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Did you know?

2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} is a proper fraction. The numerator is smaller than the denominator.
9 4 size 12{ { { size 8{9} } over { size 8{4} } } } {} is an improper fraction. The numerator is bigger than the denominator.
1 2 3 size 12{1 { { size 8{2} } over { size 8{3} } } } {} is a mixed number . A mixed number is always bigger than 1 and consists of a whole number (1) plus a fraction ( 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ).

Activity 3:

To calculate by means of computations that are suitable to be used in adding ordinary fractions [lo 1.8.3]

1. Can you still remember how to add fractions? Let us see. Work together with a friend. Take turns to say the answers. Choose any two fractions and add them. Give your answer first as an improper fraction and then as a mixed number.

Ask your teacher’s help if you struggle.

1.1
1.2

Activity 4:

To recognise and use equivalent forms [lo 1.5.1]

1. Look carefully at the following questions and then complete them as neatly as possible.

EQUIVALENT FRACTIONS

1.1 Colour 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} of the figure in blue:
1.2 Colour 2 4 size 12{ { { size 8{2} } over { size 8{4} } } } {} of the figure in green:
1.3 Colour 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} of the figure in yellow:
1.4 Colour 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} of the figure in red:
  • What do you notice?
1.6 Complete:
1
2
=
....
4
=
4
....
=
....
16

Did you know?

We call fractions that are equal in size, equivalent fractions. The word equivalent means ‘the same as’ . Thus the fractions are equal.

Do you remember?

1 unit
1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {}
1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}
1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}
1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}
1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {} 1 7 size 12{ { { size 8{1} } over { size 8{7} } } } {}
1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {}
1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {} 1 9 size 12{ { { size 8{1} } over { size 8{9} } } } {}
1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} 1 10 size 12{ { { size 8{1} } over { size 8{"10"} } } } {}
1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {} 1 11 size 12{ { { size 8{1} } over { size 8{"11"} } } } {}
1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {} 1 12 size 12{ { { size 8{1} } over { size 8{"12"} } } } {}

2. The following activity will prepare you for the addition and subtraction of fractions. Use your knowledge of equivalent fractions and answer the following. Where you are in doubt, use the diagram above.

2.1: 1 2 = 10 size 12{ { { size 8{1} } over { size 8{2} } } = { { size 8{ dotslow } } over { size 8{"10"} } } } {}

2.2: 2 3 = 6 size 12{ { { size 8{2} } over { size 8{3} } } = { { size 8{ dotslow } } over { size 8{6} } } } {}

2.3: 5 = 8 10 size 12{ { { size 8{ dotslow } } over { size 8{5} } } = { { size 8{8} } over { size 8{"10"} } } } {}

2.4: 1 4 = 12 size 12{ { { size 8{1} } over { size 8{4} } } = { { size 8{ dotslow } } over { size 8{"12"} } } } {}

2.5: 5 = 10 12 size 12{ { { size 8{5} } over { size 8{ dotslow } } } = { { size 8{"10"} } over { size 8{"12"} } } } {}

2.6: 4 10 = 5 size 12{ { { size 8{4} } over { size 8{"10"} } } = { { size 8{ dotslow } } over { size 8{5} } } } {}

2.7: 1 3 = 3 size 12{ { { size 8{1} } over { size 8{3} } } = { { size 8{3} } over { size 8{ dotslow } } } } {}

2.8: 6 = 1 2 size 12{ { { size 8{ dotslow } } over { size 8{6} } } = { { size 8{1} } over { size 8{2} } } } {}

2.9: 3 6 = 12 size 12{ { { size 8{3} } over { size 8{6} } } = { { size 8{ dotslow } } over { size 8{"12"} } } } {}

2.10: 4 6 = 9 size 12{ { { size 8{4} } over { size 8{6} } } = { { size 8{ dotslow } } over { size 8{9} } } } {}

Assessment

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards fractions;
1.2 describes and illustrates various ways of writing numbers in different cultures (including local) throughout history;
1.3 recognises and represents the following numbers in order to describe and compare them:
  • common fractions to at least twelfths;
1.5 recognises and uses equivalent forms of the numbers listed above, including:
1.5.1 common fractions with denominators that are multiples of each other;
1.6 solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including buying and selling, profit and loss, and simple budgets);
LO 5
Data handlingThe learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.
We know this when the learner:
5.3 organises and records data using tallies and tables;
5.5 draws a variety of graphs to display and interpret data (ungrouped) including:
  • a pie graph.

