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Korte theoretische samenvatting Bewerkingen
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Theoretische samenvatting Bewerkingen met rekenvoorbeelden
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Bewerkingen Gecijferdheid§1.2 Eigenschapsrekenen (blz. 9)
Handig rekenen: je vervangt de moeilijke rekenopgave door een opgave die makkelijker
tot het antwoord leidt.
1a. getalrelaties: eigenschappen van getallen, eigenlijk alles wat je van dat getal weet.
1b. de zeven eigenschappen van getallen en bewerkingen
Eigenschap Bewerking Formule vorm Rekenvoorbeeld
1 termen veranderen/ optellen a+b = (a+p) + (b-p) 8+6= (8+2) + (6-2)
transformeren, vb/ tribunecontext
geheel veranderd
aftrekken a-b= (a+p) – (b+p) 13-8= (13+2) – (8+2)
vb/ leeftijdencontext
weegschaalcontext
2 compenseren, optellen a+b= a+(b+p)-p 7+8= 7+(8+2)-2
geheel hetzelfde
aftrekken a-b= a-(b+p)+p 13-8= 13-(8+2)+2
3 wisselen/ optellen a+b=b+a 8+5=5+8
commutatieve
eigenschap
vermenigvuldigen axb=bxa 5x8=8x5
4 schakelen/ optellen a+(b+c)=(a+b)+c 5+(8+12)=(5+8)+12
associatieve
eigenschap
vermenigvuldigen ax(bxc)=(axb)xc 5x(8x12)=(5x8)x12
5 verdelen vermenigvuldigen en ax(b+c)=axb+axc 5x(10+2)=5x10+5x2
distributieve optellen
eigenschap
vermenigvuldigen en ax(b-c)=axb-axc 5x(20-3)=5x20-5x3
aftrekken
delen en optellen (a+b):c=a:c+b:c (12+8):4=12:4+8:4
delen en aftrekken (a-b):c=a:c-b:c (15-9):3=15:3-9:3
samen nemen/ vermenigvuldigen en (axb)+(cxb)= (a+c)xb (12x7)+(8x7)=(12+8)x7
distributieve optellen
eigenschap
vermenigvuldigen en (axb)-(cxb)=(a-c)xb (12x7)-(8x7)=(12-8)x7
aftrekken
delen en optellen (a:b)+(c:b)= (a+c):b (15:3)+(6:3)=(15+6):3
delen en aftrekken (a:b)-(c:b)= (a-c):b (15:3)-(6:3)=(15-6):3
6 groter en kleiner vermenigvuldigen axb=(a:p)x(bxp) 6x15=(6:2)x(15x2)
7 groter of kleiner delen a:b=(pxa):(pxb) 12:5=(2x12):(2x5)
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