WISKUNDIGE GELETTERDHEID
NOG OEFENINGE

Koers, verhouding en eweredigheid.

MATHEMATICAL LITERACY
MORE EXERCISES

Rate, ratio and proportion.

Skryf die volgende verhoudings in hulle
eenvoudigste vorm :
Write the following ratios in the simplest
form:

38
1.1  ───                           [ 1.1 ]
57

52
1.3  ───                          [ 1.3 ]
91

247
1.5  ───                          [ 1.5 ]
437

42
1.2  ───                         [ 1.2 ]
105

136
1.4  ─────                    [ 1.4 ]
221

316
1.6  ────                        [ 1.6 ]
553

Verdeel
2.1  35 albasters onder Piet en Jan in die
die verhouding 3 : 4.                     [ 2.1 ]

2.2  R 1 378 tussen A en B in die
verhouding 4 : 9.                             [ 2.2 ]

2.3  R18 214 tussen A, B en C in
verhouding 7 : 5 : 2.                     [ 2.3 ]

2.4  R323,68 tussen C en D in die
verhouding 3 : 11.                       [ 2.4 ]

2.5  96 osse tussen P en Q in die
verhouding 5 : 7.                            [ 2.5 ]

2.6  364 skape tussen R, S en T in die
verhouding 7 : 4 : 2.                      [ 2.6 ]

Divide
2.1  35 marbles between Peter and John in
the ratio 3 : 4.                                     [ 2.1 ]

2.2  R 1 378 between A and B in the
ratio 4 : 9.                                            [ 2.2 ]

2.3  R18 214 between A, B and C in
the ratio 7 : 5 : 2.                               [ 2.3 ]

2.4  R323,68 between C and D in the
ratio 3 : 11.                                          [ 2.4 ]

2.5  96 oxen between P and Q in the
ratio 5 : 7.                                            [ 2.5 ]

2.6  364 sheep between R, S and T in
the ratio 7 : 4 : 2.                              [ 2.6 ]

A, B en C koop 'n winkel. Hulle besluit om
die wins in dieselfde verhouding te verdeel
as die verhouding waarin hulle tot die
aankoopprys bygedra het.
A het R120 000, B het R100 000 en
C het R60 000 bygedra.

3.1  Skryf die verhouding van hulle bydraes
in die eenvoudigste vorm.
[ 3.1 ]
3.2  Verdeel 'n wins van R48 601
tussen hulle.                                      [ 3.2 ]
3.3  C besluit om nog R5 000 tot die fonds
by te dra.
3.3.1  Skryf die nuwe verhouding van
hulle bydraes neer.                    [ 3.3.1 ]
3.3.2  Die tweede jaar toon die winkel 'n
wins van R72 917,25. Verdeel
hierdie wins deur die nuwe
verhouding te gebruik.             [ 3.3.2 ]

A, B and C buy a shop. They decide to
divide the profit in the same ratio as the
ratio in which they contributed to buy
the shop.
A contributed R120 000, B contributed
R100 000 and C contributed R60 000.

3.1  Write down the ratio of their
contributions in its simplest form.
[ 3.1 ]
3.2  Divide a profit of R48 601
between them.                                 [ 3.2 ]
3.3  C decides to contribute another R5 000
to the fund.
3.3.1  Write down the new ratio of their
contributions.                             [ 3.3.1 ]
3.3.2  The second year the shop shows a
profit of R72 917,25.
Divide this profit by using the
new ratio.                                   [ 3.3.2 ]

4.1  As 24 albasters tussen Jan en Martiens
verdeel word, kry Jan 9 albasters.
Bereken die verhouding waarin die
albasters verdeel is.                       [ 4.1 ]

4.2  'n Bedrag van R1 968 word tussen
A, B en C verdeel. A kry R984,
B kry R615 en C kry die res.
Bereken die verhouding waarin die
geld verdeel is.                              [ 4.2 ]

4.1  When 24 marbles are divided between
John and Martin, John gets 9 marbles.
Calculate the rate at which the
marbles were divided.                  [ 4.1 ]

4.2  An amount of R1 968 is divided
amongst A, B and C. A receives
R984, B receives R615 and C the rest.
Calculate the rate at which the
division was made.                        [ 4.2 ]

Vermeerder

5.1  82 kg in die verhouding 4 : 5.       [ 5.1 ]

