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    This collection is included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: Siyavula

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Breuke - Optelling en Aftrekking

Module by: Siyavula Uploaders. E-mail the author

WISKUNDE

Gewone Breuke

OPVOEDERS AFDELING

Memorandum

14. a) nommers

b) ekwivalente

c) veelvoude

d) tellers

e) nommer

f) breuke

g) onegte

h) vereenvoudig

15.2 a)

= 12211221 size 12{ { { size 8{"12"} } over { size 8{"21"} } } } {} + 14211421 size 12{ { { size 8{"14"} } over { size 8{"21"} } } } {}

= 26212621 size 12{ { { size 8{"26"} } over { size 8{"21"} } } } {}

= 1 521521 size 12{ { { size 8{5} } over { size 8{"21"} } } } {}

b)

= 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} + 610610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}

= 11101110 size 12{ { { size 8{"11"} } over { size 8{"10"} } } } {}

= 1 110110 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}

c)

= 36453645 size 12{ { { size 8{"36"} } over { size 8{"45"} } } } {} - 25452545 size 12{ { { size 8{"25"} } over { size 8{"45"} } } } {}

= 11451145 size 12{ { { size 8{"11"} } over { size 8{"45"} } } } {}

d)

= 4646 size 12{ { { size 8{4} } over { size 8{6} } } } {} - 3636 size 12{ { { size 8{3} } over { size 8{6} } } } {}

= 1616 size 12{ { { size 8{1} } over { size 8{6} } } } {}

16.

a)

= 11231123 size 12{"11" { { size 8{2} } over { size 8{3} } } } {} + 1717 size 12{ { { size 8{1} } over { size 8{7} } } } {}

= 111421111421 size 12{"11" { { size 8{"14"} } over { size 8{"21"} } } } {} + 321321 size 12{ { { size 8{3} } over { size 8{"21"} } } } {}

p = 111721111721 size 12{"11" { { size 8{"17"} } over { size 8{"21"} } } } {}

b)

= 314−19314−19 size 12{3 { { size 8{1} } over { size 8{4} } } - { { size 8{1} } over { size 8{9} } } } {}

= 3 936−436936−436 size 12{ { { size 8{9} } over { size 8{"36"} } } - { { size 8{4} } over { size 8{"36"} } } } {}

t = 3 536536 size 12{ { { size 8{5} } over { size 8{"36"} } } } {}

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – (3 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {})

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 3 3636 size 12{ { { size 8{3} } over { size 8{6} } } } {} + 4646 size 12{ { { size 8{4} } over { size 8{6} } } } {}

= 6 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 4 1616 size 12{ { { size 8{1} } over { size 8{6} } } } {}

= 2 912912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} - 212212 size 12{ { { size 8{2} } over { size 8{"12"} } } } {}

g = 2 712712 size 12{ { { size 8{7} } over { size 8{"12"} } } } {}

d)

= 9 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - (4 912912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} + 812812 size 12{ { { size 8{8} } over { size 8{"12"} } } } {})

= 9 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 512512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 512512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {}

= 4 21242124 size 12{ { { size 8{"21"} } over { size 8{"24"} } } } {} - 10241024 size 12{ { { size 8{"10"} } over { size 8{"24"} } } } {}

v = 4 11241124 size 12{ { { size 8{"11"} } over { size 8{"24"} } } } {}

Leerders Afdeling

Inhoud

AKTIWITEIT: Optelling en aftrekking van breuke [LU 1.7.3]

14. Die optelling en aftrekking van breuke

KOM ONS HERSIEN

Die antwoorde van die volgende vrae is hieronder versteek.

Omkring hulle soos jy hulle vind en voltooi dan die sinne.

