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With a calculator:

2. Make decimal fractions from the following:

2.1 3 4 size 12{ { {3} over {4} } } {} = 3  4 = 0, ____

2.2 2 5 size 12{ { {2} over {5} } } {} = 25 =
2.3 3 5 size 12{ { {3} over {5} } } {} =
2.4 4 5 size 12{ { {4} over {5} } } {} =
2.5 5 5 size 12{ { {5} over {5} } } {} =
2.6 1 4 size 12{ { {1} over {4} } } {} =

We can convert any ordinary fraction to decimals in that way.

3. Make one-third into a decimal: 1 3 size 12{ { {1} over {3} } } {} = 1  3 =_____

Can you think of a reason why the answer is the way it is?

Without a calculator:

4. Write down equivalent fractions for each of the following and then write them as decimal fractions:

Fraction Fraction as tenths Decimal fraction
half
one third Can’t
Fraction Fraction as tenths Decimal fraction
two-thirds Can’t
one-quarter
three-quarters
one-fifth
two-fifths
three-fifths
four-fifths
one-sixth Can’t
one-eighth

(Some of the above have more than one decimal place but it is good to know about them.)

5. What about the thirds and sixths and others that cannot be made into tenths? Use division.

  • one-third = 1  3 =
  • two-thirds = 2  3 =

Use your own method for the division or use a calculator. 1 3 size 12{ { {1} over {3} } } {} = 1  3

Or one way: ? x 3 = 1

0 x 3 = 0,0

0,3 x3 = 0,9

0,03 x 3 = 0,09

0,99 (which is nearly 1)

so: (0 x 3) + ( 0,3 x 3) + ( 0,03 x 3)

0 + 0,3 + 0,03

= 0,333

(and the calculator will go on dividing: 0,333)

We say: 0,3 recurring or 0,3֯(The dot means recurring.)

TEST YOUR PROGRESS

1. Solve without a calculator:

1.1 17 × 26

1.2 153  9

2. Share 11 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

3. Share 12 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

4. Mike drinks 1 1 2 size 12{ size 11{1 { {1} over {2} } }} {} mugs of milk for breakfast. His sister, Sharon, drinks 3 4 size 12{ { {3} over {4} } } {} of a mug of milk. How much milk have they drunk altogether?

5. Write the following in expanded notation:

5.1 64,8 =
5.2 341,2 =

6. Write as decimals:

  • Three and four-fifths = ………………………
  • One and three-tenths = ………………….
  • Five and one-quarter = …………………
  • 4 1 2 size 12{ size 11{4 { {1} over {2} } }} {} = ………………….

7. From<;>; = write down the correct sign to make the following true:

  • 2,4 ____ 4,2
  • 1,7 _____2,1

8. Write down the number that is:

Answer
one tenth more than 45,9
one tenth less than 10

Assessement

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards in a variety of intervals;
1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers;
1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths;
1.3.3 common fractions in diagrammatic form;
1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement;
1.3.6 multiples of single-digit numbers to at least 100;
1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions;
1.5.1 common fractions with denominators that are multiples of each other;
1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement;
1.7 solves problems that involve comparing two quantities of different kinds (rate);
1.7.1 comparing two or more quantities of the same kind (ratio);
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders;
1.8.3 addition of common fractions in context;
1.8.6 equal sharing with remainders;
1.9 performs mental calculations involving:
1.9.2 multiplication of whole numbers to at least 10 x 10;
1.12 recognises, describes and uses:, and
1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3;
1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛);
1.12.3 the commutative, associative and distributive properties with whole numbers.
Learning outcomes(LOs)
LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment standards(ASs)
We know this when the learner:
2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules;
2.1.1 represented in physical or diagrammatic form;
2.1.2 not limited to sequences involving constant difference or ratio;
2.1.3 found in natural and cultural contexts;
2.1.4 of the learner’s own creation;
2.2 describes observed relationships or rules in own words;
2.3 determines output values for given input values using verbal descriptions and flow diagrams;
2.3.1 verbal descriptions;
2.3.2 flow diagrams.

