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Mathematics

Grade 8

Ratio and proportion

Measurement

Constructions

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?

Suggestion:

  • Always draw a table.
  • In the first column, write: ratio and money.
  • Fill in the given data.
  • Calculate a.
RATIO 3 5
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?
RATIO

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?

ACTIVITY 2

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
GAUTENG:
WESTERN CAPE:

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

Gauteng:

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

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Maciej
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Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
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Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
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Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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