MATHEMATICS Y6 SK (SEMAKAN 2017)

RUKUN NEGARA

Bahawasanya Negara Kita Malaysia
mendukung cita-cita hendak:

Mencapai perpaduan yang lebih erat dalam kalangan
seluruh masyarakatnya;

Memelihara satu cara hidup demokrasi;

Mencipta satu masyarakat yang adil di mana kemakmuran negara
akan dapat dinikmati bersama secara adil dan saksama;

Menjamin satu cara yang liberal terhadap
tradisi-tradisi kebudayaannya yang kaya dan pelbagai corak;

Membina satu masyarakat progresif yang akan menggunakan
sains dan teknologi moden.

MAKA KAMI, rakyat Malaysia,
berikrar akan menumpukan

seluruh tenaga dan usaha kami untuk mencapai cita-cita tersebut
berdasarkan prinsip-prinsip yang berikut:

KEPERCAYAAN KEPADA TUHAN
KESETIAAN KEPADA RAJA DAN NEGARA

KELUHURAN PERLEMBAGAAN
KEDAULATAN UNDANG-UNDANG
KESOPANAN DAN KESUSILAAN

(Sumber: Jabatan Penerangan, Kementerian Komunikasi dan Multimedia Malaysia)

STANDARD-BASED CURRICULUM FOR PRIMARY SCHOOL (REVISED 2017)
DUAL LANGUAGE PROGRAMME

WRITERS i
Chan Yook Lean
Gobi a/l Krishnan
Rozaili bin Mohd Ali
TRANSLATORS
Ahmad Azrul Arefe bin Ahmad Rosdi
Jeyasingam a/l Govindaraj

Ng Lee Ching
Norehan binti Mohamed Shaharoun

EDITORS
Ainol Rafezah binti Alias
Asmahanim binti Ab Rahman
Mohd ‘Udzair bin Depanaik
Nurul Shaheza binti Zamri

DESIGNERS
Roszaini binti Md Yussof
Rohaizah binti Hamzah

ILLUSTRATOR
Mohd. Faizal bin Razali

Dewan Bahasa dan Pustaka
Kuala Lumpur
2021

Serial No.: 0023 ACKNOWLEDGEMENTS

KK 513-221-0102011-49-3328-20101 The publication of this textbook involved various
ISBN 978-983-49-3328-9 parties. Sincerest appreciation and gratitude
particularly to the following:
First printing 2021
© Ministry of Education Malaysia 2021 • The Panel of Evaluators, Educational
Resources and Technology Division,
All Rights Reserved. No part of this publication Ministry of Education Malaysia.
may be reproduced or transmitted in any form
or by any means, electronic or mechanical, • The Educational Resources
including photocopying, recording or any and Technology Division, and
information storage and retrieval system without Curriculum Development Division,
permission in writing from the Director General
of Education Malaysia, Ministry of Education Ministry of Education Malaysia.
Malaysia. Negotiation is subject to the calculation
of royalty or honorarium. • The Panel of Evaluators,
Dewan Bahasa dan Pustaka.
Published for the Ministry of Education Malaysia by:
Dewan Bahasa dan Pustaka, • Officers of the English Language
Jalan Dewan Bahasa, Teaching Centre (ELTC),
50460 Kuala Lumpur. Ministry of Education Malaysia.
Telephone: 03-21479000 (8 hunting lines)
Facsimile: 03-21479643 • SK Pengkalan Rinting, Johor.
Website: http://www.dbp.gov.my
• Teacher Education Institute,
Design and Typeset: Kampus Perempuan Melayu, Melaka.
PNMB Education and Publication Sdn. Bhd.
• Dr. Shahrir Affandi bin Daud@Mohamed.
Text Typeface: Azim
Text Size: 13 point • Dato’ Mohamad Kamil bin Dato’ Haji Shafie.

Printed by: • All parties involved in the process of
Percetakan Selaseh Sdn. Bhd., publishing this book.
No. 30 & 32, Jalan Selaseh Indah,
Taman Selaseh Fasa 1,
68100 Batu Caves,
Selangor Darul Ehsan.

