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3. Kan jy die volgende doen?

3.1 8 - 4 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {}

3.2 3 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} - 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

  • Belangrik : Voordat jy breuke kan optel of van mekaar aftrek, moet die noemers dieselfde wees.
  • bv. 2 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {} - 1 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}
  • 2 – 1 = 1 en
  • 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {} - 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {} ( 4 – 6 --- dit kan nie. Gaan vat een hele : 1 = 7 7 size 12{ { { size 8{7} } over { size 8{7} } } } {} )
  • ( 4 + 7 = 11 --- ja, 11 – 6 = 5)Antwoord: 5 7 size 12{ { { size 8{5} } over { size 8{7} } } } {}
  • Jy kan ook alle gemengde getalle herlei na onegte breuke en dan die noemers dieselfde maak.
  • bv. 18 7 13 7 = 5 7 size 12{ { { size 8{"18"} } over { size 8{7} } } - { { size 8{"13"} } over { size 8{7} } } = { { size 8{5} } over { size 8{7} } } } {} (18 – 13 = 5: Die noemers is dieselfde. Trek die tellers van mekaar af.)

4. Doen nou die volgende:

4.1 4 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} + 4 16 42 size 12{ { { size 8{"16"} } over { size 8{"42"} } } } {}

4.2 36 - 15 6 11 size 12{ { { size 8{6} } over { size 8{"11"} } } } {}

4.3 1 8 + 0, 625 3 8 size 12{ { { size 8{1} } over { size 8{8} } } +0,"625" - { { size 8{3} } over { size 8{8} } } } {}

4.4 4 5 10 + 7 1 2 + 6 3 4 size 12{4 { { size 8{5} } over { size 8{"10"} } } +7 { { size 8{1} } over { size 8{2} } } +6 { { size 8{3} } over { size 8{4} } } } {}

4.5 7 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} - 4 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

4.6 7 a - a 4 size 12{ { { size 8{a} } over { size 8{4} } } } {} a / 4

4.7 9 a + 6 ab 3 b size 12{ { { size 8{9} } over { size 8{a} } } + left ( { { size 8{6} } over { size 8{ ital "ab"} } } - { { size 8{3} } over { size 8{b} } } right )} {}

4.8 - 6 + 2 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

4.9 5 - (4 4 9 size 12{ { { size 8{4} } over { size 8{9} } } } {} + 2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} )

4.10 3 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} a - 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} a

AKTIWITEIT 5

Vermenigvuldiging en deling van rasionale getalle (breuke)

LU 1.2.6 LU 1.6.2
  • Jy het dit in graad 7 gedoen – kom ons verfris net die geheue.

1. Vermenigvuldiging:

  • Belangrik : Alle gemengde getalle moet as breuke geskryf word.Dan kan jy oorkruis kanselleer.
  • Probeer nou die volgende:
  • 1 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} × 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} × 4

2. Deling:

  • Die resiprook speel ‘n groot rol by deling van breuke.
  • Maak gebruik van ‘n voorbeeld om die term te verduidelik.

bv. 1 3 ÷ 2 3 size 12{ { { size 8{1} } over { size 8{3} } } div { { size 8{2} } over { size 8{3} } } } {}

  • Albei getalle is breuke
  • Maak ÷ ‘n × - teken en kry resiprook van die deler (breuk ná die ÷-teken).
  • Kanselleer net soos by vermenigvuldiging.

3. Doen nou die volgende:

3.1 8 ÷ 8 11 size 12{ { { size 8{8} } over { size 8{"11"} } } } {}

3.2 18 ÷ 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

3.3 5 6 ÷ 5 2 size 12{ { { size 8{5} } over { size 8{6} } } div { { size 8{5} } over { size 8{2} } } } {}

3.4 -2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ÷ -1 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {}

3.5 6 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} mn ÷ -6 m 3

3.6 4 xy 3 ab ÷ 2x 3a size 12{ { { size 8{ - 4 ital "xy"} } over { size 8{3 ital "ab"} } } div { { size 8{ - 2x} } over { size 8{3a} } } } {} -