Table 1
a b h t t s o n k o m m a
v e r e e n v o u d i g h
e d b l k o a e n r a j f
e k a l e e a m d o e p b
l h s e n m l e i n r o r
v m r r s e d r g e j o e
o n t s a r f s s g h g u
u s n x l m g b t t p   k
d e e k w i v a l e n t e
e l o y o n f k u v w    

a) Ons kan breuke optel of aftrek slegs indien die .................................................. dieselfde is.

b) Indien die noemers verskil, moet ons .................................................. breuke met dieselfde noemers vind.

c) Ons kan die gemeenskaplike noemer maklik d.m.v. .................................................. vind.

d) Ons tel slegs die .................................................. bymekaar.

e) Die .................................................. bly onveranderd wanneer ons optel of aftrek.

f) Wanneer ons gemengde getalle optel, tel ons eers die natuurlike getalle bymekaar en dan

die ..................................................

g) Wanneer ons gemengde getalle aftrek, kan ons dit eers na ................................................. breuke verander.

h) Antwoorde moet sover moontlik altyd .................................................. word.

15.1 Onthou jy nog?

Figure 1
Figure 1 (graphics1.png)

Dus: 13+45515+12151715121513+45515+121517151215alignl { stack { size 12{ { { size 8{1} } over { size 8{3} } } + { { size 8{4} } over { size 8{5} } } } {} # = { { size 8{5} } over { size 8{"15"} } } + { { size 8{"12"} } over { size 8{"15"} } } {} # = { { size 8{"17"} } over { size 8{"15"} } } {} # =1 { { size 8{2} } over { size 8{"15"} } } {} } } {}

15.2 Bereken die volgende:

a) x=47+23x=47+23 size 12{x= { { size 8{4} } over { size 8{7} } } + { { size 8{2} } over { size 8{3} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

b) y=12+35y=12+35 size 12{y= { { size 8{1} } over { size 8{2} } } + { { size 8{3} } over { size 8{5} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) d=45−59d=45−59 size 12{d= { { size 8{4} } over { size 8{5} } } - { { size 8{5} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

d) k=23−12k=23−12 size 12{k= { { size 8{2} } over { size 8{3} } } - { { size 8{1} } over { size 8{2} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

16. Werk saam met ’n maat en bereken:

a) p=723+417p=723+417 size 12{p=7 { { size 8{2} } over { size 8{3} } } +4 { { size 8{1} } over { size 8{7} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

b) t=514−219t=514−219 size 12{t=5 { { size 8{1} } over { size 8{4} } } - 2 { { size 8{1} } over { size 8{9} } } } {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

c) g=634−212+123g=634−212+123 size 12{g=6 { { size 8{3} } over { size 8{4} } } - left (2 { { size 8{1} } over { size 8{2} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

d) v=978−334+123v=978−334+123 size 12{v=9 { { size 8{7} } over { size 8{8} } } - left (3 { { size 8{3} } over { size 8{4} } } +1 { { size 8{2} } over { size 8{3} } } right )} {}

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

17. UITDAGING!

Deel in groepe van drie. Voltooi die volgende tabel deur die aantal ure wat julle verlede week aan tuiswerk bestee het, in te vul:

Table 2
  NAAM Maan Dins Woens Don Vry
Bv. Nomsa 1 1 2 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 2 1 4 2 1 4 size 12{2 { { size 8{1} } over { size 8{4} } } } {} 3 3 4 3 3 4 size 12{3 { { size 8{3} } over { size 8{4} } } } {} 1 1 2 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 1 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
1. ............................................... ............ ............ ............ ............ ............
2. ............................................... ............ ............ ............ ............ ............
3. ............................................... ............ ............ ............ ............ ............

Beantwoord die volgende vrae:

a) Hoeveel uur het elkeen van jou groeplede altesaam aan tuiswerk bestee?

1. _________________________________

2. _________________________________

3. _________________________________

b) Who Wie het die meeste tyd aan huiswerk bestee? _______________________

c) Wie het die minste geleer? _________________________________

d) Bereken die verskil tussen jou antwoorde by b en c.

___________________________________________________

___________________________________________________

___________________________________________________

___________________________________________________

e) Vra nou ’n ander groep om jul antwoorde te kontroleer.

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.

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