MATHEMATICS Y6 SK (SEMAKAN 2017)

3 Are 51 and 53 composite numbers? Explain.

51 can be divided 51 53 53 can be divided
by numbers 1, 3, 17, 51 ÷ 1 = 51 53 ÷ 1 = 53 by numbers 1 and
and 51 without any 51 ÷ 3 = 17 53 ÷ 53 = 1
remainder. 51 is a 51 ÷ 17 = 3 53 without any
composite number. 51 ÷ 51 = 1 remainder. 53 is a

prime number.

51 is a composite number. 53 is a prime number.

4 Number I have classified
numbers from 59
Prime number Composite number until 73 accordingly.

59 61 60 62 64

66

71 69 70

What are the missing numbers?

5 Complete the flow charts.

a 85 can 85 can be 85 can also be 85 is
be divided divided by itself. divided by numbers .
and .
by number 1.

b can can be
be divided can be divided divided by
numbers 3 and 29.
by number 1. by itself.

1.3.1 €€Discuss composite numbers between 75 up to 100. 43

TRY IT OUT NUMBER
TEMPLATES

Tools/Materials Number templates and coloured pencils.

Task SCAN ME
1 Scan the QR code and print out the number template.

2 Colour all the composite numbers in red and prime numbers in yellow.

3 Collect and compile pupils’ work as a scrapbook.

79 67 61 23
100 88
52 81 78 15
47
80 91 54 16
99 10
31 17 2 53
11
73 43 19 89
80 95
82 56 90 86
97
37 23 41 3
52 30
24 85 56 4

LET’S DO IT

1 Are 47 and 74 prime numbers or composite numbers? Give reasons for
your answer.

2 Identify and classify prime numbers and composite numbers.

49 71 39 61 88 46 56

91 19 27 9 94 15 13

3 List all composite numbers which has digit 3 at the ones
place value, up to 100.

44 1.3.1

SOLVE THE PROBLEMS

1 Rizal and Sharvina show their first 4 095 180 4 095 188
number cards. Rizal forms a number

pattern in ascending order by sixes.
Sharvina forms a number pattern in
ascending order by eights. At which
position in their number patterns will
the numbers be the same?

Rizal Sharvina

Solution

Understand the problem Plan the strategy

Rizal 4 095 180 ascending order by sixes Build Rizal and Sharvina’s
Sharvina 4 095 188 ascending order by eights number patterns.

Solve

Rizal’s number patttern Rizal’s fifth number and
+6 +6
+6 +6 Sharvina's third number
are the same.

4 095 180, 4 095 186, 4 095 192, 4 095 198, 4 095 204, ...

Sharvina’s number patttern +8
+8 +8

4 095 188, 4 095 196, 4 095 204, 4 095 212, ...

Check Sharvina’s number pattern

Rizal’s number pattern 11

1 4 095 188
+ 16
4 095 180
+ 24 4 095 204

4 095 204 third number

fifth number

The third number in Sharvina’s number pattern is the same as
the fifth number in Rizal's number pattern.

€€Explain and emphasise the steps in problem-solving using Polya's model. 45
1.4.1

2 The picture shows a number wheel. Jamal 67 87 91
turns the wheel and gets a composite number. 77 73
Rishi gets a prime number.
The difference between the two numbers is 14.
What number did Jamal get for that turn?

Solution 53

Understand the problem

• Jamal gets a composite number.
• Rishi gets a prime number.
• The difference between the two numbers is 14.
• What number did Jamal get?

Plan the strategy Rishi might
Classify composite and prime numbers. get 53, 67,

or 73.

Jamal Composite number Prime number
might get 77 53
87 67
77, 87, 91 73
or 91.

Solve First Try Second Try

Use the Jamal gets 77. Jamal gets 87.
trial and Rishi gets 53. Rishi gets 73.
Difference Difference
error 77 – 53 = 24 87 – 73 = 14
method.

Jamal got 87 for that turn.

Yanti gets a composite number and Dayang gets
a prime number when they turn the same number

wheel. The product of their numbers is 4 823.
What is the sum of the numbers?

€€Guide pupils to find keywords in the question. 1.4.1
46

Palm oil export to country X is

3 214 4666 tonnes and 1 229 434 tonnes to
country Y. The export to country Z is

93 606 tonnes more than country X.

H ow many tonnes of palm oil are exported to countries Y and Z in total?

Solution

Understand • Country X, 214 466 tonnes.
the problem • Country Y, 1 229 434 tonnes.
• Country Z has 93 606 tonnes more than country X.
• Find the total number of palm oil exported to
countries Y and Z.

Plan the Country X 214 466 Draw
strategy 93 606 a diagram.

Country Z 214 466

Country Y 1 229 434

Solve 214 466 + 93 606 + 1 229 434 =

11 1 11

214 466 308 072

+ 93 606 + 1 229 434

308 072 1 537 506

Check 2 17 4 10 2 10 7 10 6 12

1 537 506 308 072

− 1 229 434 − 93 606

308 072 214 466

214 466 + 93 606 + 1 229 434 = 1 537 506

The total number of palm oil exported to countries Y and Z is
1 537 506 tonnes.

€€Provide more questions on constructing number sentences orally using 47
1.4.1 question cards.

4 A n electronics factory produces 2.46 million units of
light-emitting diode (LED). All the units are packed equally
into 80 boxes .The electronics factory delivers
2 boxes to Azlan Electric Shop. How many units of LED
are received by the shop?

Solution

Given • 2.46 million units of LED.
Asked for • Packed equally into 80 boxes.
• 2 boxes are sent to Azlan Electric Shop.

Number of units of LED received by Azlan Electric Shop.

Number sentence 2.46 million ÷ 80 × 2 =

Calculate 2.46 million ÷ 80 × 2 =

2.46 million = 2.46 × 1 000 000
= 2 460 000

30 750 Check the answer
using a calculator.
80 2 4 6 0 0 0 0
−2 40 1 1
60 3 0 7 5 0
−0 × 2
60 0 6 1 5 0 0
−56 0
4 00
−4 00
00
−0
0

2.46 million ÷ 80 × 2 = 61 500
The number of units of LED received by Azlan Electric Shop is 61 500 units.

48 €€Vary questions on mixed operations of multiplication and division 1.4.1
involving brackets.

5 A company delivered 0.03 million seats
to a new stadium. Then, it sent another
30 containers of seats to the stadium.
Each container carried 580 seats.
What is the total number of seats

delivered to the new stadium?

Solution

Given Delivered 0.03 million seats.
30 containers carried 580 seats each.

Asked for Total number of seats delivered to the new stadium.

Number sentence 0.03 million + 30 × 580 =

Calculate 0.03 million + 30 × 580 = (0.03 × 1 000 000) + 30 × 580

= 30 000 + 30 × 580 2

= 30 000 + 17 400 580
× 30
= 47 400 1 7 400

30 000
+ 1 7 400

47 400

Check 580 I check the answer using this
number sentence.
47 400 30 1 7 4 0 0
– 30 000 −15 0 (47 400 – 30 000) ÷ 30 = 580
2 40
1 7 400 −2 40
00
−0
0

0.03 million + 30 × 580 = 47 400
The total number of seats delivered to the new stadium is 47 400 seats.

€€Carry out activities in pairs to create number sentences based on problems 49
1.4.1 given to reinforce pupils' understanding.