5.2  R735 in die verhouding 5 : 9.       [ 5.2 ]

5.3  21,7 m in die verhouding 7 : 11.     [ 5.3 ]

5.4  28,4 kg in die verhouding 4 : 3.     [ 5.4 ]

5.5  R324 in die verhouding 8 : 5.        [ 5.5 ]

5.6  34,2 liter in die verhouding 9:5.    [ 5.6 ]

5.7  220 volt in die verhouding 55:3.    [ 5.7 ]

Increase

5.1  82 kg in the ratio 4 : 5.                    [ 5.1 ]

5.2  R735 in the ratio 5 : 9.                    [ 5.2 ]

5.3  21,7 m in the ratio 7 : 11.                [ 5.3 ]

5.4  28,4 kg in the ratio4 : 3.                  [ 5.4 ]

5.5  R324 in the ratio 8 : 5.                     [ 5.5 ]

5.6  34,2 liter in the ratio 9 : 5.                [ 5.6 ]

5.7  220 volt in the ratio 55 : 3.               [ 5.7 ]

Die verhouding van seuns tot dogters
in 'n klas is 8 : 7. Daar is 45 leerlinge
in die klas. Hoeveel seuns en
dogters is daar in die klas?            [ 6. ]

The ratio of boys to girls in a class
is 8 : 7. There are 45 pupils in
the class. How mant boys and girls
are there in the class?                [ 6. ]

In 'n klas is daar 23 seuns en
22 dogters.
7.1  Skryf die verhouding seuns : dogters in
sy eenvoudigste vorm.                   [ 7.1 ]
7.2  Drie seuns verlaat die skool en dus
die klas en 4 dogters word tot die
klas toegelaat.
Skryf die nuwe verhouding
seuns : dogters neer.                    [ 7.2 ]
7.3  Die klas het nog steeds 23 seuns en
22 dogters. Leerlinge verlaat die
skool en word tot die klas toegelaat.
Die totale aantal leerlinge in die klas
is nou 44 en die verhouding s : d = 6 : 5.
Bereken die aantal seuns en dogters
in die klas en sê hoeveel seuns die
klas verlaat het of toegelaat is tot
die klas. Herhaal vir die dogters.
[ 7.3 ]

A class contains 23 boys and 22 girls.
7.1  Write the ratio boys : girls in its
simplest form.                                 [ 7.1 ]
7.2  Three boys leave school and thus
the class and 4 girls are admitted to
the class. Write down
the new ratio boys : girls.            [ 7.2 ]
7.3  The class still contains 23 boys and
22 girls. Pupils leave the school and
are admitted to the school and the
class. The total number of pupils in
the class is now 44 and the ratio
boys : girls = 6 : 5.
Calculate the number of boys and
girls in the class and then say how
many boys left the class or were
Repeat for the girls.                        [ 7.3 ]

'n Blik bevat rooi, groen en geel
lekkers in die verhouding
r : gr : ge = 3 : 4 : 5.
Daar is 12 rooi lekkers in die blik.
Bereken die aantal groen en
geel lekkers asook die totale
aantal lekkers in die blik.
[ 8. ]

A tin contains red, green and
yellow sweets in the ratio
r : g : y = 3 : 4 : 5.
There are 12 red sweets in the tin.
Calculate the number of green and
yellow sweets and the total number
of sweets in the tin.                         [ 8. ]

'n Sak bevat 10 kg van 'n 3 : 2 : 1 (22)
kunsmis.
9.1  Verduidelik die betekenis van die
verhouding en die syfer 22.          [ 9.1 ]
9.2  Bereken die massa van die
voedingstowwe in die sak.          [ 9.2 ]
9.3  Bereken die massa N, massa P en
die massa K in die sak.               [ 9.3 ]

A bag contains 10 kg of 3 : 2 : 1 (22)
fertiliser.
9.1  Explain the meaning of the ratio
and the 22.                                       [ 9.1 ]
9.2  Calculate the mass of nutrients
in the bag.                                          [ 9.2 ]
9.3  Calculate the mass of N of P and
K in the bag.                                     [ 9.3 ]