Memorandum

ACTIVITY 1

1.1 Equal parts of a whole

1.2 Nominator

1.3 size 12{ div } {}

1.4 Say in how many equal parts the whole is divided

1.5 Smaller

1.6 Nominator

1.7 Equivalents

1.8 Larger

1.9 Say with how many equal parts I work / are coloured in

1.10 Divide the nominator and denominator by the same number

2. 2.1 b and c

  • c and e
  • a en b

2.4 Not equal parts

2.5 (i) 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

(ii) 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

(iii) 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(iv) 3 8 size 12{ { { size 8{3} } over { size 8{8} } } } {}

(v) 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(vi) 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {}

(vii) 2 10 size 12{ { { size 8{2} } over { size 8{"10"} } } } {} / 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}

(viii) 4 10 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} / 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

(ix) 3 10 size 12{ { { size 8{3} } over { size 8{"10"} } } } {}

(x) 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

(xi) 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}

ACTIVITY 2

1.

B 8 1 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 7 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}
C 6 1 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} 5 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {}
D 8 1 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 7 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}
E 3 1 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} 2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}
F 12 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
G 16 8 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 8 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
H 16 4 4 16 size 12{ { { size 8{4} } over { size 8{"16"} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 12 12 16 size 12{ { { size 8{"12"} } over { size 8{"16"} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
I 8 2 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 6 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
J 12 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 6 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {} / 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
K 8 2 2 8 size 12{ { { size 8{2} } over { size 8{8} } } } {} / 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} 6 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} / 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}

ACTIVITY 4

1.5 Fractions all equal

1.6 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} = 2 4 size 12{ { { size 8{2} } over { size 8{4} } } } {} = 4 8 size 12{ { { size 8{4} } over { size 8{8} } } } {} = 8 16 size 12{ { { size 8{8} } over { size 8{"16"} } } } {}

2. 2.1 5 10 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} 2.6 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

2.2 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {} 2.7 3 9 size 12{ { { size 8{3} } over { size 8{9} } } } {}

2.3 8 10 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} 2.8 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2.4 3 12 size 12{ { { size 8{3} } over { size 8{"12"} } } } {} 2.9 6 12 size 12{ { { size 8{6} } over { size 8{"12"} } } } {}

2.5 10 12 size 12{ { { size 8{"10"} } over { size 8{"12"} } } } {} 2.10 6 9 size 12{ { { size 8{6} } over { size 8{9} } } } {}

3. 3.1 12 21 size 12{ { { size 8{"12"} } over { size 8{21} } } } {} 3.4 15 18 size 12{ { { size 8{15} } over { size 8{"18"} } } } {}

3.2 14 16 size 12{ { { size 8{"14"} } over { size 8{16} } } } {} 3.5 9 10 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}

3.3 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} 3.6 21 27 size 12{ { { size 8{21} } over { size 8{"27"} } } } {}

4. 10 12 size 12{ { { size 8{"10"} } over { size 8{"12"} } } } {} = 5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} = 6 9 size 12{ { { size 8{6} } over { size 8{9} } } } {} 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} = 4 6 size 12{ { { size 8{4} } over { size 8{6} } } } {}

3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} = 6 8 size 12{ { { size 8{6} } over { size 8{8} } } } {} 8 10 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} = 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} 3 10 size 12{ { { size 8{3} } over { size 8{"10"} } } } {} = 6 20 size 12{ { { size 8{6} } over { size 8{"20"} } } } {}

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
how to fabricate graphene ink ?
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
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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 5. OpenStax CNX. Sep 23, 2009 Download for free at http://cnx.org/content/col10994/1.3
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