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Wiskunde

Graad 8

Heelgetalle, vergelykings en meetkunde

Module 7

Heelgetalle en die ordening daarvan

HEELGETALLE

KLASOPDRAG 1

  • Kom ontdek stap vir stap meer omtrent ... wat is heelgetalle, die ordening daarvan en hoe kan jy dit noteer?

1. Wat beteken dit as jy sê ’n persoon is “negatief” ? Verduidelik dit in ’n wiskundige konteks.

2. Wat dink jy is ’n “negatiewe getal” ? Maak gebruik van ’n illustrasie om jou verduideliking te staaf.

3. Noem twee voorbeelde waar jy op hierdie aarde van “negatiewe” getalle gebruik sal maak.

4. Gee ’n definisie van heelgetalle:

5. Watter simbool stel die versameling heelgetalle voor?

6. Hoe sal jy die volgende op ’n getallelyn voorstel (grafies)?

x ≥ -3 ; x size 12{ in } {} Z .

(hoe sal jy die bogenoemde in woorde uitdruk? - alle heelgetalle groter of gelyk aan -3)

-3-2-1012

[ingekleurde kolletjies - dui aan die getal is ingesluit -- dus gelyk aan ook’n ronde sirkel (nie ingekleurde kolletjie) - dui aan die spesifieke getal is nie ingesluit nie]

Verskillende tipes van notasies:

  • Grafies: d.m.v. die gebruik van ’n getallelyn
  • Versamelingskeurdernotasie: { x / x Z , x ≥ -3 }

(lees dit so: versameling x wat so is dat x Z en x groter of gelyk is aan -3)

  • Intervalnotasie: [-3; ∞) , slegs reële getalle kan so aangedui word.

(Getalle groter as -3 tot oneindig aan die positiewe kant)

6.1 Stel nou die volgende grafies (d.m.v. ’n getallelyn) voor:

Trek jou getallelyn:

6.1.1 x <2 , x Z

6.1.2 x ≥ -2 , x ∈ Z

6.1.3 2 ≤ x <5

KLASOPDRAG 2

  • Kom ontdek stap vir stap meer omtrent ... die optel en aftrek van heelgetalle.

Kan jy nog die volgende uit Module 1 onthou?

(+) × of ÷ (+) →

(+) × of ÷ ( - ) →

( - ) × of ÷ ( - ) →

(Bogenoemde gaan jy nodig kry selfs by optel en aftrek van heelgetalle, want onthou:jy mag nooit twee tekens langs mekaar hê nie, jy moet die twee tekens te alle tye met mekaar vermenigvuldig)

Kan jy nog die eienskappe van 0 (nul) onthou? Kyk bietjie hier ....

b × 0 =

b + 0 =

b - 0 =

b 0 size 12{ { {b} over {0} } } {} =

0 b size 12{ { {0} over {b} } } {} =

1. Kan jy die volgende opdragte m.b.v. ’n getallelyn uitvoer?

1.1 3 + 4

1.2 8 - 12

2. Die temperatuur in Bloemfontein is 4 °C. Dit daal met 8 °C.Wat is die temperatuur, huidiglik?

3. Bereken die volgende:

3.1 -5 - 18

3.2 15 - 8 - 17 + 5

3.3 - 30 + 7 - 4

3.4 - 8 + (-5) + (+7)

4. Kan jy aan ’n manier dink om 3.2; 3.3 en 3.4 te doen?

(’n Kort pad ?)

Hoe sal jy die volgende doen?

  • Trek - 5 af van 3

Besluit watter getal moet eerste kom: 3 - (-5)

Onthou nou die reël - vermenigvuldig die twee tekens wat langs mekaar staan.

( - ) × ( - ) → ( + )

  • Dus: 3 + 5 = 8 (Kyk nou hoe maklik is dit)

5. Bereken nou die volgende:

5.1 - 9 - ( -6)

5.2 -18 + (-13) - (-7)

5.3 20 - (25 + 50)

5.4 10 - (16 - 18)

6. Bereken die verskil tussen -31 en -17

7. Vervang ___ deur ’n ( + ) of ( - ) om die volgende bewerings waar te maak:

7.1 - 6 ___ (-3) = -9

7.2 5 ___ (-5) = 10

HUISWERKOPDRAG 1

1. Bereken elk van die volgende:

1.1 13 - 18 + 4 - 17

1.2 - 9 - ( -8 ) + ( - 16 )

1.3 - ( -16 )² + ( -3)²

1.4 ( - 13 )² - ( - 13 )

1.5 [ a + (- b ) ] + b

1.6 [ a + (- b )] + (- a )

1.7 (- b ) + [(- b ) + a ]

1.8 (- y )² - (- x )² - (- x ²)

2. Doen telkens eers ’n berekening en sê dan of die volgende waar of onwaar is.

2.1 - (- x ) = x

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Source:  OpenStax, Wiskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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