Memorandum

ACTIVITY 1: recognising and representing decimal fractions

1.1 Missing numbers: 10; 1; one-tenth

1.2 Calculator answers: 10; 1; 0,1

0,1 means one-tenth

2.1

x 1 000 x 100 x 10 x 1 x 0,1
(a) 1 4 5 6 3
(b) 4 6 0 1 9
(c) 8 5
(d) 3 1 7
(e) 4 5 6 2

2.2 (b) 4 x 1 000 + 6 x 100 + 0 x 10 + 1 x 1 + 9 x 0,1

(c) 0 x 1 000 + 0 x 100 + 0 x 10 + 8 x 1 + 5 x 0,1 or just: 8 x 1 + 5 x 0,1

(d) 0 x 1 000 + 0 x 100 + 3 x 10 + 1 x 1 + 7 x 0,1 or just: 3 x 10 + 1 x 1 + 7 x 0,1

(e) 0 x 1 000 + 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1 or just: 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1

ACTIVITY 2: comparing decimal fractions

1.1<

1.2 

1.3<

1.4<

1.5 

1.6<

2. Encircled number: 49,1

3.1 10,9

3.2 5,4

3.3 5,9

3.4 8,2

3.5 7

3.6 99,1

3.7 5,9

3.8 9,9

ACTIVITY 3: converting from fractions to decimal fractions and vice versa

1. Discussion

2. With a calculator

  • 0,75
  • 2.2 0,4
  • 2.3 0,6
  • 2.4 0,8

2.5 0,8

2.6 0,25

3. 0,33333

4.

Fraction Fraction as tenths Decimal fraction
half Five tenths 0,5
One-third Can’t 0,3333
Two-thirds Can’t 0,6666
One-quarter Can’t; 0,25
Three-quarters Can’t; 0,75
One-fifth Two-tenths 0,2
Two-fifths Four-tenths 0,4
Three-fifths Six-tenths 0,6
Four-fifths Eight-tenths 0,8
One-sixth Can’t 0,1666
One-eighth Can’t; 0,125
  • 0,333
  • 0,666

Test your progress

1.1 442

1.2 17

2. one and one-tenth or 1,1 sausage rolls

3. one and two-tenths or 1 and a fifth sausage rolls (or 1,2)

4. two and a quarter mugs

  • 6 x 10 + 4 x 1 + 8 x 0,1
  • 3 x 100 + 4 x 10 + 1 x 1 + 2 x 0,1
  • 3,8
  • 1,3
  • 5,25
  • 4,5
  • <
  • <
  • 46
  • 9,9