6 Teguh Berjaya Company gains a profit of RM3.4 million. The company
has 5 subsidiaries. Each subsidiary receives a bonus of RM0.26 million
from the profit. What is the balance of the profit?

Solution

Given • Profit of Teguh Berjaya Company is RM3.4 million.
• 5 subsidiaries.
• Each subsidiary receives a bonus of RM0.26 million.

Asked for Balance of profit.

Number sentence RM3.4 million – 5 × RM0.26 million =

Calculate

13 RM 3 . 4 million
– RM 1 . 3 million
RM 0 . 2 6 million
×5 RM 2 . 1 million

RM 1 . 3 0 million

Check RM 0 . 2 6 million

RM 3 . 4 million 5 RM 1 . 3 0 million
– RM 2 . 1 million −0
13
RM 1 . 3 million −1 0
30
− 30
0

RM3.4 million – 5 × RM0.26 million = RM2.1 million
The balance of profit of Teguh Berjaya Company is RM2.1 million.

€€Pupils can use a calculator to check their answers. 1.4.1
50

7 A businessman owns 4 clothing stores P, Q , R, and T.

He distributes 1 million pieces of clothes equally to his
8

4 stores. Store R has 0.004 million pieces of unsold

clothes. What is the number of clothes in store R now?

Solution

• 4 stores P, Q , R, and T.

• 1 million pieces of clothes distributed equally to 4 stores.
8

• Store R has 0.004 million pieces of unsold clothes.

• What is the number of clothes in store R now?

1 million pieces of clothes distributed equally to 4 stores.
8

1 P 1 Q 1 R 1 T
8 8 8 8
million ÷ 4 million ÷ 4 million ÷ 4 million ÷ 4

Has 0.004 million
pieces of unsold clothes

Add the number of Total number of clothes in store R
clothes received and
the number of unsold 1 million ÷ 4 and 0.004 million
8
clothes.

1 million ÷ 4 + 0.004 million = Convert 1 million to
8 8

1 million ÷ 4 + 0.004 million = 125 000 ÷ 4 + 4 000 a decimal of a million
8 and solve it.

= 31 250 + 4 000

= 35 250

1 million ÷ 4 + 0.004 million = 35 250
8

The number of clothes in store R is 35 250 pieces.

€€Give other examples for pupils to try various strategies to solve problems, 51
1.4.1 such as simulation.

8 A telecommunication company received 1.602 million prepaid cards worth

RM5 each and 3 million prepaid cards worth RM10 each. All the cards
4

will be distributed equally to 1 000 telephone shops. How many prepaid

cards are allocated for one shop?

Solution

Types of Number of cards
prepaid cards 1.602 million

RM5

RM10 3 million
4

Total cards Distributed equally to 1 000 telephone shops

How many prepaid cards are allocated for one shop?

(1.602 million + 3 million) ÷ 1 000 =
4

Step 1 Step 2 Step 3

1.602 million = 1.602 × 1 000 000 1 2 352 000 =
1 000
= 1 602 000 1 602 000 2 352
+ 750 000
34 million = 3 × 1 000 000
4 2 352 000

= 0.75 × 1 000 000

= 750 000

Check the answer based on this
number sentence.

2 352 × 1 000 − 1.602 million =

(1.602 million + 3 million) ÷ 1 000 = 2 352
4

The number of prepaid cards allocated for one shop is 2 352 units.

52 €€Guide pupils to record important information concisely. 1.4.1

9 A publishing company prints 1 million Malay language Underline
10 the important
information.
newspapers and 0.002 million English language

newspapers daily. What was the total number of newspapers
printed in February 2020?

Solution

Malay language English language
0.002 million
1 million Number of newspapers
10 printed daily.

February 2020 had FEBRUARY 2020
29 days because 2020
SUN MON TUE WED THU FRI SAT
was a leap year.
1

23456 78

9 10 11 12 13 14 15

16 17 18 19 20 21 22
23 24 25 26 27 28 29

( 1 million + 0.002 million) × 29 =
10

(110 million + 0.002 million) × 29 = (100 000 + 2 000) × 29 1
= 102 000 × 29
102 000
Check = 2 958 000 × 29

2 958 000 ÷ 29 – 0.002 million = 102 000 – 2 000 918 000

= 100 000 +2 040 000

= (1100000000000) million 2 958 000

= 1 million
10

( 1 million + 0.002 million) × 29 = 2 958 000
10

The total number of newspapers printed in February 2020 was 2 958 000.

€€Using story cards, provide more exercises on forming number sentences 53
1.4.1 orally based on problems given.

10 p primary school pupils and 0.85 million secondary school pupils €

took part in an online health quiz. The total number of participants €

is 1.05 million. Calculate the value of p in a whole number.

Solution

•  p primary school pupils

• 0.85 million secondary school pupils
• Total number of participants is 1.05 million.

• Find the value of p in a whole number.

1.05 million

p 0.85 million
p + 0.85 million = 1.05 million

p + 0.85 million = 1.05 million
p = 1.05 million – 0.85 million
p = 0.2 million
p = 0.2 × 1 000 000
p = 200 000

Check

200 000 + 0.85 million = (1200000000000) million + 0.85 million
= 0.2 million + 0.85 million

= 1.05 million

200 000 + 0.85 million = 1.05 million

The value of p is 200 000.

There are m number of primary school boys. The difference in

the number of secondary school boys and primary school boys
who took part in the health quiz is 0.515 million. The number of

secondary school boys is 0.6 million. Find the value of m.

€€Give problem-solving questions on basic operations, that is addition, subtraction,€ 1.4.1
54 multiplication, and division involving unknown to strengthen pupils’ mastery of skills.

11 Zing Shoe Factory produces m pairs of sport shoes.

The factory distributes 0.086 million pairs to each
warehouse in 13 states. 1 482 000 pairs of shoes €

are not yet distributed. Calculate the value of m in €

decimal of a million.

Solution

• Produces m pairs of sport shoes.

• Distributes 0.086 million pairs of sport shoes
to each warehouse in 13 states.

• 1 482 000 pairs are not yet distributed.

• Calculate the value of m in decimal of a million.

m pairs of sport shoes

1 482 000 pairs of sport shoes are not yet distributed

0.086 million m – 13 × 0.086 million = 1 482 000

m – 13 × 0.086 million = 1 482 000 1
m – 13 × 86 000 = 1 482 000
m – 1 118 000 = 1 482 000 86 000
m = 1 482 000 + 1 118 000 × 13
m = 2 600 0000
m = 2.6 million 1

Check 2.6 million – 13 × 0.086 million = 258 000
+ 860 000

1 1 18 000

21 9
5 10 10
0.0 8 6 million
× 13 2. 6 0 0 million
– 1 . 1 1 8 million
11
1 . 4 8 2 million
0 258
+00 860 1.482 million = 1.482 × 1 000 000

1 . 1 1 8 million

= 1 482 000

2.6 million – 13 × 0.086 million = 1 482 000

The value of m is 2.6 million.

€€Give examples that involve unknown to strengthen pupils’ mastery of skills. 55
1.4.1

LET’S DO IT MONDAY 7 MARCH 2022
Number pattern
1 Wan writes a
number pattern 6 008 351, 6 009 351, 6 010 351, 6 011 351, ...
on a whiteboard.
What is the
seventh number
in the number
pattern?