10.1  Bereken die volume verf benodig om
20,8 m2 te verf as 1 liter verf 'n
oppervlakte van 5,2 m2 bedek.
[ 10.1 ]

10.2  Bereken die oppervlakte wat deur
5,8 liter verf bedek word as 17,6 m2
bedek word deur 2,8 liter verf.
[ 10.2 ]

10.3  'n Blik bevat 4,2 liter verf. 2,5 liter van
hierdie verf bedek 'n oppervlakte van
11,5 m2. Sal die verf in die blik genoeg
wees om 'n oppervlakte van 21,4 m2
te bedek? Verduidelik.                [ 10.3 ]

10.1  Calculate the volume of paint needed
to cover 20,8 m2 if 1 litre of paint
covers an area of 5,2 m            [ 10.1 ]

10.2  Calculate the area covered by
5,8 litres of paint if 17,6 m2 is
covered by 2,8 litres of paint.
[ 10.2 ]

10.3  A tin contains 4,2 litres of paint.
2,5 litres of this paint covers an area
of 11,5 m2. Will the tin contain
enough paint to cover an area of
21,4 m2? Explain.                        [ 10.3 ]

11.1  'n Motor gebruik 21,082 liter petrol om
'n afstand van 254 km te reis. Hoeveel
petrol sal die motor gebruik as dit 'n
afstand van 613 km ry?              [ 11.1 ]

11.2  Hoe ver sal die motor met 14,2 liter
petrol ry met dieselfde
brandstofverbruiik?                       [ 11.2 ]

11.1  A car uses 21,082 litres of petrol
to travel 254 km. How much petrol
will the car use if it travels
613 km?                                      [ 11.1 ]

11.2  How far will the car drive using
14,2 liter petrol at the same
petrol comsumption?                  [ 11.2 ]

'n Motor ry 253,5 km in 2 uur en
36 minute.
12.1  Toon aan dat 2 uur 36 minute gelyk
is aan 2,6 uur.                                [ 12.1 ]

12.2  Hoe ver sal die motor in
3 uur en 48 minute ry, as
dit teen dieselfde spoed ry?       [ 12.2 ]

12.3  Hoe lank sal dit neem om 415 km
teen dieselfde spoed af te lê?
[ 12.3 ]

A car travels 253,5 km in 2 hours and
36 minutes.
12.1  Show that 2 hours 36 minutes is equal
to 2,6 hours.                                  [ 12.1 ]

12.2  How far will the car travel in
3 hours and 48 minutes, if it travels at
the same speed?                       [ 12.2 ]

12.3  How long will it take to travel
415 km at the same speed?
[ 12.3 ]

Tien mans kan 'n sekere werk in
3 dae verrig.
13.1  Hoe lank sal 6 mans neem om
dieselfde werk te verrig as hulle teen
dieselfde tempo werk?               [ 13.1 ]
13.2  Hoe lank sal 12 mans neem om
dieselfde werk te verrig as hulle
teen dieselfde tempo werk?     [ 13.2 ]
13.3  Hoeveel mans is nodig om die
werk in 7 dae te voltooi?           [ 13.3 ]
13.4  Hoeveel mans is nodig om die
werk in 2 dae te voltooi?           [ 13.4 ]

Ten men can finish a job in 3 days.

13.1  How long will 6 men take to finish
the same job if they work at
the same rate?                       [ 13.1 ]
13.2  How long will 12 men take to finish
the same job if they work at
the same rate?                       [ 13.2 ]
13.3  How many men are needed to
finish the job in 7 days?        [ 13.3 ]
13.4  How many men are needed to
finish the job in 2 days?        [ 13.4 ]

Twintig kinders kry elk 8 lekkers uit .
'n bottel.
14.1  Hoeveel lekkers sal elke kind kry
as daar 40 kinders is?
[ 14.1 ]
14.2  Hoeveel lekkers sal elke kind kry
as daar 8 kinders is?
[ 14.2 ]
14.3  Hoeveel kinders is daar as elke
kind 16 lekkers kry?
[ 14.3 ]
14.4  Hoeveel kinders is daar as elke
kind 4 lekkers kry?
[ 14.4 ]

Twenty children each get 8 sweets
from a bottle.
14.1  How many sweets will each child
get if there are 40 children?
[ 14.1 ]
14.2  How many sweets will each child
get if there are 8 children?
[ 14.2 ]
14.3  How many children are there if
each child gets 16 sweets?
[ 14.3 ]
14.4  How many children are there if
each child gets 4 sweets?
[ 14.4 ]