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Grade 8

Ratio and proportion



Module 15

The concept ratio and ratios in their simplest form

Activity 1

Explaining the concept of ratio and expressing ratios in their simplest form

[lo 1.4, 1.5]

1. The [ : ] sign means that you can express two or more quantities (of the same kind) as a ratio, e.g., if you receive R10 and I receive R15, we could express the two amounts as a ratio: 10 : 15.

Note: Units are not named when we deal with ratios.

2. Ratios can also be written as fractions and be simplified,

2 3 size 12{ { {2} over {3} } } {} 10 15 size 12{ { {"10"} over {"15"} } } {} e.g.:

10 : 15 = = 2 : 3 (The ratio is now expressed in its simplest form.)

3. How are the following ratios expressed in its simplest form? 1 1 4 size 12{ { {1} over {4} } } {} : 1 1 8 size 12{ { {1} over {8} } } {} ?

Suggestion: Write mixed numbers as fractions and treat the problem as division of fractions.

4. Now write each of the following ratios in its simplest form:

4.1: 18 : 24 : 30

4.2: 3 1 2 size 12{ { {1} over {2} } } {} : 4 1 2 size 12{ { {1} over {2} } } {}

4.3: 70 min : 1 1 4 size 12{ { {1} over {4} } } {} h

4.4: 7,5 kg : 500 g

4.5: 30 m : 300 cm

5. Given: ratio 3 : 5.

5.1 What is the smaller amount if the bigger amount is R50?


  • Always draw a table.
  • In the first column, write: ratio and money.
  • Fill in the given data.
  • Calculate a.
MONEY (R) a 50

6. Job opportunities in Langa:

Draw a table and calculate the following:

  • How many men are there in Langa if the ratio in numbers between men and women is 3 : 7 , and the number of women is 2 520?

7. At present, education policy in South Africa requires the following in schools: one educator for every 35 learners.

7.1 How many educators may be appointed at the Morningstar Primary School if 315 learners have been enrolled?

7.2 What must the number of learners be if the school has 23 educators?

8. The Education Department attempts to ensure a proportional ratio between educators and learners in all schools:

8.1 How many teachers are in excess and are therefore paid by the school's management council if a particular school has 700 learners and 32 educators?

8.2 What does it cost the parents to pay the salaries of the extra teachers if a teacher earns R4 982,55 per month?


Using ratios for easy comparison of particular data and for the division of any unit

[lo 1.4, 1.5, 3.7, 4.1]

a) Comparing data by making use of ratios

1. Building costs of low cost housing developments in the Western Cape increased from R1 000 to R1 220 /m² between 2000 and 2003 as opposed to an increase from R1 330 to R2 102/m², in Gauteng.

1.1 How would you indicate that the increase is fair?

1.1.1 Express all the data as ratios.

2000 2003

1.1.2 Express each ratio as a decimal number or a percentage. (Make use of your calculator.)


Western Cape:

1.1.3 Which ratio is larger?

1.1.4 Is the increase fair?

1.1.5 To what would you ascribe the difference?

b) Division by making use of ratios

1. Mr Verkuil of the Langverwacht Primary School won R 150 500 in the Lotto last Saturday. He set aside R50 000 for personal use and decided to divide the rest of the money between the school's Aids project and the Helpmekaar Fund for needy farm workers.

He decided to divide the money to the ration of 3 : 5. How much money will each fund obtain?

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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