ii

CONTENTS

PREFACE v 2 FRACTIONS, DECIMALS, AND
PERCENTAGES
1 WHOLE NUMBERS AND OPERATIONS 1 61

Read and Say Numbers 1 Division of Fractions 61

Think Smart 3 Dividing Proper Fractions with Whole

Number Patterns 4 Numbers 61

Think Smart 8 Dividing Mixed Numbers with Whole

Recognise Fraction of a Million and Numbers 63

Decimal of a Million 9 Dividing Proper Fractions with Proper

Convert Numbers 11 Fractions 64

Decimal of a Million and Fraction Dividing Mixed Numbers with Proper

of a Million to Whole Numbers 11 Fractions 65

Think Smart 12 Think Smart 66

Whole Numbers to Decimal of a Million and Basic Operations 68

Fraction of a Million 13 Multiplication of Decimals 68

Basic Operations 15 Think Smart 69

Division of Decimals 70

Addition 15 Convert Decimals to Percentages 73

Subtraction 19 Addition and Subtraction of Percentages 75

Multiplication 22 The Value of Quantity and The Value of

Division 25 Percentages 77

Think Smart 26 Think Smart 77

Mixed Operations 28 Mixed Operations 80

Addition and Subtraction 28 Addition and Subtraction 80

Multiplication and Division 30 Multiplication and Division 82

Addition and Multiplication 31 Addition and Multiplication 84

Subtraction and Multiplication 32 Think Smart 85

Addition and Division 33 Subtraction and Multiplication 86

Subtraction and Division 34 Addition and Division 88

Basic Operations and Mixed Operations Think Smart 89

Involving Unknown 35 Subtraction and Division 90

Think Smart 35 Think Smart 91

Try It Out 92

Think Smart 36 Solve the Problems 93

Think Smart 38 Let’s Practise 99

Prime Numbers and Composite Numbers 42 Let's Explore 102

Try It Out 44 3 MONEY

Solve the Problems 45 103

Let’s Practise 58 Recognise Cost Price, Selling Price, Profit,

Let's Explore 60 and Loss 103

Recognise Discount, Rebate, and

Voucher 107

Discount 107

Rebate 108

Think Smart 109

Voucher 110

iii

CONTENTS

Recognise Invoice, Bill, Receipt, and Regular Pentagon 172
Service Tax
Invoice 112 Regular Hexagon 174
Bill 112
Receipt and Service Tax 113 Regular Heptagon 175
Interest and Dividend 114
Interest 116 Regular Octagon 176
Dividend 116
Try It Out 117 Think Smart 177
Recognise Asset, Liability, Insurance, 119
and Takaful Recognise Circles 178
Asset and Liability 120
Insurance and Takaful 120 Centre of a Circle, Diameter, and Radius 178
Solve the Problems 121
Let’s Practise 123 Let’s Draw Circles 180
Let's Explore 133
136 Think Smart 182

Solve the Problems 183

Let’s Practise 185

Let's Explore 186

7 COORDINATES, RATIO, AND

PROPORTION 187

SELF-TEST 137 Distance Between Two Coordinates 187
Think Smart 188
4 TIME 141 Ratio Between Two Quantities 191
Think Smart 195
Recognise Time Zone 141 Try It Out 195
Think Smart 146 Determine the Proportionate Quantity 197
Solve the Problems 148 Think Smart 198
Try It Out 152 Solve the Problems 201
Let’s Practise 153 Think Smart 203
Let's Explore 154 Let’s Practise 205
Let's Explore 206

5 MEASUREMENT 155 8 DATA HANDLING AND
LIKELIHOOD
Solve the Problems 155 207
Length and Mass 155
Length and Volume of Liquid 158 Complete Pie Chart and Interpret Data 207
Mass and Volume of Liquid 160
Let’s Practise 163 Think Smart 210
Let's Explore 164
Try It Out 211

Likelihood 213

Certain or Impossible 216

6 SPACE 165 Equally Likely 217

More Likely or Less Likely 217

Let's Form Angles 165 Think Smart 218
50° Angle 165
90° Angle 166 Try It Out 218
108° Angle 166
Try It Out 167 Solve the Problems 220
Draw and Measure Interior Angles of
Regular Polygons Let’s Practise 223
Equilateral Triangle 168
Square 169 Let's Explore 224
171
iv SELF-TEST 225
GLOSSARY 231
ANSWERS 233

PREFACE

The publication of the Standard-Based Curriculum for Primary School (Revised 2017) has reached
the sixth year. This textbook is based on the National Education Philosophy and focuses on
the challenges in the 21st century and the Malaysia Education Blueprint (MEB) 2013-2025, the
New Economic Model and the latest learning theories, as well as the latest assessment methods.
The Mathematics Year 6 Textbook focuses on building holistic human capital, balanced in terms
of physical, emotional, intellectual, and socio-cultural aspects of the Malaysian society, as well
as the integration of the Cross Curricular Elements (CCE), Information and Communication
Technology, and Entrepreneurship as we head towards world-class education.