2 The following are eight number cards.

97 83 47 36 73 79 90 96

Mary is asked to find the difference between the largest composite number
and the smallest prime number.
a What is her answer?
b State whether her answer is a prime number or a composite number.

3 A manufacturer of COVID-19 vaccine distributes 4 170 million doses of
vaccine to Country X. Country Y receives 1.06 million doses lesser than
Country X. What is the total number of doses of vaccine distributed by
the manufacturer?

4 ABZ Printing Company prints 0.063 million books. All the books are packed
equally into 90 boxes. The company delivers 4 boxes to
Alma Book Store. How many books are delivered to Alma Book Store?

5 Karim Electronic Company sends 2 170 million earphones to
wholesaler A and 6 boxes of earphones to wholesaler B. Each
box has 0.009 million earphones. How many earphones
are sent to wholesalers A and B in total?

56 1.4.1

6 The table shows the number of blue pens and black pens in boxes M and N.

Box M N
Black
Pen Blue
Number 0.04 million
of pens 2 million
5

A multinational company donated a box of M and 8 boxes of N to several
schools in Johor in conjunction with World Children's Day. Calculate the
difference in the number of blue pens and black pens donated by the company.

7 Factory Q produces 0.05 million containers of baulu cakes.
The cakes are distributed equally to supermarket T and
9 other supermarkets. Supermarket T sold 2 900 containers
of the cakes. What is the number of containers of unsold
cakes in supermarket T?

8 In conjunction with the holy month of Ramadan, the number of boxes of honey
dates A and honey dates B marketed weekly are as follows:

Honey dates A Honey dates B
0.45 million boxes
1 million boxes
2

What is the total number of boxes of honey dates A and honey dates B
marketed in 4 weeks?

9 An oil company produces 1 83 million gallons of petrol. 0.017 million gallons are
stored and the rest are distributed equally to 97 petrol stations. Does each
station receive 0.014 million gallons? Prove it.

1.4.1 57

LET'S PRACTISE

1 Write the numbers in numerals or words.
a 3 518 042 b 1 090 256 c 4 007 980 d 5 040 019
e eight million seven hundred nine thousand one hundred and eighty-one

f nine million two hundred fifty-three thousand
g two million fifty thousand eight hundred and six

2 Five number cards are arranged in a certain pattern as below.

8 007 056 8 007 068 8 007 080 x y

a State the pattern. b What are the values of x and y ?

3 Classify the following numbers into composite numbers and prime numbers.

1 1 8 24 29 35 41 67 80

4 Write the numbers in words or numerals.
a 1 34 million b one-eighth of a million c five and seven-tenths of a million

5 Convert decimal of a million or fraction of a million into whole numbers.
1
a 0.2 million b 1.095 million c 5 million d 4 38 million e 6 190 million

6 Complete the following table.

Whole number 3 500 000

Decimal of a million 0.6 million 2.8 million

Fraction of a million 3 million 9 58 million
4

7 Solve these. b 1 21 million + 1.192 million =
d 14 × 0.46 million =
a 8 500 000 + 790 680 =

c 8.01 million – 4 110 million – 2 650 000 =

8 Calculate. State answers in decimal of a million.

a 7 × 1 110 million = b 9.225 million ÷ 3 =
b 6 41 million ÷ 25 =
9 a 8.551 million ÷ 17 =

State the answer in a State the answer in fraction of
whole number. a million.

1.1.1,
1.1.2, 1.1.3,
1.1.4, 1.1.5,
58 1.2.1, 1.3.1

10 Calculate. b 6 130 million ÷ 9 × 7 =
a 0.8 million – 440 000 + 1 52 million = State the answer in fraction
Give the answer in decimal of a million.

of a million.

c 1.05 million + 8 × 9 million = d 4 × (1.36 million – 1 million) =
10 4

e 3.7 million + 1 21 million ÷ 6 = f (5.03 million – 2 34 million) ÷ 8 =

11 Find the value of k.

a k – 0.7 million + 1.02 million = 590 000 b k ÷ 2 × 5 = 0.01 million
c k + 1.2 million × 4 = 7 34 million
d 8.007 million – k ÷ 6 = 7.9 million
e (k + 0.013 million) × 24 = 408 000 f (6 83 million – k) ÷ 10 = 0.46 million

12 Solve the following problems.

a A battery factory produces 4.082 million batteries of AA size. The factory produces
size C batteries which are 1 54 million lesser than the number of AA size, and
860 000 batteries of size D. What is the total number of size C and D batteries

produced?

b A library has 1 41 million books. Damaged books are kept in 3 boxes. Each box has
0.003 million books. How many books are in good condition?

c 5 printing machines are used to print 3 87 million pamphlets. Each machine can print
equal numbers of pamphlets. How many pamphlets can be printed by 7 printing
machines of the same type?

d A factory produced 2 million table tennis balls. 0.04 million balls are separated for
5
orders while the remaining balls are distributed equally to 100 sports store. Is the

number of table tennis balls distributed to the stores less than 4 000 balls? Prove it.

e In conjunction with the festive season, Siti Cake Shop received orders for peanut
and dahlia biscuits. The table shows the number of orders received by each
supermarket.

Biscuit Peanut Dahlia

Number of jars 0.06 million 1 million
8

What is the total number of jars of peanut biscuits and dahlia biscuits
ordered by 15 supermarkets?

1.2.1, 59
1.4.1

GAME BOARD AND
RULES FOR MARKER

MOVEMENTS

LET'S EXPLORE

Tools/Materials 16 question cards, dice, papers, pens,
100-squared grid, and 4 markers
SCAN ME

of different colours 1 2 3 4 5 6 7 8 9 10

Participants 5 pupils (4 players 11 12 13 14 15 16 17 18 19 20
and a referee) 21 22 23 24 25 26 27 28 29 30

How to play 31 32 33 34 35 36 37 38 39 40

1 Choose a marker and determine turns. 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
2 The first player rolls the dice and move the marker 61 62 63 64 65 66 67 68 69 70
according to the number shown on 71 72 73 74 75 76 77 78 79 80
the dice.
3 Determine whether the marker lands on a prime
number square or a composite number square. 81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
4 If it lands on a prime number square, choose a
question from the prime number room. If it lands on
a composite number, choose from the composite RULES TO MOVE MARKER FOR
number room. CORRECT ANSWER
5 Write down calculations and answers on a piece
Move 19 spaces to the right

of paper. Move 16 spaces to the right
6 The referee checks each answer. If the answer is Move 8 spaces to the right

correct, the player moves the marker based on rules
given. If incorrect, the marker remains.
7 Take turns until the fourth round of play. Move 10 spaces to the right
8 The player with the largest number, wins. Move 13 spaces to the right

Prime Number Room Composite Number Room

1 4 21 million + 2.9 million = 1 8 170 million – 5.084 million =

2 6 83 million ÷ 15 = 2 9 × 3 million =
10
3 3.92 million – 120 000 + 3 25 million = 3 2 87 million ÷ 20 × 6 =
1 1
4 4.09 million + 5 × 4 million = 4 6 × (0.98 million – 4 million) =

5 (5 million – 2 190 million) ÷ 7 = 5 0.4 million + 1 51 million ÷ 4 =
6 9.2 million – k ÷ 4 = 8.9 million. Calculate
6 (k + 0.1 million) × 19 = 2 394 000. Find the

value of k. the value of k.
7 C ountry A had 4 35 million patients of
7 I n a patriotic song competition, Fella
COVID-19. The number showed a weekly
gets 2 53 million votes while Razif gets twice
rise of 0.007 million patients. What was the the number of votes. What is their total
number of votes?
total number of patients by the third week?

