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To recognise, classify and represent fractions (positive numbers)  (Page 2/2)

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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

prostaglandin and fever
Maha Reply
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad 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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