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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

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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