optelling.
• m.a.w enige getal geplus met 0 bly dieslefde
• 1 word genoem die indentiteitselement vir maal
• m.a.w enige getal gemaal met 1 bly dieslefde
, Belangrike Terme:
➢ Faktor: ’n Faktor van ’n getal deel volkome in ‘n getal in, sonder dat daar ’n res is.
o Bv. Die faktore van 20 is F20 = (1, 2, 4, 5, 10, 20)
➢ Veelvoude: Die veelvoude van ‘n getal word verkry deur die getal te
vermenigvuldig met natuurlike getalle.
o Bv. Die eerste 5 veelvoude van 5 is V5 = (5, 10, 15, 20, 25…)
➢ Priemgetal: ’n Priemgetal het slegs 2 faktore nl. 1 en die getal self.
o Bv. 17 is ’n priemgetal omdat dit slegs 2 faktore het, nl. 1 en 17
➢ Saamgestelde Getal: ’n Saamgestelde getal het meer as 2 faktore.
o Bv. 8 is ’n saamgestelde getal F8 = (1, 2, 4, 8)
➢ Universele Getal: 1 is die enigste universele getal (dit is nie ’n priemgetal of 'n
saamgestelde getal nie)
➢ Kwadraat: ‘n Getal wat met homself gemaal word (vierkantsgetal)
o Bv. 16 is ’n kwadraat omdat is 4 x 4 = 16
GGD en KGV
VERHOUDINGS
• Maak seker dat al die eenhede dieselfde is
• Verdeel elke deel van die verhouding met die grootste syfer wat die antwoord in
heelgetalle gaan los
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