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Wiskunde

Gewone breuke

Opvoeders afdeling

Memorandum

18.1

OPTELLING

1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {} + 3 7 size 12{ { { size 8{3} } over { size 8{7} } } } {}

2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} + 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} + 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

PRODUK

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

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

6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {}

2

1 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}

b) Getallelyn / Teller x Teller

Noemer x Noemer

d)

(i) 21 10 size 12{ { { size 8{"21"} } over { size 8{"10"} } } } {}

= 2 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

(ii) 12 3 size 12{ { { size 8{"12"} } over { size 8{3} } } } {}

= 4

(iii) 84 9 size 12{ { { size 8{"84"} } over { size 8{9} } } } {}

= 9 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {}

19.1

a) 1

b) 1

c) 1

d) 1

19.2 Produk is elke keer 1

19.4 a) 20 17 size 12{ { { size 8{"20"} } over { size 8{"17"} } } } {}

b) 1 40 size 12{ { { size 8{1} } over { size 8{"40"} } } } {}

c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {}

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {}

19.5 c) 5 31 size 12{ { { size 8{5} } over { size 8{"31"} } } } {} : Maak eers onegte breuk ( 31 5 size 12{ { { size 8{"31"} } over { size 8{5} } } } {} )

d) 8 73 size 12{ { { size 8{8} } over { size 8{"73"} } } } {} : Maak eers onegte breuk ( 73 8 size 12{ { { size 8{"73"} } over { size 8{8} } } } {} )

20. a) 1 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 3 size 12{ { { size 8{5} } over { size 8{3} } } } {} x 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

= 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} m = 83, 3 . size 12{ {3} cSup { size 8{ "." } } } {} cm

b) 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} x 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} = 5 18 size 12{ { { size 8{5} } over { size 8{"18"} } } } {} m

= 27, 7 . size 12{ {7} cSup { size 8{ "." } } } {} cm

22.

(a) 32

(b) 15

(c) 25

(d) 25

(e) 45

(f) 2

(g) 8

(h) 7

(i) 7

(j) 6

(k) 6

(l) 8

(m) 8

(n) 8

(o) 100

Leerders afdeling

Inhoud

Aktiwiteit: vermenigvuldiging van breuke [lu 1.7.3, lu 2.1.5]

18. VERMENIGVULDIGING VAN BREUKE

18.1 Vermenigvuldiging van breuke met natuurlike getalle

Jy weet reeds dat vermenigvuldiging eintlik herhaalde optelling is.

a) Kyk of jy die volgende tabel kan voltooi:

b) Kyk goed na die voltooide tabel. Kan jy aan ’n korter manier / metode dink om die antwoorde te vind?

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

c) LET OP!

Jy kan ook dié metode volg:

1. Skryf albei getalle as breuke, bv. 6 × 1 4 = 6 1 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } = { { size 8{6} } over { size 8{1} } } times { { size 8{1} } over { size 8{4} } } } {}

2. Vermenigvuldig die tellers met mekaar: 6 × 1 = 6

3. Vermenigvuldig die noemers met mekaar: 1 × 4 = 4

4. Vereenvoudig die antwoord: 6 4 = 1 2 4 = 1 1 2 size 12{ { { size 8{6} } over { size 8{4} } } =1 { { size 8{2} } over { size 8{4} } } =1 { { size 8{1} } over { size 8{2} } } } {}

d) Bereken:

(i) 7 × 3 10 size 12{7 times { { size 8{3} } over { size 8{"10"} } } } {}

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___________________________________________________

___________________________________________________

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(ii) 2 3 × 6 size 12{ { { size 8{2} } over { size 8{3} } } times 6} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

(iii) 12 × 7 9 size 12{"12" times { { size 8{7} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

e) Op ’n getallelyn sou ons 6 × 1 4 size 12{6 times { { size 8{1} } over { size 8{4} } } } {} so kon voorstel:

f) Stel die volgende op ’n getallelyn voor: x = 4 × 2 3 size 12{x=4 times { { size 8{2} } over { size 8{3} } } } {}

18.2 Vermenigvuldiging van breuke met breuke

a) Kyk goed na die volgende voorbeelde:

(i) Die helfte ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ) van ’n driekwart ( 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} ) kan so voorgestel word:

Dus: 1 2 × 3 4 = 3 8 size 12{ { { size 8{1} } over { size 8{2} } } times { { size 8{3} } over { size 8{4} } } = { { size 8{3} } over { size 8{8} } } } {}

(ii) Een derde ( 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} ) van ’n half ( 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ) lyk so:

Dus 1 3 × 1 2 = 1 6 size 12{ { { size 8{1} } over { size 8{3} } } times { { size 8{1} } over { size 8{2} } } = { { size 8{1} } over { size 8{6} } } } {}

b) Maak nou soortgelyke sketse vir:

(i) 1 5 × 1 2 size 12{ { { size 8{1} } over { size 8{5} } } times { { size 8{1} } over { size 8{2} } } } {}

(ii) 3 10 × 1 2 size 12{ { { size 8{3} } over { size 8{"10"} } } times { { size 8{1} } over { size 8{2} } } } {}

c) LET OP!

As ons ’n breuk met ’n breuk vermenigvuldig, bv. 2 3 × 3 8 size 12{ { { size 8{2} } over { size 8{3} } } times { { size 8{3} } over { size 8{8} } } } {}

1. Vermenigvuldig ons eers die tellers met mekaar: 2 × 3 = 6

2. Dan vermenigvuldig ons die noemers met mekaar: 3 × 8 = 24

3. Ons vereenvoudig ook waar nodig: 6 ÷ 6 24 ÷ 6 = 1 4 size 12{ { { size 8{6~ div ~6} } over { size 8{"24"~ div ~6} } } = { { size 8{1} } over { size 8{4} } } } {}

d) Onthou jy nog?

Om te kan vereenvoudig , moet jy altyd die teller en die noemer deur dieselfde getal deel .

e) Het jy geweet?

Ons kan ook van kansellering gebruik maak om die produk te bepaal.

Questions & Answers

the diagram of the digestive system
Assiatu Reply
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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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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