Questions & Answers

What are the ways in which computer work as mind
baraka Reply
How does the computer serve as model for mind
baraka
in what ways does the computer serve as model for the mind?
Erick Reply
what ways does the computer serve as a model for the mind?
Erick
Ways in which computer work as Brain mind
baraka
learning is facilitated by
Quitta Reply
What
Angel
What is Repression?
Sharmin Reply
Repression, In psychoanalytic theory, the exclusion of distressing memories, thoughts, or feelings from the conscious mind. Often involving sexual or aggressive urges or painful childhood memories, these unwanted mental contents are pushed into the unconscious mind.
Forqan
in psychoanalytic terms a basic defense mechanism that shuts out anxiety arousing thoghts feelings and memories from one consciousness
Berrel
Repression is holding something painful inside because you're afraid to let it out for fear of what trouble it might csuse
Connie
It helps students to understand the behavior of people they encounter.
Anjonette Reply
what are the types of learning?
Ogbeyemi Reply
auditory, visual, kinesthetic, reading/writing
frederick
thanks @Frederick. But I still want to understand something. Classical conditioning, Operants conditioning and Observational learning are not types of learning?
Ogbeyemi
I believe there are several types of learning besides just the four I mentioned.
frederick
so, I can also say those I mentioned are part of learning?
Ogbeyemi
i would say so
frederick
Operant conditioning is a type of associative learning process through which the strength of a behavior is modified by reinforcement or punishment.
Forqan
what is psychology
Mukoone Reply
in simple explanation, it is the study and understanding of the human behavior
Edmar
the scientific study of the human mind and its functions, especially those affecting behaviour in a given context.
naina
the scientific study of human mind and behaviour
NishaOfficial
but I thought psychology is not limited to humans. I think it is the scientific study of behavior and mental process of organisms
Ogbeyemi
processes*
Ogbeyemi
what happened to my reply?
Trish
the study of human behavior, the reasons for the behavior, and ways to change the undesirable behaviors into desirable behaviors
RD
psychology is the study of the soul or mind of man through scientific studies relating to environmental factors and human behaviours.
Audley
not only man but animals as well
Audley
psychology is the study of the mind and behaviors*
Emely
the definition you gave Audley is incorrect
Emely
Hey Audley, also humans are animals, so the correct way to say it is.. Not only man but other animals as well. 👍🏽
Emely
Audley, you are both correct in the definition of psychology. Yours was textually from the book, while the other was simple and to the heart of it where a novice would understand.
Bosie
Emely, you stated that man is a animal as well. Explain?
Bosie
_____are the memory images that are related to particular place ,date and time .
Raghav Reply
what is psychology
Ayado Reply
can join your discussions
Ayado
he or she can
Edward
I have been wondering of minor Autism I have estrange daughter that has I have been divorced and things like the ex wife sister told bad things about Me, Which I was not there to defend my self was said. one part) the other is the ex wife mom took care of her and never gave her kind of up bringing
Edward
Much and now she is 28 has a pension cause of her Autism she has everyone like her 2brothers her mom and her father had said to go on andfor-get the past she had not wanting to only seen her once I tried to make contact online she does not my contact from G circle
Edward
too bad
Ibrahim
God bless you Edward 🙏 I pray that God heals you and your family he will make things right
Joseph
Ibrahim it's too bad you couldn't take the time to give encouragement to your brother with a few more positive words at the end were all brothers and sisters in Christ 🙏
Joseph
hi
Bong
hello
Marcela
hello
Manuel
hello everyone
artgalang
what is rootology
Glory Reply
Rootology is a blend of 13 concentrated herbal extracts that support against sneezing, congestion, sinus pressure, runny nose, itchy watery eyes, and headache.
Labdhee
a child playing with the friend without complaining is called
Valerie Reply
free child
Nisha
psycosocial development
Anita
playful & sporty child
Jaga
The scope of Experimental Psychology is widening with the invention of new tools and instruments for experiments.
Den Reply
like what kind?
MissRoyal
hello, what kind of people talk throught here
Marcela Reply
the kind looking for answers
Juan
?
John
thought is autonomous. it is up to us compartmentalizing these random various thoughts that we too often incorrectly give them the title of (ideas)
John
what is the scope of experimental psychology?
Fareha
who is pavlo
ROGATH Reply
he believed in classic conditioning
just
he created classical conditioning
naina
Ivan Petrovich Pavlov was a Russian physiologist known primarily for his work in classical conditioning.
lavanya
he developed the theory is classical conditioning on a dog
NishaOfficial
Hello... Gyatri, angel and thinker.. I am MJ.
Mujtaba Reply
hi
naina
Hello
Jeanica
How are you...?
Mujtaba
Fine
Jeanica
Where are you from?
Jeanica
hi everyone 😊
Luis
I'm not trying to be a killjoy but I don't think this is a conversation thread for meeting new people.
Aspen
there are plenty of apps for that
Aspen
hai
kumpulan
@Aspen German well you're right there are other apps that offers ways into meeting new people. however I don't see anything wrong in here? just saying hi and hello.
Luis
but if they turn it into something like a "dating app" then for me that's another story. just saying. 😊.
Luis
hello Everyone
artgalang
Hello Luis, this app is for friends to everyone. 😊🙏
Jeanica
Anyone having problem can leave
Mujtaba
Hi
Red
Hi
Esther
Hello
Jeanica
hello^^
Girlie
is this a Psychology Course GC?
artgalang
Hi I'm from Philippines 🇵🇭
Esther
hellow
Erick
Can anyone.... What is basic criteria for abnormalities...?
Mujtaba
Is here any psychologist or psychiatrist.
Mujtaba
hi Jeanica yes I know that 😊
Luis
hello
Fermin
yes psychologist I am
kirti
me too
artgalang
Can you please explain me Diathesis stress model and its application
Mujtaba
And how can it applied..
Mujtaba
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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