The content of this textbook is systematically designed with eight topics to meet the
requirements of the Dokumen Standard Kurikulum dan Pentaksiran (DSKP) published by the
Curriculum Development Division, Ministry of Education Malaysia. This textbook emphasises
the concepts and skills in the Learning Standard to prioritise pupils’ engagement in
learning. This book includes several sections of practice in the Let’s Do It, Let’s Practise, and
Self-Test to help pupils assess their levels of competency in each skill that they have learned.
These exercises will help teachers carry out assessment of the pupils to achieve the desired
performance standard. Teacher’s Notes enables teachers to implement learning activities
effectively. Suggestions of websites are provided for pupils to explore the knowledge learned
and to carry out additional exercises through information technology.

The aim of this textbook is to be the source of knowledge for the pupils through various
strategies and activities that have been integrated to the learning process. Apart from
that, this textbook serves the purpose of assisting the teachers to implement a systematic
teaching and learning process, as well as to create a wide range of teaching strategies in
order to achieve the learning objectives. Additional information is also included in the Tips and
Do you know? sections. Learning materials are also provided in the Quick Response (QR) code
and Augmented Reality (AR) to enhance the effectiveness of the learning process.

In order to cultivate pupils’ cognitive skills, reasoning questions are posed by the mascot
and the feedback to the questions can be discussed with teachers or peers. In addition, the
Higher Order Thinking Skills (HOTS) questions are prepared in the Think Smart and Let’s Practise
sections to challenge pupils’ critical thinking. Project-based learning or games are also provided
in the Try It Out and Let's Explore to assist pupils’ understanding and enhance their skills.

This textbook has been designed in a user-friendly manner with the elements to attract
pupils’ interest in mathematics. The elements of national integration and patriotism are also
incorporated through the use of names and characters. The users of this textbook may find the
explanation of the icons used in the next page.

Chan Yook Lean
Gobi a/l Krishnan
Rozaili bin Mohd Ali

v

FUNCTIONS OF THE ICONS

TOPIC Exercises to assess

6 SPACE Topic based on LET’S DO IT pupils’ mastery of
newly learned skills.
learning area.
THINK Questions to challenge
SUBTOPIC SMART the intellectual ability,
The learning standard that needs to Higher Order Thinking
be mastered. Skills (HOTS), and
encourage critical and
MASCOT creative thinking.
Poses questions that stimulate pupils’
mind to encourage reasoning. Recreational
activities in the form
Emphasis on the learning LET'S of edutainment.
activities and suggestions on
additional activities. EXPLORE

CONTENT STANDARD AND Exercises to evaluate and reinforce
LEARNING STANDARD the skills acquired in each topic.
NUMBER
LET’S PRACTISE

1.1.1

Skill indicators to be mastered based Exercises for revision to reinforce
on the DSKP for Mathematics Year 6. pupils’ understanding.

SELF-TEST

TIPS GLOSSARY
Useful information on skills
learned. List of mathematical terms and their
meanings that encompasses all topics.
Activities to enhance the skills
learned. List of answers for Think Smart,
Let’s Practise, and Self-Test.
TRY IT OUT
ANSWERS
Additional information for
pupils’ knowledge. Type “AR Matematik Thn. 6
SK/DLP” in Google Play
vi (Google) or App Store (Apple)
and download it.

SCAN ME QR code contains learning
materials that need to be
scanned using QR scanner.

1 WHOLE NUMBERS

AND OPERATIONS

READ AND SAY NUMBERS

1 The infographic below shows the number of users of various devices who
are able to access the Internet in a country.

Desktop Smartphone
computer 10 000 000
2 800 806

Laptop
4 405 792

Smart Smartwatch
television 246 015
1 237 483

a What is the number of users of smart television who are able to access
the Internet?

millions hundred ten one hundreds tens ones
thousands thousands thousands

1 2 3 7 4 83

one million two hundred thirty-seven thousand four hundred and
eighty-three

Say the number of users of smartphone and desktop
computer who are able to access the Internet.

1.1.1 €€Emphasise saying numbers correctly based on place values. 1
€€Carry out activities on saying numbers at random based on information

from the infographic above.

b Four million forty-five thousand
usNaeucrmsce4wbsesh4rot0hoa5ef rleaI7np9attebo2rlpenetot seven hundred and ninety-two.

Did Rani say the number
correctly? Discuss.

2 I write the number I write in

in words. numerals.

TUESDAY 11 JANUARY 2022 TUESDAY 11 JANUARY 2022
eight million and eighty
7 290 005
seven million two hundred 8 000 080
ninety thousand and five

3 ''

Write three million five hundred four
thousand and thirteen'' in numerals.

Number Place value
of digit 1

1 000 000 millions

1 000 000 000 billions

3 504 130 3 504 013 1 000 000 000 000 trillions

Who wrote the
numerals correctly?

Jaslin Aizam

2 €€Use flash cards for activities in saying and writing numbers in numerals or 1.1.1
words.