60 €€Vary questions for the activity in Let’s Explore to prevent pupils from memorizing 1.1.5, 1.2.1, 1.3.1,
answers. 1.4.1

€€Scan the QR code. Print out the game board and rules for marker movements.

2 FRACTIONS, DECIMALS,
AND PERCENTAGES

DIVISION OF FRACTIONS

DIVIDING PROPER FRACTIONS WITH WHOLE NUMBERS
1

Anis, please cut 54 parts of this
pudding into 2 equal parts.

Alright, mother.

What is the fraction of one part after 4 puddings are cut into 2 equal parts?
5

4 ÷ 2 = 1
5 5

4 is cut into 2 equal 4 ÷ 2 All will be 4 . €
5 5 10

parts. There are 4 parts The simplest form
of 110 .
1 of 4 is 2 .
10 10 5

4
10

4 ÷ 2 = 25
10 ÷ 2

4 ÷ 2 = 2 2
5 5 5
The fraction of one part will be 25.

€€Conduct simulation to explain the concept of dividing a proper fraction with € 6611
2.1.1 a whole number.

€€Scan the AR for the explanation on the concept of dividing proper fractions with

whole numbers.

2 Divide 43 of the pizza into 6 equal parts.
What is the fraction of each part?

3 ÷ 6 =
4

1 1 CONCEPT OF
4 8 DIVIDING
FRACTIONS
11
44

3 ÷ 6 = 3 ÷ 6 6 = 6 SCAN ME
4 4 1 1

= 3 × 1 Inverse operation and divisor.
4 6 Perform cancellation.

1 1
3 6
= 4 ×

1 2
8
= 3 of the pizza is divided into 9 equal parts.
4
What is the fraction of one part? Discuss.
3 ÷ 6 = 1
4 8

Each part will be 1 .
8

3 8 ÷ 4 =

9

8 ÷ 4 = 8 ÷ 4
9 9

= 8
9

=

8 ÷ 4 =
9

€€Make sure pupils do not cancel numerator with a numerator or denominator with € 2.1.1
62 a denominator while performing the cancellation.

DIVIDING MIXED NUMBERS WITH WHOLE NUMBERS

1 1 m
4
I'm going to cut € 1m 1m
2 41 m of this ribbon

into 3 strips of
equal length.

1 strip 1 strip 1 strip

What is the length, in fractions, of each ribbon strip?

2 41 m ÷ 3 = m TIPS

2 41 ÷ 3 = 9 ÷ 3 • Convert the mixed numbers, 2 41 to
4 1 9
improper fraction, 4 .

3 1 3 31 .
9 3 1
= 4 × • Inverse to

1 • Perform cancellation (if needed).

= 3 • Multiply numerator with numerator.
4
• Multiply denominator with denominator.

2 41 m ÷ 3 = 3 m • State the answer in the simplest form.
4

The length of each ribbon strip is 3 m.
4

2 2 25 ÷ 20 =

2 25 ÷ 20 =  152 ÷ 20 Is the answer for 2 25 ÷ 20
1 the same as 20 ÷ 2 52 ?
Explain.
3 1
12 20
= 5 ×

3 5
25
=

2 52 ÷ 20 = 3
25

€€Remind pupils to identify numerators and denominators that can be cancelled
2.1.1 first. 63

€€Emphasise that inverses only involve divisor and operation.

DIVIDING PROPER FRACTIONS WITH PROPER FRACTIONS

1 How many attempts can IIuhsaev e41 21 ofothf e wwaateter.r
be made? for every attempt to see
the distance of the water
21 ÷ 41 =
rocket's movement.

1
2

1

42
1 1 1 4
2 ÷ 4 = 2 × 1

1

= 2
1

=2

21 ÷ 41 = 2

The number of attempts is 2.

2 How many 1 are there in 2 ?
6 3

2
3

32 ÷ 61 = 2
3

1 =
6

€€Use the method of folding paper and shading a diagram to divide € 2.1.1
64 two proper fractions.

DIVIDING MIXED NUMBERS WITH PROPER FRACTIONS

1 How many 1 kg are there in 1 21 kg?
4

1 21 kg ÷ 1 kg =
4
1 21 kg 1
4 kg

Method 1

1 11 11 11
22
4 4 4 4 Divide the diagrams into €

1 1 11 4 equal parts.

2 2 44

1 21 3
2

Method 2 2

1 21 ÷ 41 = 3 × 4 There are 6 parts
2 1 of 41 .
1
=6

1 21 kg ÷ 1 kg = 6
4

There are 6 parts of 1 kg in 1 21 kg.
4

2 6 92 ÷ 7 =
8

Sara’s answer Hanis’ answer

6 92 ÷ 87 = 56 ÷ 7 6 92 ÷ 87 = 56 ÷ 7 Whose answer is correct?
9 8 9 8 Why?

1 8
56 8
= 9 × 8 = 9 × 7
56 7
1
7 64
9
= 9 =
49

= 7 91

2.1.1 €€Give other examples of dividing two fractions with the same denominator. € 65

For example: 2 51 ÷ 1 = 11 × 5
5 5 1

3 71 ÷ = 1
14

What is the value in  ?

Simple example. 1 ÷ = 1 Let’s check
the answer.
7 14

6 ÷ 2 = 3 = 1 ÷ 1

2 =6÷3 7 14 1 1 2
2 7 7 1
÷2= ÷
= 1 × 14
= 1 × 1
71 7 2
1

= 2

1 ÷ 2 = 1 = 1
7 14
14

The value in is 2.

4 ÷ 3 = 8 54
4

Calculate the value in  .

Relate division ÷ 3 = 8 54
with multiplication. 4
Simple example.
6 ÷ 2 = 3 ÷ 3 = 44
6 = 3 × 2
45

11 3
44 4
= 5 ×

= 33 1
5

= 6 53

6 53 ÷ 3 = 8 54
4

The value in is 6 53 .

 1 ÷ = 1
2

THINK Complete  ,  , and with digits 1, 2, or 3 so that the
SMART number sentence will be true.

66 €€Encourage pupils to check the answer by filling in the unknown value in a 2.1.1
number sentence and solve it.

LET’S DO IT

1 Calculate.

a 1 ÷ 5 = × = b 6 ÷ 9 = × =
5 7

c 2 31 ÷ 28 = × = d 9 43 ÷ 30 = × =

2 Calculate.

a 1÷1=   b 5 ÷ 2 =   c 7 ÷ 2 =  
8 7 9 3
26

d 4 61 ÷ 5 = e 10 52 ÷ 4 = f 1 57 ÷ 3 =
9 5 4

3 Solve these.

a How many 1 are there in 2 ? b How many 5 are there in 1 170 ?
5 9 6

c T here are 42 parts of 41 m in 10 21 m of fabric. Is the statement true?
Prove it.