Assessering

Leeruitkomstes(LUs)
LU 1
Getalle, Verwerkings en Verwantskappe Die leerder is in staat om getalle en die verwantskappe daarvan te herken, te beskryf en voor te stel, en om tydens probleemoplossing bevoeg en met selfvertroue te tel, te skat, te bereken en te kontroleer.
Assesseringstandaarde(ASe)
Dit word bewys as die leerder:
1.2 die volgende getalle kan herken, klassifiseer en voorstel om hulle te beskryf en te vergelyk:
1.2.2 desimale, breuke en persentasies;
1.2.5 optel- en vermenigvuldiginginverses;
1.2.6 veelvoude en faktore;
1.2.7 irrasionele getalle in die konteks van meting (bv. vierkants- en derdemagwortels van nie perfekte vierkante en derdemagte?);
1.3 ekwivalente vorms van die bogenoemde rasionale getalle herken en kan gebruik;
1.6 skat en bereken deur stappe te kies wat geskik is om probleme op te los wat die volgende behels:
1.6.1 afronding;
1.6.2 veelvoudige stappe met rasionele getalle (insluitend deling met breuke en desimale);
1.7 ‘n reeks tegnieke gebruik om berekeninge te doen, insluitend:
1.7.1 die gebruik van kommutatiewe, assosiatiewe en distributiewe eienskappe met rasionale nommers;
1.7.2 die gebruik van ‘n sakrekenaar;
1.9 die volgende herken en gebruik:
1.9.1 algoritmes vir die vind van ekwivalente breuke;
1.9.2 die kommutatiewe, assosiatiewe en distributiewe eienskappe met rasionale getalle (die ver­wagting is dat leerders hierdie eienskappe sal kan gebruik sonder om noodwendig die name van die eienskappe te ken).

Memorandum

AKTIWITEIT 1

1. Natuurlike getalle

Telgetalle

Heelgetalle

Rieële getalle

2. a b size 12{ { {a} over {b} } } {} ; b ≠ 0

2 size 12{ sqrt {2} } {}
  • Q
  • Q 1

4.

  • 1 + 4 size 12{ sqrt {4} } {} ; -4
  • 2 3 size 12{ { { - 2} over {3} } } {} ; 12 1 5 size 12{ { {1} over {5} } } {}
  • 9 + 4 size 12{ sqrt {9+4} } {} ; 1 + 2 2 size 12{ { {1+ sqrt {2} } over { sqrt {2} } } } {}

6. Gelyk in waarde

7. 4 14 size 12{ { {4} over {"14"} } } {} = 6 24 size 12{ { {6} over {"24"} } } {} ens.

  • Egte breuk
  • Onegte breuk
  • Gemengde getal
  • Desimale getal
  • Repeterende desimale getal
  • Persentasie

AKTIWITEIT 2

1. 2,15

  • 0,625
  • 3,25
  • 5,75
  • 2,875
  • 6, 000 7 size 12{ { {6,"000"} over {7} } } {} = 0,8571 . . . ≈ 0,86
  • 7, 000 9 size 12{ { {7,"000"} over {9} } } {} = 0,777 . . . =
    of 0,8
  • 6 8 1000 size 12{ { {8} over {"1000"} } } {} = 6 1 125 size 12{ { {1} over {"125"} } } {}
  • 4 65 100 size 12{ { {"65"} over {"100"} } } {} = 4 13 20 size 12{ { {"13"} over {"20"} } } {}
  • 375 1000 size 12{ { {"375"} over {"1000"} } } {} = 3 8 size 12{ { {3} over {8} } } {}
  • 7 75 1000 size 12{ { {"75"} over {"1000"} } } {} = 7 3 40 size 12{ { {3} over {"40"} } } {}
  • 13 65 100 size 12{ { {"65"} over {"100"} } } {} = 13 13 20 size 12{ { {"13"} over {"20"} } } {}
  • 125 1000 size 12{ { {"125"} over {"1000"} } } {} = 1 8 size 12{ { {1} over {8} } } {}

7.1 3 9 size 12{ { {3} over {9} } } {} = 1 3 size 12{ { {1} over {3} } } {}

7.2 45 99 size 12{ { {"45"} over {"99"} } } {} = 5 11 size 12{ { {5} over {"11"} } } {}

7.3 23 990 size 12{ { {"23"} over {"990"} } } {}

7.4 3 900 size 12{ { {3} over {"900"} } } {} = 1 300 size 12{ { {1} over {"300"} } } {}

9. 0, 4 size 12{ {4} cSup { size 8{ cdot } } } {} 5 size 12{ {5} cSup { size 8{ cdot } } } {} = x

x = 0,4545 . . . 

100 x = 45,4545 . . .