THINK 539
SMART 1 647

Use the digit cards above to form four seven-digit numbers beginning
with digit 3. Two even number digits must always be adjacent.
Say and write the numbers in numerals.

LET’S DO IT

1 Say the numbers. c 6 031 095 d 3 006 070
a 2 189 234 b 9 273 180

2 Write the numbers in words. c 5 700 106 d 10 000 000
a 4 238 452 b 8 093 120

3 Write the numbers in numerals.
a nine hundred fifteen thousand one hundred and twenty-five
b two million five hundred three thousand three hundred and sixty-one
c eight million seven hundred fifty thousand and forty-three
d six million three thousand nine hundred and seven
e three million and six
f five million fifteen thousand and seventy-eight
g four million three hundred and two
h seven million nine hundred and nineteen

4 0 3 4 1 5 7 0

Form three seven-digit numbers from the digit cards above. Say and write
the numbers in words.

5 Say a number involving the value of millions. Write the number in numerals
and words.

1.1.1 3

NUMBER PATTERNS

THURSDAY 13 JANUARY 2022

1 Arrange the number cards in a number pattern in ascending order by eight hundreds.

+ 800 + 800 + 800 + 800

2 390 795 2 391 595 2 392 395

I use a calculator to calculate €
the next number.

2 394 795 2 393 995 2 393 195

What is the ninth
number in this

pattern?

second number third number

fourth number

fifth number 1.1.2
€€Begin the lesson with numbers such as 3 000 000 and simple number patterns
4 such as adding 100 and 1 000 to stimulate pupils' understanding at various

levels of mastery.
€€The scientific calculator is only used as teaching aid to represent and

determine number pattern.

2

3 095 475 3 096 475 3 097 475

What is the above number pattern?

3 3 890 740 4 890 740 5 890 740 6 890 740
2 890 740

–1 000 000 –1 000 000 –1 000 000 –1 000 000

Count backwards from 6 890 740 in millions.
This number pattern is in descending order by millions.

4 Identify the number pattern from A to E. State the pattern.

The value of the number becomes smaller. The number pattern is in descending order.

The hundreds digit for the three numbers are different.

7 657 850, 7 657 450, 7 657 050, 7 656 650, 7 656 250

Calculate the difference.

7 657 850 7 657 450
− 7 657 450 − 7 657 050

400 400

This number pattern is in descending order by four hundreds .

1.1.2 €€Ask pupils to find the next number in the number pattern above. 5

5 Look at the number pattern below. What is the value of x ?
1 307 295 1 355 530 1 403 765 x 1 500 235

Find the difference between two numbers.

12 9 11 11
4 15 4 2 10 3 10 13
1 403 765
1 355 530 1 403 765 + 48 235
– 1 307 295 – 1 355 530
1 452 000
48 235 48 235

Add 1 403 765 and 48 235 to get

the value of x.

The value of x is 1 452 000 .

What is another method to find the value of x?

State the sixth number in the number pattern.

6 The number cards below are arranged in descending order. What is the value of p ?
5 086 423 5 079 373 5 072 323 p 5 058 223

Step 1 Find the difference between two adjoining numbers.

7 16 3 12 5 079 373
−5 072 323
5 086 423
−5 079 373 7 050

7 050

Step 2 Subtract 7 050 from 5 072 323 to find the value of p.

6 12 2 12

5 072 323
− 7 050

5 065 273

The value of p is 5 065 273 .

€€Conduct a quiz in pairs for pupils to identify ascending and descending 1.1.2
6 number patterns.

7 Look at the number pattern below. What is the value of p?
100, 600, 3 600, 21 600, 129 600, p, q

Multiply the previous number by 6. 1 53

×6 ×6 ×6 ×6 ×6 129 600
×6
100, 600, 3 600, 21 600, 129 600, p, q
777 600

Now, calculate the value of q.

The value of p is 777 600 .

8 What is the number pattern below? State the value of t.

128 64 32 16 t

2 2
64 1 2 8 32 6 4

– 128 –6 4
0 0

128, 64, 32, 16, t t = 16 ÷ 2

÷2 ÷2÷2÷2 =8

The number pattern is in descending order divided by twos.

The value of t is 8 .

9 Study the pattern of the figures below.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

Pattern 1 × 1 = 1 2 × 2 = 4 3 × 3 = 9 4 × 4 = 16 5 × 5 = 25

If this pattern continues, what is the product for Figure 7?

1.1.2 €€Guide pupils to find the product for Figure 7. 7

Study the following number pattern.

1 = 1 × 1

THINK 121 = 11 × 11
SMART
12 321 = 111 × 111

1 234 321 = ×

What are the values in the empty boxes?

LET’S DO IT

1



The picture shows a number pattern.
a State the number pattern.
b What is the sixth number?
c Based on the number pattern, at which position is 4 964 116?