4 Find the value in .

a 1 ÷ = 1 b ÷ 9 = 1 56
8 6 10

c 1 21 ÷ =2 d ÷ 4 = 2
5

5 Calculate. 6 Complete these. 5
as 8
a What is 1 ÷ 3? a as
2 3 81 ÷

b How many 3 are there in 3 ? 3 ÷ 2 121 ÷ 3
7 5 4

c Divide 7 91 by 32. b as as 2 21

d Is 1 41 ÷ 3 the same as 3 21 ÷ 1 3 41 ÷ 1 1 21 ÷
10 3 2

3 ÷ 1 41 ? Prove it.
10

€€Provide more exercises for drilling by giving simple questions and questions that 67
2.1.1 are in progressive forms.

BASIC OPERATIONS

MULTIPLICATION OF DECIMALS

1 The diagram shows the positions of R, € 0.4 km
S, and T. The distance of ST is 0.3 times €

the distance of RS. What is the distance, R ST
in km, from S to T?

0.3 × 0.4 km = km

Method 1 Shade 0.4 Shade 0.3

0.4 = 4 × 10 0.3 = 3 × 10 There are 12 €
10 × 10 10 × 10
overlapping squares.
= 14000  = 13000 
12 = 0.12
100

Method 2 0.3 × 0.4 = 3 × 140  Method 3
10
1
= 3 × 4 1 decimal place
10 × 10 0.3 1 decimal place
× 0.4
= 12 2 decimal places
100 12
+0 0 0
= 0.12
0.1 2

0.3 × 0.4 km = 0.12 km The distance from S to T is 0.12 km.

2 81.2 × 4.9 = The position of decimal point TIPS
of the product depends on the
11 total number of decimal places

8 1.2 of the number multiplied.
× 4.9

73 0 8
+ 324 8 0

39 7.8 8

81.2 × 4.9 = 397.88

€€Pupils can check the answers using other methods such as by using € 2.2.1
68 a calculator.

3 Calculate the mass of the ostrich egg.

The mass of a The mass of an 4.5 × 260.13 g = g
kiwi egg ostrich egg is 4.5 2 decimal places
times the mass of a 21 1 decimal place
is 260.13 g. 31
kiwi egg. 3 decimal places
2 6 0.1 3
× 4.5
1 3 0 0 6 5
+1 040520
1 1 7 0.5 8 5

4.5 × 260.13 g = 1 170.585   g
The mass of the ostrich egg is 1 170.585 g.

4 0.6 × 0.39 = Method 2 Method 3

Write 0 and the 25 0.6 × 0.39 = 6 × 39
decimal point before 2. 10 100
0.3 9
Method 1 × 0.6 = 6 × 39
25 2 3 4 10 × 100
+00 00
0.3 9 = 234
× 0.6 10 × 100
0.2 3 4
= 234
1 000

=

Do method 2 and
method 3 give the
answer of 0.234?

THINK 1 . 3 × 6 . 2 = 8.06 or 6 . 2 × 1 . 3 = 8.06
SMART
Rearrange the position of numbers 1, 2, 3, and 6 €
to complete the number sentence below.
. × . = 8.06

2.2.1 €€Encourage pupils to use various methods of calculation such as lattice 69
multiplication.

DIVISION OF DECIMALS

1 I will pour 2.5 of the orange juice equally into
a few bottles. Each bottle contains 0.5 .

2.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5

How many bottles will be needed?
2.5 ÷ 0.5 =

Method 1 0 0.5 1.0 1.5 2.0 2.5
0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

Method 2 Method 3

Step 1 Step 2 2.5 ÷ 0.5 = 25  ÷ 5  
10 10
5
0.5 2.5 5 25 51
× 10 × 10 10
–25 = 25  × 5  
0 10
11

2.5 ÷ 0.5 = 5 =5

The number of bottles that will be needed is 5.

2 0.5 Is the calculation
0.3 ÷ 0.15 = 3 1.5 shown here correct?

0.3 0. 1 5 –0 Discuss.
× 10 × 10 15

–1 5
0

70 €€Convert divisor and dividend to whole numbers by multiplying by 10, 100, or € 2.2.2
1 000 depending on the number of decimal places of the divisor.

3 My price is I am only How much more is the price of a
RM0.80. pen that costs RM6.00 compared to
RM6.00. a pen that costs RM0.80?

RM6.00 ÷ RM0.80 =

Step 1 Step 2

RM0.80 0.80 6.00 7.5
EACH × 100 × 100 80 6 0 0.0

RM6.00 –56 0
EACH 400

–400
0

RM6.00 ÷ RM0.80 = 7.5

The price of a pen that costs RM6.00 is 7.5 times more compared to €
a pen that costs RM0.80.

4 A tea bag 0.1 kg of tea
0.002 kg

Delicious Tea

0.1 kg

How many tea bags of 0.002 kg can you get from 0.1 kg of tea leaves?

0.1 kg ÷ 0.002 kg =

Step 1 Step 2

0.002 0. 100 50
× 1 000 × 1 000 2 100

–10
00

–0
0

0.1 kg ÷ 0.002 kg = 50

I can get a total of 50 tea bags from 0.1 kg of tea leaves.

If the weight of 1 tea bag is 0.005 kg,
how many tea bags will I get from 0.1 kg €

of tea leaves? Discuss.

2.2.2 €€Show other calculation methods to get the answers.€ 71

For example, 0.1 ÷ 0.002 = 1 ÷ 1 2 .
10 000

5 × 0.4 = 2.68 6 Solve it. = 0.012
Find the value of . 0.093 ÷

Simple example. Simple example. 0.093 ÷ = 0.012
× 3 = 6 6÷ =3
0.093 ÷ 0.012 =
=6÷3 6÷3=

× 0.4 = 2.68 Step 1 Step 2
= 2.68 ÷ 0.4
0.012 0.093 .
Step 1 Step 2 × 1 000 × 1 000 12 9 3.0 0

0.4 2.68 . –
× 10 × 10 4 2 6.8
–
–
–
– 0
0

LET’S DO IT

1 Calculate. b 0.9 × 1.1 = c 4.8 × 2.5 =
a 0.7 × 0.3 = e 3.7 × 50.08 = f 2.8 × 0.14 =
d 8.91 × 1.6 =
b 0.8 ÷ 0.02 = c 3.417 ÷ 3.4 =
2 Calculate. e 36.848 ÷ 5.6 = f 7.2 ÷ 0.75 =
a 9.5 ÷ 1.9 =
d 0.33 ÷ 0.006 =

3 Solve these.

The number in are

the product of the two numbers 2.88 7.2
0.6
below it. are the dividends. 0.5

Find the values in and .

€€Provide various forms of questions such as calculating the product€ 2.2.1, 2.2.2
72 or the quotient.

€€Conduct 21st Century Learning activity such as Showdown to answer questions
to enhance pupils' understanding.

CONVERT DECIMALS TO PERCENTAGES

1 Alia sold a cake in the morning.
Then, she sold another half in €
the evening. Altogether, Alia sold €
1.5 cakes.

Convert 1.5 to percentage.

1.5 =  %

Method 1 Represent the
cakes with a
100-squared grid.

1 = 100 = 100% 21 = 0.5 1.5 = 1 + 0.5
100 = 150××1100 = 100% + 50%
= 150%

Method 2 = 15000

1.5 = 1 150 = 50%

= 15 Method 3
10

= 15 ×100% 1.5 = 1.50 × 100%
10

= 150% = 150%

1.5 = 150 %

2

Complete the values of percentages.

