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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

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
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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