2 7 208 185 7 105 285 7 002 385 x 6 796 585

Five number cards are arranged in a pattern. State the value of x.

3

200 1 600 12 800 p q

a What is the number pattern above?

b State the value of p and q.

4

Figure 2 Figure 3

Figure 1

The figure above shows an arrangement of matchsticks in a pattern.
What is the number of matchsticks in Figure 5?

€€Carry out a Think-Pair-Share activity to arrange a set of numbers in ascending 1.1.2
8 or descending pattern and state the pattern.

€€Calculators can be used in the Think Smart activity.

RECOGNISE FRACTION OF A MILLION AND DECIMAL OF A MILLION

1
LANGKAWI: The total number of tourists
to this island is only 1 21  million until October
this year. Chief Executive Officer of the

Langkawi Development Authority (LADA),
Dr. Hezri Adnan said the total is lesser than
the total number of tourists last year, which
is 3 190 million.

Adapted and retrieved October 8, 2021 from https://bit.ly/3AB5CX0

1 21 million one and one over three and
two million nine-tenths of

3 190 million a million

one and a half million

2 43 million is two and three-fourths of a million. What is another way of

saying this fraction?

2 WEDNESDAY 19 JANUARY 2022

Nancy, say the Production in Week 1
number of face
masks. Kumar, say Item Number of items
the number of hand
Face mask 0.75 million
sanitisers.
Hand sanitiser 1.2 million

Zero point seven
five million.

One point two
million.

1.1.3 €€Carry out activities on saying decimal of a million and fraction of a million 9

1.1.4 at random using numeral cards or word cards.
€€Emphasise how to say decimal of a million and fraction of a million correctly.

3 THURSDAY 20 JANUARY 2022

Write the following numbers in numerals.

three-fifths of a million seven point four zero
one million
3 million
5 7.401 million

4 Three pupils write five and three quarters of a million in numerals.

Anisah Kathleen Ravi Who wrote the
number correctly?

Discuss.

5 34 million 5 41 million 5 38 million

LET’S DO IT

1 Say the numbers.

a 3 million b 9.5 million c 0.87 million d 6 43 million e 1.023 million
10

2 Write the numbers in words.
1
a 5 million b 7.6 million c 1.034 million d 8 21 million e 5.902 million

3 Write the numbers in numerals.

a two-fifths of a million b zero point seven million

c six and three-eighths of a million d four point zero two six million



€€Conduct 21st Century Learning activity (Rally Robin) to enhance pupils' 1.1.3
10 acquisition of skills in saying and writing numbers in numerals and words. 1.1.4

CONVERT NUMBERS

DECIMAL OF A MILLION AND FRACTION OF A MILLION TO WHOLE NUMBERS

Peninsular Malaysia has a forest area of 5.78 million hectares and

4.91 million hectares of Permanent Reserved Forest. Sarawak has
4 130 million hectares of permanent forest estates while 0.674 million
hectares are permanent protected areas. As for Sabah, the Sabah Forestry
department has allocated 3 53 million hectares of state land as
forest reserves.

Adapted and retrieved October 8, 2021, from https://bit.ly/3xxHx1y

1 Convert 5.78 million to a whole number.
5.78 million =

5.78 million = 5 millions + 0.7 millions + 0.08 millions

Method 1 = 5 millions + 7 hundred thousands + 8 ten thousands

Place millions hundred ten thousands hundreds tens ones
value 00 0 0
thousands thousands
Digit
value 57 8

Method 2 5.78 million = 5.78 × 1 million
= 5.780000 × 1 000 000
= 5 780 000

5.78 million = 5 780 000

2 0.674 million =

0.674 million = 0.674 × 1 million Use method 1 as shown
above to solve question 2.
= 0.674000 × 1 000 000
= 674 000

0.674 million = 674 000

Convert 8.91 million to a whole number.

€€Carry out quizzes where pupils match decimal of a million with whole numbers.
1.1.5 11

3 Convert 4 130 million to a whole number. 4 130 = 4.3
4 130 million =

Method 1
4 130 million = 4 130 × 1 million
= 4.300000 × 1 000 000

= 4 300 000

Method 2 4 130 million = 4 130 × 1 million iCmopnrvoeprte4r  f13r0atcotioann, 4103.

= 43 × 1 000 000
10

= 4 300 000

4 130 million = 4 300 000

4 3 53 million = 1 million = 1 000 000

3 53 million = 3 million + 3 million 1 million 1 million 1 million 1 million 1 million
5 5 5 5 5 5

= 3 000 000 + 600 000 200 000 200 000 200 000 200 000 200 000

= 3 600 000 3 million = 600 000 2 million = 400 000
3 35 million = 3 600 000 5 5

FRACTION OF
A MILLION
CHART

Convert 1 52 million to a whole number.

