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Wiskunde

Gewone breuke

Opvoeders afdeling

Memorandum

  • b)
10 10
1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

Answers is the same

(i) = 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

x = 3 8 size 12{ { { size 8{3} } over { size 8{8} } } } {}

y = 18 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

(ii) = 7 x 8 3 size 12{ { { size 8{8} } over { size 8{3} } } } {}

= 56 3 size 12{ { { size 8{"56"} } over { size 8{3} } } } {}

  1. = 6 1 size 12{ { { size 8{6} } over { size 8{1} } } } {} x 5 4 size 12{ { { size 8{5} } over { size 8{4} } } } {}

= 30 4 size 12{ { { size 8{"30"} } over { size 8{4} } } } {}

m = 7 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(iv) = 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {} x 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {}

n = 2 63 size 12{ { { size 8{2} } over { size 8{"63"} } } } {}

  • b)

(i) x = 3 8 size 12{ { { size 8{3} } over { size 8{8} } } } {} 9 24 size 12{ { { size 8{9} } over { size 8{"24"} } } } {}

= 3 8 size 12{ { { size 8{3} } over { size 8{8} } } } {} x 24 9 size 12{ { { size 8{"24"} } over { size 8{9} } } } {}

x = 1

(ii) k = 15 18 size 12{ { { size 8{"15"} } over { size 8{"18"} } } } {} 45 6 size 12{ { { size 8{"45"} } over { size 8{6} } } } {}

= 15 18 size 12{ { { size 8{"15"} } over { size 8{"18"} } } } {} x 6 45 size 12{ { { size 8{6} } over { size 8{"45"} } } } {}

k = 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {}

(iii) c = 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {}

= 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} x 6 5 size 12{ { { size 8{6} } over { size 8{5} } } } {}

c = 14 15 size 12{ { { size 8{"14"} } over { size 8{"15"} } } } {}

(iv) f = 11 12 size 12{ { { size 8{"11"} } over { size 8{"12"} } } } {} 6 5 size 12{ { { size 8{6} } over { size 8{5} } } } {}

= 11 12 size 12{ { { size 8{"11"} } over { size 8{"12"} } } } {} x 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {}

= 55 72 size 12{ { { size 8{"55"} } over { size 8{"72"} } } } {}

23.3 c)

(i) b = 2 1 4 size 12{2 { { size 8{1} } over { size 8{4} } } } {} 3 2 size 12{ { { size 8{3} } over { size 8{2} } } } {}

= 9 4 size 12{ { { size 8{9} } over { size 8{4} } } } {} x 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

b = 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(ii) e = 3 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {}  2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 19 5 size 12{ { { size 8{"19"} } over { size 8{5} } } } {} x 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

e = 38 25 size 12{ { { size 8{"38"} } over { size 8{"25"} } } } {}

e = 1 13 25 size 12{ { { size 8{"13"} } over { size 8{"25"} } } } {}

  1. g = 3 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {}  1 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {}

= 25 7 size 12{ { { size 8{"25"} } over { size 8{7} } } } {} x 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {}

= 25 9 size 12{ { { size 8{"25"} } over { size 8{9} } } } {}

g = 2 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {}

(iv) r = 15 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}  5 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

= 31 2 size 12{ { { size 8{"31"} } over { size 8{2} } } } {} x 4 21 size 12{ { { size 8{4} } over { size 8{"21"} } } } {}

= 62 21 size 12{ { { size 8{"62"} } over { size 8{"21"} } } } {}

r = 2 20 21 size 12{ { { size 8{"20"} } over { size 8{"21"} } } } {}

Leerders afdeling

Inhoud

Aktiwiteit: deling met breuke [lu 1.7.3, lu 2.1.5]

23. Kom ons kyk nou na DELING MET BREUKE!

23.1 Deling van heelgetalle deur breuke en andersom :

a) Werk saam met ’n maat en kyk goed na die volgende probleme.

Ma bak vyf koeke en wil graag vir jou en jou maats elkeen ’n halwe ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ) stuk gee. Hoeveel maats kan van die koek eet?

  • Op ’n getallelyn lyk dit so:

Dus: 5 ÷ 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} = 1010 kinders kan elkeen 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} koek kry.

Ma bak weer, maar hierdie keer net een reghoekige koek. Sy besluit om die helfte daarvan tussen haar vyf kinders te verdeel. Watter breuk kry elkeen?

  • Kom ons maak ’n skets daarvan!

12345

Kan jy sien dat elke kind een tiende ( 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} ) van die koek sal kry?Dus: 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ÷ 5 = 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

b) Voltooi die tabel:

5 ÷ 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} = ............ 5 × 2 1 size 12{ { { size 8{2} } over { size 8{1} } } } {} = ............
1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ÷ 5 1 size 12{ { { size 8{5} } over { size 8{1} } } } {} = ............ 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} × 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} = ............

Wat merk jy op? ___________________________________________________

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c) Het jy geweet?

Enige deelsom met breuke kan in ’n vermenigvuldigingsom verander word! Ons doen dit deur die deler in sy resiprook te verander. Ons “keer dus die deler om”!