  • –  99 x = 45

x = 45 99 size 12{ { {"45"} over {"99"} } } {} = 5 11 size 12{ { {5} over {"11"} } } {}

AKTIWITEIT 3

2.1 17 x5 20 x5 size 12{ { {"17"x5} over {"20"x5} } } {} = 85%

2.2 19 40 size 12{ { {"19"} over {"40"} } } {} × 100 1 size 12{ { {"100"%} over {1} } } {} = 47,5%

2.3 38 x2 50 x2 size 12{ { {"38"x2} over {"50"x2} } } {} = 76%

2.4 45 60 size 12{ { {"45"} over {"60"} } } {} × 100 1 size 12{ { {"100"%} over {1} } } {} = 75%

3.1 55 100 size 12{ { {"55"} over {"100"} } } {} = 11 20 size 12{ { {"11"} over {"20"} } } {}

3.2 15 , 5 100 size 12{ { {"15",5} over {"100"} } } {} = 0,155 = 155 1000 size 12{ { {"155"} over {"1000"} } } {} = 31 200 size 12{ { {"31"} over {"200"} } } {}

3.3 33 200 size 12{ { {"33"} over {"200"} } } {}

3.4 2 0 30 { 0 size 12{ { {2 { {0}}} over {"30 {"{0}}} } } {} = 2 30 size 12{ { {2} over {"30"} } } {}

4.a) 33 800 size 12{ { {"33"} over {"800"} } } {} × 25500 1 size 12{ { {"25500"} over {1} } } {} size 12{ approx } {} 1 052

b) 3 5 size 12{ { {3} over {5} } } {} × 25500 1 size 12{ { {"25500"} over {1} } } {} = 15 300

c) 85 1000 size 12{ { {"85"} over {"1000"} } } {} × 25500 1 size 12{ { {"25500"} over {1} } } {} = 2 167,5 size 12{ approx } {} 2 168

  • (14,5) 15300 1052 size 12{ { {"15300"} over {"1052"} } } {} = 7650 526 size 12{ { {"7650"} over {"526"} } } {} = 3825 263 size 12{ { {"3825"} over {"263"} } } {}
  • 25 500 – 18 520 = 6 980

4.4

4.5 3 5 size 12{ { {3} over {5} } } {} x 2 1 size 12{ { {2} over {1} } } {} = 6 5 size 12{ { {6} over {5} } } {} = 1 1 5 size 12{1 { {1} over {5} } } {}

AKTIWITEIT 5

1. 5 1 4 size 12{ { {5} over { {} rSub { size 8{1} } { {4}}} } } {} × 5 2 size 12{ { {5} over {2} } } {} x 4 1 1 size 12{ { { { {4}} rSup { size 8{1} } } over {1} } } {} = 25 2 size 12{ { {"25"} over {2} } } {} = 12 1 2 size 12{"12" { {1} over {2} } } {}

3.1 8 1 size 12{ { {8} over {1} } } {} ÷ 8 11 size 12{ { {8} over {"11"} } } {} = 8 1 1 size 12{ { { { {8}} rSup { size 8{1} } } over {1} } } {} × 11 8 1 size 12{ { {"11"} over { { {8}} rSub { size 8{1} } } } } {} = 11

3.2 18 1 size 12{ { {"18"} over {1} } } {} × 8 7 size 12{ { {8} over {7} } } {} = 144 7 size 12{ { {"144"} over {7} } } {} = 20 4 7 size 12{"20" { {4} over {7} } } {}

3.3 5 1 6 3 size 12{ { { { {5}} rSup { size 8{1} } } over { { {6}} rSub { size 8{3} } } } } {} × 2 1 5 1 size 12{ { { { {2}} rSup { size 8{1} } } over { { {5}} rSub { size 8{1} } } } } {} = 1 3 size 12{ { {1} over {3} } } {}

3.4 8 1 3 1 size 12{ { { - { {8}} rSup { size 8{1} } } over { { {3}}"" lSub { size 8{1} } } } } {} × 9 3 1 6 2 size 12{ { { - { {9}} rSup { size 8{3} } } over { { {1}} { {6}} rSub { size 8{2} } } } } {} = 3 2 size 12{ { {3} over {2} } } {} = 1 1 2 size 12{1 { {1} over {2} } } {}

3.5 2 7 9 mn 4 size 12{ { { { {2}} { {7}} rSup { size 8{9} } ital "mn"} over {4} } } {} × 1 6 2 m 3 size 12{ { {1} over { - { {6}}"" lSub { size 8{2} } m rSup { size 8{3} } } } } {} = 9n 8m 2 size 12{ { { - 9n} over {8m rSup { size 8{2} } } } } {}

3.6 4 2 xy 3 1 a b size 12{ { { - { {4}} rSup { size 8{2} } ital "xy"} over { { {3}}"" lSub { size 8{1} } { {a}}b} } } {} × 3 a 2 x size 12{ { { { {3}} { {a}}} over { - { {2}} { {x}}} } } {} = 2y b size 12{ { {2y} over {b} } } {}

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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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