100%  %  %  %  %
1.0 1.7 2.0 2.2 3.0

€€Carry out paper-folding activities to enhance the understanding of percentages.
2.3.1 The % symbol must be written when writing percentages. 73

3 State 175% in decimal.
175% =

100% 25% 25%
25%

100% 75%

Method 1 Method 2

175% = 100% + 75% 175% = 175
100
= 100 + 75
100 100 = 175 ÷ 100

= 1.00 + 0.75 = 1.75

= 1.75

175% = 1.75

4 State 910% in decimal. Are the two answers
910% = the same?
Discuss.
Method 1 Method 2
1
910% = 910 910% = 910 × 100
= 
=

= 

LET’S DO IT

Complete the table.

Decimals 1.08 6.7

Percentages 345% 206%

74 €€Ask pupils to convert decimals to percentages or vice versa. 2.3.1

ADDITION AND SUBTRACTION OF PERCENTAGES

1 a Calculate the total percentage of vitamin B6, calcium, and iron for a
serving of 30 g of grains with 125 m of skimmed milk as below.

DEGLRIACIINOUSS Content of 46% + 24% + 16% =
Vitamins and Minerals
1
% per 30 g serving
4 6%
Vitamin B6 --------- 46% 2 4%
Calcium ----------- 24% + 1 6%
Iron ---------------- 16%
8 6%

46% + 24% + 16% = 86%
The total percentage of vitamin B6, calcium, and iron is 86%.

b What is the difference in percentage between calcium and iron?

24% – 16% =

1 14

2 4%
– 1 6%

8%

24% – 16% = 8% %

The difference in percentage between calcium and iron is 8%.

2 67% – 18% – 9% = Step 1 Step 2

xxxxxxxxxx 5 17 4 9%
xxxxxxxxxx – 9%
xxxxxxx 6 7%
– 1 8% 4 0%
67% – 18% – 9% = 40%
4 9%

Try to add 18% and 9% first. Then,
deduct the total from 67%. Is the

answer the same? Discuss.

2.3.2 €€Remind pupils to write the percentage symbol in their answers. 75
€€Encourage pupils to eat a balanced diet every day.

3 Made of What is the percentage of

Wool is 80% more than wool used in this winter
synthetic fiber. jacket compared to
synthetic fiber?
10% of synthetic fiber.

Synthetic fiber 10% 80% more 1 0%
Wool 10% + 8 0%

%

The percentage of wool used is  %.

LET’S DO IT 2

Solve this cross-number puzzle. 1 8

4
36

57

Horizontal Vertical
1 50% + 28% = 2 84% + 39% + 60% =
3 76% + 25% + 93% + 8% = 4 217% + 304% =
5 101% – 36% = 6 320% – 95% =
7 800% – 47% – 209% = 8 406% – 248% – 77% =

76 €€Build cross-number puzzles involving various questions of addition and 2.3.2
subtraction of percentages. Encourage pupils to come out with their own

questions in groups.

THE VALUE OF QUANTITY AND THE VALUE OF PERCENTAGES

1 What is the length of 90% of 2.5 m of the rope? The length of my rope €
is 2.5 m.

90% of 2.5 m = 90% × 2.5 m

90% × 2.5 m = m

Method 1 90
100
90% × 2.5 m = × 2.5 m

= 9 × 2.5 m
10

= 22.5 m
10

= 2.25 m

Method 2 90 The length of this rope is 90% €
100 of your rope, James.
90% × 2.5 m = × 2.5 m

= 0.9 × 2.5 m 4

= 2.25 m 2.5 m
× 0.9

2.2 5m

90% × 2.5 m = 2.25 m
The length of 90% of 2.5 m of the rope is 2.25 m.

2 Calculate the volume of 240% of 1.8 of juice.

240% × 1.8 =

240% × 1.8 = 240 × 1.8 THINK
100 SMART

= × 1.8 Given 200% × 5.5 = 11,

= × % × 2.75 = 11

= . What is the value in ?
240% of 1.8 of juice is

2.3.3 €€Carry out a quiz to convert percentages to decimals or fractions. € 77
For example, 130% = 1.3 or 130% = 1 130 .

3 Based on the table, calculate the jumping Attempt Jumping
distance of the second attempt compared to distance (m)
the first attempt in percentage. First
Second 1.6
1.68 m compared to 1.6 m = %
1.68

1.68 × 100% = %
1.6

Step 1 Step 2 Step 3

1.68 × 100% 1.6 1 6 8.0 1 05
1.6 × 10 × 10 161 680
–1 6
= 1.68 × 100  %
1.6 08
–0
= 168 %
1.6 80
– 80

0

1.68 m compared to 1.6 m is 105 %.

4 Initially, I wanted to plant What is the percentage of 1.75 acres
1.4 acres of green plants. compared to 1.4 acres?

In the end, € 1.75 × 100% =
I managed to plant € 1.4

1.75 acres. 1.75 1.75 × 100  %
1.4 1.4
× 100% =

= 117.45 %

=%

1.75 acres compared to 1.4 acres is %.

5 4.05 kg % . Is the answer 450%
0.9 kg × 100% = 0.9 4.05 9 4 0.5 or 4.5%?

× 10 × 10 –

–

78 €€Emphasise that the symbol % must be written for the value of percentages. 2.3.3

LET’S DO IT

1 Calculate the value of quantities for each of the following.

a 80% of 4.8 kg b 50% of 7.6

c 360% of 29.5 m d 470% of 54.32 km

e 125% of 1.6 hours f 500% of 20.2 minutes
2 Calculate the percentage.

a I am Amir. 1.2 kg I am Ben.
0.6 kg

The mass of Amir’s red beans is % compared to the mass of
Ben’s red beans.

b Q
P 8.64

3.6

The volume of water in container Q is % compared to the volume of
water in container P.

c 20.77 m compared to 6.2 m.
d 0.72 hour compared to 0.45 hour.

3 Solve these.

a State the length, in m, for 230% of 6.5 m clothes.
b W hat is the percentage of 10.2 kg of old newspapers collected compared to

the 8.5 kg target at the beginning?

c Target of pocket money to be saved on Monday RM1.50
Pocket money which was successfully saved RM1.80
What is the percentage of pocket money which was successfully
saved compared to the targeted amount?

2.3.3 €€Guide pupils to determine the correct method to get the answer. 79

MIXED OPERATIONS

ADDITION AND SUBTRACTION

1 The volume of the three water 1 43 0.8
containers P, Q, and R is as shown P QR
in the picture. How much more is the
volume of water, in , in containers P My answer in
and Q compared to container R? decimal is 0.95 .

1 + 43 – 0.8 =

Calculation 1

3 = 0.75 Step 1 Step 2
4
1 .00 0 17
+ 0.75
1 .75
1 .75 − 0.80

0.95

Calculation 2 0.8 = 180 My answer in fraction
is 2190 .
1 + 3 – 0.8 = 1 + 3 × 5 – 8 × 2
4 4 × 5 10 × 2

= 20 + 15 – 16
20 20 20

= 35 – 16 TIPS
20 20

= 19 Solve the operations
20 from left to right.

1 + 43 – 0.8 = 0.95 or 19
20
2190 more
The volume of water in containers P and Q is 0.95 or than in
container R.

Is 1 + 3 – 0.8 = the same as 1 + 0.75 – 4 =  ?
4 5

Discuss.