SCAN ME

2 81 million p 2 21 million 2 85 million q 3 million

THINK Based on the number line above, state the values of p and q
SMART
in whole numbers.

€€Use fraction charts, fraction strips, or number lines to explain the relationship 1.1.5
12 between whole numbers and fraction of a million.

€€Scan QR code to obtain the fraction of a million chart.

WHOLE NUMBERS TO DECIMAL OF A MILLION AND FRACTION OF A MILLION

1 State 700 000 in decimal of a million.

700 000 = million

Method 1

Place millions hundred ten thousands hundreds tens ones

value thousands thousands

Digit 0 700 0 00
value 700 000 = 0.7 million

The digit value in the millions place value is 0. Place the decimal point between the millions
place value and hundred thousands place value. Ignore the digit 0 after 7. Write the word million.
The answer is 0.7 million.

Method 2 700 000 = ( 1700000000000  ) million

= 7 million
10

= 0.7 million

700 000 = 0.7 million

2 Convert 5 230 000 to a decimal of 3 State 800 000 in fraction of
a million. a million.

5 230 000 = million 800 000 = million

5 230 000 800 000 = ( 1800000000000  ) million
= (5 230 000. ÷ 1 000 000) million
8 ÷ 2
= 5.23 million = 10 ÷ 2 million

5 230 000 = 5.23 million = 4 million
5

Convert 3 725 000 to a 800 000 = 45  million
decimal of a million.

€€Vary questions on the relationship of decimal of a million and fraction of a 13
1.1.5 million to whole numbers and vice versa.

€€Emphasise that fraction of a million must be written in the simplest form.

4 Convert 1 900 000 to a 5 Are the values in the three cards equal?
fraction of a million. Discuss.

1 900 000 = million

1 900 000 = ( 11 900 000  ) million
000 000

= 19 million 6 375 000 million 6 83 million 6.375 million
10

= 1 190 million

1 900 000 = 1 190 million

LET’S DO IT

1 Convert decimal of a million to whole numbers.

a 0.4 million = b 0.12 million = c 1.08 million =

d 1.5 million = e 0.032 million = f 9.013 million =

2 Convert fraction of a million to whole numbers.

a 9 million = b 1 million = c 1 million =
10 2 4

d 9 34 million = e 8 45 million = f 6 87 million =

g 2 51 million = h 3 85 million = i 7 83 million =

3 Complete the following table.

Whole number 500 000 2 750 000

Decimal of 2.3 million
a million

Fraction of 6 81 million 1 45 million
a million

4 3 625 000 is equal to 3 58 million. Prove it.

€€Carry out activities on saying whole numbers, fraction of a million, and decimal of 1.1.5
14 a million of equal values.

€€Give examples of fraction of a million with denominators of 2, 4, 5, 8 and 10 only.

BASIC OPERATIONS

ADDITION

1 The table shows the population of three districts in Seberang Perai in 2020.

District in Seberang Perai North Middle South
467 800 235 100
Population 405 100

Retrieved October 8, 2021, from https://bit.ly/2VHO1O7

What is the total population of all three districts in Seberang Perai?
405 100 + 467 800 + 235 100 =

1 1 1 1 State the population in
405 100 decimal of a million.
+ 467 800 8 72 900
+ 235 1 00
872 900
1 108 000

405 100 + 467 800 + 235 100 = 1 108 000
The total population of all three districts in Seberang Perai is 1 108 000.

2 4 305 612 + 780 107 = Arrange the digits
in the correct
1 place value.

4 305 6 12
+ 780 1 07
5 085 7 1 9

4 305 612 + 780 107 = 5 085 719

3 9 408 + 3 071 592 + 68 043 =

Method 1 Method 2 3 081 000
+ 68 043
9 408 11 11
3 07 1 592
+ 68 043 3 07 1 592
+ 9 408

3 081 000

Solve it. Which method is easier?

1.2.1 €€Vary calculation methods such as by arranging the numbers with the larger 15
number on top, and by estimating to check the answers.

4 5 240 780 + 0.65 million =

Step 1 Step 2

0.65 million = 0.650000 × 1 000 000 5 240 780
+ 650 000
= 650 000 5 890 780

5 240 780 + 0.65 million = 5 890 780

5 2 130 million + 4 100 000 =

Give the answer in a whole number
and in decimal of a million.

Calculation 1

2 130 million = 2.3 million 1 000 000
= 2.300000 ×

= 2 300 000

2 130 million + 4 100 000 = 2 300 000 + 4 100 000
= 6 400 000

Calculation 2

2 130 million = 2 million + 3 million 4 100 000 = ( 4 100 000 ) million
10 1 000 000

= 2.0 million + 0.3 million = 41 million
10
= 2.3 million

= 4.1 million

2  130 million + 4 100 000 = 2.3 million + 4.1 million
= 6.4 million

2 130 million + 4 100 000 = 6 400 000 or 6.4 million

Can you give the answer in fraction?