Dus:

÷ 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} =
´ 2 1 size 12{ { { size 8{2} } over { size 8{1} } } } {} = 10

d) Verbind kolom A met die korrekte antwoord in kolom B:

A B
÷ deur 5 × met 4 3 size 12{ { { size 8{4} } over { size 8{3} } } } {}
÷ deur 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} × met 3
÷ deur 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} × met 5
÷ deur 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} × met 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}
÷ deur 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} × met 8 7 size 12{ { { size 8{8} } over { size 8{7} } } } {}

e) Bereken die volgende:

i) x = 3 4 ÷ 2 size 12{x= { { size 8{3} } over { size 8{4} } } div 2} {}

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ii) y = 7 ÷ 3 8 size 12{y=7 div { { size 8{3} } over { size 8{8} } } } {}

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iii) m = 6 ÷ 4 5 size 12{m=6 div { { size 8{4} } over { size 8{5} } } } {}

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iv) n = 2 7 ÷ 9 size 12{n= { { size 8{2} } over { size 8{7} } } div 9} {}

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23.2 Deling van breuke deur breuke:

a) Werk weer saam met ’n maat en bestudeer die volgende:

x = 6 25 ÷ 3 5 size 12{x= { { size 8{6} } over { size 8{"25"} } } div { { size 8{3} } over { size 8{5} } } } {}

Ek weet ek moet die volgende stappe volg:

1. Verander die ÷ in ×

2. Draai die breuk na die ÷ (deler) om – kry dus resiprook

3. Vermenigvuldig soos gewoonlik: teller × teller noemer × noemer size 12{ { { ital "teller" times ital "teller"} over { ital "noemer" times ital "noemer"} } } {}

Dus: 6 25 ÷ 3 5 = 6 25 × 5 3 size 12{ { { size 8{6} } over { size 8{"25"} } } div { { size 8{3} } over { size 8{5} } } = { { size 8{6} } over { size 8{"25"} } } times { { size 8{5} } over { size 8{3} } } } {}

Ek kanselleer waar ek kan:
2 6
5 25
×
5 1
3 1

Die antwoord is dus 2 × 1 5 × 1 = 2 5 size 12{ { { size 8{2 times 1} } over { size 8{5 times 1} } } = { { size 8{2} } over { size 8{5} } } } {}

b) Probeer die volgende op jou eie:

i) x = 3 8 ÷ 9 24 size 12{x= { { size 8{3} } over { size 8{8} } } div { { size 8{9} } over { size 8{"24"} } } } {}

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ii) k = 15 18 ÷ 45 6 size 12{k= { { size 8{"15"} } over { size 8{"18"} } } div { { size 8{"45"} } over { size 8{6} } } } {}

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iii) c = 7 9 ÷ 5 6 size 12{c= { { size 8{7} } over { size 8{9} } } div { { size 8{5} } over { size 8{6} } } } {}

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iv) f = 11 12 ÷ 6 5 size 12{f= { { size 8{"11"} } over { size 8{"12"} } } div { { size 8{6} } over { size 8{5} } } } {}

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23.3 Deling met gemengde getalle:

a) Kan jy die volgende probleem vir ’n maat verduidelik?

’n Gesin eet 1 en ’n halwe ( 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} ) pizza. As elkeen net een kwart ( 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} ) van die pizza eet, uit hoeveel lede bestaan die gesin?

  • Ek moet 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ÷ 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} bereken.
  • Dis makliker as ek dit teken:

It’s easier if I draw it:

  • Die antwoord is dus 6.
  • Wiskundig skryf ek dit so:

y = 1 1 2 ÷ 1 4 3 2 ÷ 1 4 3 2 × 4 1 12 2 6 alignl { stack { size 12{y=1 { { size 8{1} } over { size 8{2} } } div { { size 8{1} } over { size 8{4} } } } {} #= { { size 8{3} } over { size 8{2} } } div { { size 8{1} } over { size 8{4} } } {} # = { { size 8{3} } over { size 8{2} } } times { { size 8{4} } over { size 8{1} } } {} #= { { size 8{"12"} } over { size 8{2} } } {} # =6 {}} } {}

  • Ek verkies om ’n getallelyn te gebruik:

b) Het jy geweet?

Ons verander gemengde getalle eers in onegte breuke voordat ons die antwoord bereken.

c) Probeer op jou eie:

i) b = 2 1 4 ÷ 3 2 size 12{b=2 { { size 8{1} } over { size 8{4} } } div { { size 8{3} } over { size 8{2} } } } {}

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ii) e = 3 4 5 ÷ 2 1 2 size 12{e=3 { { size 8{4} } over { size 8{5} } } div 2 { { size 8{1} } over { size 8{2} } } } {}

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iii) g = 3 4 7 ÷ 1 2 7 size 12{g=3 { { size 8{4} } over { size 8{7} } } div 1 { { size 8{2} } over { size 8{7} } } } {}

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iv) r = 15 1 2 ÷ 5 1 4 size 12{r="15" { { size 8{1} } over { size 8{2} } } div 5 { { size 8{1} } over { size 8{4} } } } {}

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Assessering

Leeruitkomste 1: 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.

Assesseringstandaard 1.7: Dit is duidelik wanneer die leerder skat en bereken deur geskikte bewerkings vir probleme wat die volgende behels, kies en gebruik:

1.7.3: optelling, aftrekking en vermenigvuldiging van gewone breuke.

Leeruitkomste 2: Die leerder is in staat om patrone en verwantskappe te herken, te beskryf en voor te stel en probleme op te los deur algebraïese taal en vaardighede te gebruik.

Assesseringstandaard 2.1: Dit is duidelik wanneer die leerder numeriese en meetkundige patrone ondersoek en uitbrei op soek na ‘n verwantskap of reëls, insluitend patrone;

2.1.5: voorgestel in tabelle.

Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
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 7. OpenStax CNX. Oct 21, 2009 Download for free at http://cnx.org/content/col11076/1.2
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