€€Emphasise that when subtracting decimals in vertical form, the decimal points 2.4.1
80 must be aligned.

€€Carry out question and answer session on converting fractions to decimals or €
vice versa to enhance pupils’ competency in calculation.

2 4 kg of sugar 3.15 kg of sugar used € 1 21akdgdoefdsiung. ar
to make kuih.

What is the current mass, in kg, of sugar?

4 kg – 3.15 kg + 1 21 kg = kg

Step 1 Step 2

9 1 1 21 = 1 + 1
3 1010 2
0.85
4.00 + 1.50 = 1 + 0.5
– 3.1 5
2.35 = 1.5
0.85

4 kg – 3.15 kg + 1 21 kg = 2.35 kg
The current mass of sugar is 2.35 kg.

3 20 51 – (9.5 + 7) =

Card 1 Card 2

Step 1 Step 2 Step 1 Step 2

1 20 51 – 10.2 9.5 20 51 – 16.5
= 20.2 – 10.2 + 7.0 = 20.2 – 16.5
9.5
+7 = 10 1 6.5 = 3.7

1 0.2

Which calculation is correct?

€€Guide pupils to master the conversion of fractions to decimals and vice versa for 81
2.4.1 faster calculations.€

For examples, 1 = 0.5, 0.2 = 1 , 4 = 0.8.
2 5 5

MULTIPLICATION AND DIVISION

1 These 4 sacks of grains will be How many smaller packets will be produced?

repacked with equal mass into 4 × 1 51 kg ÷ 0.16 kg =
smaller packets of 0.16 kg.

Step 1 Step 2

1 51 = 1 + 1 0.16 4.80
5 × 100 × 100
= 1.0 + 0.2
Step 3
= 1.2

1 .2 30
×4 16 4 8 0

4.8 −48
00
4 × 1 51 kg ÷ 0.16 kg =
−0
0

30

30 smaller packets will be produced.

Try to divide 1 51 kg by 0.16 kg and multiply the quotient

with 4. Is your answer the same? Discuss.

2 34 × 8 ÷ 1.5 =

Method 1 Method 2

Step 1 Step 2 12
3 3 8
2 4 × 8 ÷ 1.5 = 4 × 1.5

3 × 8 = 6 1.5 6.0 1 0.5
4 × 10 × 10
1 = 2 × 10
Step 3 0.5 × 10

4 = 20
15 6 0 5

−60 = 4
0

3 × 8 ÷ 1.5 = 4

4

82 €€Emphasise that a ÷ b can be written as a . 2.4.1
b

3 The height of robot P is 3 times

the height of robot Q, while

the height of robot R is 1 of the
height of robot Q. 2

What is the height of robot R?

0.75 m ÷ 3 × 1 = m
2
0.75 m
Step 1 P QR

0.25

3 0.75
−0
07
−6
15
− 15
0

Step 2

0.125 × 1 = 0.125
2
0.25

1

0.75 m ÷ 3 × 1 = 0.125 m
2

The height of robot R is 0.125 m.

4 14.6 ÷ 1 ×6=
4

Step 1 Step 2 Can we multiply first
then divide?
14.6 ÷ 41 = 14.6 × 4 52 Discuss.
1
12 58.4
= 14.6 × 4 ×6
1 4.6
= 58.4 ×4 350.4

58.4

14.6 ÷ 1 × 6 = 350.4
4

€€Provide various questions according to pupils’ levels of performance. 83
2.4.1 €€Remind pupils to solve the operations from left to right.

ADDITION AND MULTIPLICATION I
LOVE
1 9.5 m of black thread and 3 rolls of red MALAYSIA
thread which is 4.2 m each are used for
cross-stitching. What is the total length of Cross-stitch
thread used?

9.5 m + 3 × 4.2 m = m

Step 1 Step 2

4.2 11
×3
9.5
1 2.6 + 1 2.6

2 2. 1

9.5 m + 3 × 4.2 m = 22.1 m
The total length of thread used is 22.1 m.

2 6 bottles of orange concentrate
with the volume €

of 0.28 each is mixed into €
a container with 10 43 of water €

to make the orange drink.

6 × 0.28 10 34

What is the total volume, in , of the orange drink?

6 × 0.28 + 10 43 =

Step 1 Step 2

14 1.68 + 10 34 = 1.68 + 10.75 11
= 12.43
0.28 1 .68
× 6 + 1 0.75
1.68
1 2.43

6 × 0.28 + 10 43 = 12.43
The total volume of the orange drink is 12.43 .

€€Carry out simulation to explain the concept of addition and multiplication to 2.4.1
84 enhance pupils’ understanding.

€€Emphasise that multiplication must be solved first in mixed operations involving
addition and multiplication.

3 Calculate the total mass, in g, of vitamins C and D tablets.

(15 × 0.1 g) + (60 × 1 g) = g
5 The mass of 1
vitamin C tablet
Step 1 Step 2 Step 3

0. 1 12 × 1 = 12 1 .5 0 . 1 g
× 15 5 + 1 2.0 15 tablets
60
05 1 3.5
+01 0 1 The mass of 1
vitamin D tablet
1.5
1
0 in the front can be omitted. 5 g

1 60 TABLETS
5
(15 × 0.1 g) + (60 × g) = 13.5 g

The total mass of vitamins C and D tablets is 13.5 g. 60 tablets

4 16 × (5.5 + 3 41 ) =

Solve the operation Step 1 Step 2
in brackets first.
5.5 = 5 150 ÷ 5 16 × 8 43 = 4 × 35 2
÷ 5 4
16 35
×4
= 5 21 = 140 1
1 40

5.5 + 3 41 = 5 21 ×× 2 + 3 41
2

= 5 42 + 3 41

= 8 34

16 × (5.5 + 3 41 ) = 140

THINK 10 × (41 +  ) = 10
SMART State the value of in decimals.

2.4.1 €€Show various calculation methods to enhance pupils’ understanding. 85

SUBTRACTION AND MULTIPLICATION There is 1 kg of soda
1 10

SODA bicarbonate in the bottle. €
BICARBONATE
100 g I put 3 tablespoons of soda

bicarbonate into the water to

wash away pesticide residues

on the apple skin. The mass

of each tablespoon of soda

bicarbonate is 0.005 kg.

What is the balance, in kg, of soda bicarbonate in the bottle?

1 kg – 3 × 0.005 kg = kg
10

Step 1 Step 2

3 tablespoons of soda 1 110 = 0.1 9
0 1010
bicarbonate 0 . 0 0 5
×3 0.1 00
−0.0 1 5
0.0 1 5
0.085

1 kg – 3 × 0.005 kg = 0.085 kg
10

The balance of soda bicarbonate in the bottle is 0.085 kg.

2 34 × 84 – 1.295 = 3 9.35 × 3 – 5 =
5

Step 1 Step 2 Step 1

3 × 21 = 63 99 9.35 × 3 =
4 2 101010 5
84
63.000
1 − 1.295

6 1.705 Step 2

3 –5=
4
× 84 – 1.295 = 61.705

€€Instil the importance of cleanliness and health. 2.4.1
86 €€Emphasise that multiplication must be solved first before subtraction.

4 The picture shows the difference in 2.07 m

length for two pieces of flannel used
for hydroponic cultivation. Find the

length, in m, of 5 pieces of the yellow 1 m
2
flannel.