€€Emphasise the need to convert decimal and fraction of a million to 1.2.1
16 whole numbers before solving addition based on the questions’ requirement.

6

P Online learning R
2 110 million pupils in four states 0.89 million pupils

Q S
6 25 million pupils 1.04 million pupils

a Calculate the total number of pupils who participated in online learning
in states R and S. Give the answer in a whole number.

0.89 million + 1.04 million =

Step 1 Step 2

1 1.93 million = 1.930000 × 1 000 000
0.89 million = 1 930 000
+ 1.04 million

1.93 million

0.89 million + 1.04 million = 1 930 000

T he total number of pupils who participated in online learning in states
R and S is 1 930 000.

b Add the number of pupils who participated in online learning in states
P and Q .

2 110 million + 6 52 million = million

2 110 million + 6 25 × 2 million = 2 110 million + 6 140 million
× 2

= 8 150 ÷÷ 5 million
5

= 8 21 million Now, use
another method

2 110 million + 6 25 million = 8 21 million to solve this.

The total number of pupils who participated in online learning

in states P and Q is 8 21 million.

€€Vary questions based on the data given in example 6 above. 17
1.2.1

7 4.052 million + 3 83 million = million

3 38 million = 27 million
8

= 3.375 million 1

3.3 7 5 4 . 0 5 2 million
+ 3 . 3 7 5 million
8 2 7.0 0 0
−2 4 7 . 4 2 7 million
30
−2 4 State the answer in a
60 whole number.
− 56
40
−40
0

4.052 million + 3 38 million = 7.427 million

8 2.12 million + 680 000 + 1 45 million =
State the sum in decimal of a million.

680 000 = ( 1608000000000  ) million 1 54 million = 1 million + 4×2 million
5×2
= ( 6 8. ÷ 100) million
= 1 million + 8 million
= 0.68 million 10

1 1 = 1.0 million + 0.8 million

2. 12 million = 1.8 million
0.68 million
+ 1.80 million Afiyah Siew Lin
4.60 million

2.12 million + 680 000 + 1 54 million = 4.6 million 4 53 million 460 000

Who holds the card that has the same value
as 4.6 million?

18 €€Encourage pupils to check their answers using a calculator. 1.2.1

SUBTRACTION
1 The pictures show four types of digital thermometer produced by a factory.

ABC D

a Calculate the difference in the number of digital thermometer A and
digital thermometer B.

4 305 127 – 3 180 127 =

millions hundred ten thousands hundreds tens ones
thousands
thousands 5 1 2 7
10 0 1 2 7
2 5 0 0 0
0
43 8
2
–3 1

11

4 305 127 – 3 180 127 = 1 125 000 State the answer in
The difference in the number of digital thermometer A fraction of a million.

and digital thermometer B is 1 125 000.

b How many more is the number of digital thermometer A

compared to the number of digital thermometer C?

4 305 127 – 0.96 million =

Step 1 Step 2

0.96 million = 0.960000 × 1 000 000 12
= 960 000 3 2 10

4 305 127 – 0.96 million = 3 345 127 4 305 127
– 960 000

3 345 127

The number of digital thermometer A is 3 345 127 more than
the number of digital thermometer C.

€€Emphasise the arrangement of digits according to the correct place values in order
1.2.1 to carry out subtraction in vertical form. 19

c How much lesser is the number of digital thermometer D compared to

the number of digital thermometer B?

3 180 127 – 7 million =
10

Card P Card Q

3 180 127 – 7 million = 3 180 127 – 70 000 3 180 127 – 7 million = 3 180 127 – 700 000
10 = 3 110 127 10 = 2 480 127

Which card shows the correct calculations? Discuss.

2 RM8.75 million – RM3.906 million = million

7 17 4 10 State the answer in a
whole number.
RM 8 . 7 5 0 million
– RM 3 . 9 0 6 million

RM 4 . 8 4 4 million

RM8.75 million – RM3.906 million = RM4.844 million

3 Subtract 6 41 million from 9 35 million. State the balance in a whole number.
9 35 million – 6 41 million =

Method 1 Method 2

9 53 million – 6 41 million = 9 35 × 4 million – 6 41 × 5 million 9  35 million = 9.6 million
× 4 × 5 = 9 600 000

= 9 2120 million – 6 250 million 6 41 million =

= 3 270 million 9 600 000
–
= 3 million +

= 3 000 000 +

=

Complete the calculations. Compare method 1 to method 2.
Which is easier?