5 × (2.07 m – 1 m) = m
2

Solve the Step 1 Step 2
operation in
brackets first. 1 = 0.5 23
2
1 .5 7
1 10 ×5

2.0 7 7.85

− 0.5 0

1 .5 7

5 × (2.07 m – 1 m) = 7.85 m
2

The length of 5 pieces of the yellow flannel is 7.85 m.

5 (9.2 – 7) × ( 4 – 0.6) =
5

Step 1 Step 2 Step 3

9.2 4 × 22 = 8 2.2
– 7.0 5 × 10 × 0.2
2.2
= 0.8 44
+0 0 0
0.8 – 0.6 = 0.2
0.4 4
(9.2 – 7) × ( 4 – 0.6) = 0.44
5 Is this calculation
correct? Discuss.

60.6 – 30 × 56 = 5.1 × 5
6
30.6

= 25.5 1

€€Encourage pupils to talk about daily life situations that involve mixed 87
2.4.1 operations to enhance their understanding.

€€Talk about the benefits of hydroponic cultivation towards the environment.

ADDITION AND DIVISION Success Motivation Camp

1 Calculate the total duration of the 2.5 hours 4 21 hours
morning session and slot 1 in the
afternoon session based on the MORNING AFTERNOON
diagram.
2.5 hours + 4 21 hours ÷ 3 = SESSION SESSION

SLOT 1 SLOT 2 SLOT 3

hours

Method 1 Method 2

Solve the division first. Step 1 Step 2

Step 1 1 .5 4 21 ÷ 3 = 9 ÷ 3 1 21 = 1.5
4 21 ÷ 3 = 4.5 ÷ 3 2 1 2.5 + 1.5 = 4
= 1.5 3 4.5
−3 3
Step 2 15 9 1
−1 5 = 2 × 3
2.5 + 1.5 = 4 0
3 1
2
=

= 1 21

2.5 hours + 4 21 hours ÷ 3 = 4 hours
The total duration of the morning session and slot 1 in the afternoon session €

is 4 hours.

2 3 ÷ 1.5 + 1 =
10

Calculation 1 Calculation 2

0.5 1.5 3.0 2 1
10
3 1.5 0.5 15 3 0 2 +
−0 + 0. 1
15 1 −30 = 2.0 + 0.1
−1 5 0.6 10
0 0

= 2.1

Which calculation is correct?
Discuss.

88 €€Emphasise that 3 ÷ 1.5 can be written as 13.5 equals 3150. 2.4.1
€€Vary questions on division involving whole numbers and decimals to enhance

the concept.

0.75 km 1 km
5

3 KEDAI SERBANEKA

BUKA

Restaurant€ Convenience Bookstore Restaurant€
R shop M T

The above picture shows a convenience shop M which is located in
the middle of restaurants R and T. What is the distance, in km, from
restaurant R to convenience shop M?

(0.75 km + 1 km) ÷ 2 = km
5
Step 2

Step 1 0.4 7 5

1 × 22 = 2 0.75 2 0.950
5 × 10 + 0.20 −0
09
= 0.2 0.95 −8
15
(0.75 km + 1 km) ÷ 2 = 0.475 km − 14
5 10
−10
0

The distance from restaurant R to convenience shop M is 0.475 km.

4 (2.4 + 6) ÷ (1 + 2 )=
5

Step 1 Step 2 Step 3

2.4 1 + 25 = + ÷ = ×
+ 6.0 =

=

THINK 10 + 1 ÷ = 11
5 in decimals.

SMART State the value of

2.4.1 €€Ask pupils to create stories based on the number sentences to enhance € 89
their understanding.

SUBTRACTION AND DIVISION Gotong-royong plan

1 In a gotong-royong programme, € Site P

2.25 hours is allocated for site P and €
3 21 hours for all the mini sites. The time mini site

taken for each mini site is the same.

How much more time is taken for the gotong-royong, in hours, on site P
compared to one mini site?

2.25 hours – 3 21 hours ÷ 4 = hours

Step 1 Step 2 Step 3

Solve division first. Convert 2.25 to 9 × 2 − 7 = 18 − 7
4 × 2 8 8 8
3 21 ÷ 4 = 7 ÷ 4 fraction.
2
2.25 = 2 12050÷÷2255 = 11
7 4 8
= 2 ÷ 1 = 2 41
= 1 83
7 1 = 9
= 2 × 4 4

= 7 2.25 hours – 3 21 hours ÷ 4 = 1 83 hours
8

The time taken for the gotong-royong on site P is 1 38 hours more than one mini site.

2 1 21 ÷ 0.25 – 5 = Step 1 Step 2 Step 3
6–5=
Remember! 0.25 1 .50 6
1 21 = 1.5 × 100 × 100 25 1 5 0

−1 50
0

€€Instil moral values such as gotong-royong and helping each other. 2.4.1
90 €€Emphasise that the division must be solved first.

3 I cut 1 21 m from 5.7 m of cable. I give the

remaining cable in equal length to 3 groups

of pupils to make this electric circuit.

What is the length of cable, in m, for each
group of pupils?

(5.7 m – 1 21 m) ÷ 3 =

Step 1 Step 2

1 21 = 1.5 5.7 1 .4
− 1.5
3 4.2
4.2 −3

12

(5.7 m – 1 21 m) ÷ 3 = 1.4 m −1 2
0

The length of cable for each group of pupils is 1.4 m.

4 (85 – 0.35) ÷ (10 – 9 21 ) =

Step 1 Step 2
(10 – 9 21 ) = 9 22 – 9 21
Convert 5 to decimal. =
8
0.625
0.625
8 5.000 − 0.3 5 0

−0

50

−4 8 Step 3

20

− 16 ÷ = ×
=
40

−40

0

THINK (6.25 – 4 41 ) ÷ (a – 3) = 1
SMART What is the value of a?

€€Modify the questions to suit pupils' level of performance. 91
2.4.1

TRY IT OUT

Tools/Materials Manila cards, 100-squared grids, pens, coloured pencils, rulers,
and task cards.

Participants 4 pupils in a group

Task 1 Each group chooses a skill that they have learned such as

fractions, decimals, or percentages.

2 Divide the manila card into four parts. Each pupil is given a task to complete

their part. Write the title as “Think Board”.

Example of “Think Board”

Picture Story The initial target of the
Object Title sale of recycled items is
RM20. In the end, the
Symbol sale reached RM50.

Percentage

RM50 of RM20 = %

50 × 100% = 250%
20

3 Present your group work and display it on the noticeboard.
4 Do corrections from the comments given.

LET’S DO IT

1 Solve these. 3 1
5 2
a 2 m + 1.7 m – m = b 4 × 1.39 kg ÷ kg =

c 8.5 hours + 3 × 1 hours = d 7 × (0.25 day + 5 43 days) =
2
e 8.5 – 4 × 1 21 = 3
f 2 ÷ 0.8 × 5 =

2 Calculate.

a 10 – 2.6 ÷ 1 = b (32.25 – 41) ÷ 4 =
2 d (45.2 + 15) ÷ (1 + 41) =
c (40 21 – 8.5) × (7 – 4.15) =

€€Carry out group activities so that each pupil has a chance to fill in each part € 2.4.1
92 of the Think Board.

€€Guide pupils to prepare materials for the Try It Out activity.