20 €€Emphasise that fraction of a million which has different denominator must be 1.2.1
made equal first before subtracting.

4 Three number cards K, L, and M are as follows.

K 2.035 million L 6 41 million M 715 000

a Find the difference of value in cards L and K.
State the answer in a whole number.

6 41 million – 2.035 million =

Step 1 Step 2 Step 3

6 41 million = 6 million + 1 million 2.035 million 4 10
4 = 2.035000 × 1 000 000
= 2 035 000 6 250 000
= 6 000 000 + 250 000 – 2 035 000

= 6 250 000 4 215 000

6 41 million – 2.035 million = 4 215 000
The difference of value in cards L and K is 4 215 000.

b Subtract the value of cards M and K from the value of card L.
State the answer in decimal of a million.

6 41 million – 715 000 – 2.035 million =

Step 1 Step 2

6 41 million = 25 million 715 000 = (1701050000000) million
4

6 . 2 5 million = 0.715 million

4 2 5 . 0 0 million Step 3
−2 4

1 0 5 12 4 10

−8 6 . 2 5 0 million 5 . 5 3 5 million

20 – 0 . 7 1 5 million – 2 . 0 3 5 million
− 20
5 . 5 3 5 million 3 . 5 0 0 million
0

6 41 million – 715 000 – 2.035 million = 3.5 million

€€Encourage pupils to solve number sentences in vertical form. 21
1.2.1 €€Remind pupils to identify what the question requires before converting and

solving operations.

MULTIPLICATION State the answer in
decimal of a million and
1 A factory produces 1 150 000 bars of soap
weekly. How many bars of soap are fraction of a million.
produced in 8 weeks?
8 × 1 150 000 =

14
1 150 000
× 8
9 200 000

8 × 1 150 000 = 9 200 000

The number of soap produced in 8 weeks
is 9 200 000 bars.

2 32 × 25 000 =
State the answer in decimal of a million.

Method 1 Method 2 Step 1
Step 1
1 25000 ×
1 0 6 11 5 0 0 0 0 0 0 3
25 000 8 04 100000 00 2
0 0 000
× 32 32 × 25 000 = 800 000
50 000
Step 2
+750 000
800 000 800 000 = ( 1800000000000  )million
Step 2
= 8 million
(800 000. ÷ 1 000 000) million 10
= 0.8 million
= 0.8 million
32 × 25 000 = 0.8 million

€€Emphasise that the answers must be given in whole numbers, fraction of a million, 1.2.1
22 or decimal of a million based on what the questions require.

3 9 × 0.75 million =

State the answer in decimal of a million or fraction of a million.

WEDNESDAY 16 FEBRUARY 2022

Calculation 1 My answer is in
decimal of a million.
64

0.7 5 million
×9

6.7 5 million

WEDNESDAY 16 FEBRUARY 2022

Calculation 2 6

0.75 = 75 ÷ 5 9 × 0.75 million = 9 × 3 million 4 27
100 ÷ 5 1 4 −2 4
3
15 ÷ 5 = 27 million
20 ÷ 5 4
=
= 6 43 million
3
= 4

I answered in
fraction of a million.

9 × 0.75 million = 6.75 million or 6 43 million

State the answer in a whole number.

€€Train pupils to convert fraction of a million and decimal of a million to whole numbers
1.2.1 and vice versa. 23

4 4 × 1 190 million =

Calculation 1 Calculation 2

4 × 1 190 million = 4 × 1.9 million 4 × 1 190 million = 2 × 19 million
10
4

= 4 × 1.900000 × 1 000 000 = 38 5
5
= 4 × 1 900 000 million

= 7 600 000 = 7 53 million

4 × 1 190 million = 7 600 000 or 7 53 million

12 × 3 million =
4

A 0.009 million B 0.09 million C 0.9 million D 9 million

5 Calculate the product of 5 and 1.25 million. State the answer in fraction of a million.
5 × 1.25 million =

Method 1 Method 2

12 5 × 1.25 million = 5 × 1 41 million

1 . 2 5 million = 5 × 5 million
×5 4

6 . 2 5 million = 5 × 5 million
1 4

6.25 million = 6 12050 ÷ 2255  million = 25 million
÷ 4

= 6 41 million = 6 41 million

5 × 1.25 million = 6 41 million Which method is easier?

24 €€Ask pupils to write answers for questions 4 and 5 in decimal of a million. 1.2.1

DIVISION Each plastic
package has
1 10 pairs of gloves.

1 200 000 pairs of
gloves are to be
packed equally
into several plastic

packages.

How many plastic packages of gloves are produced? Give the answer
in a whole number and in decimal of a million.

1 200 000 ÷ 10 =

Calculation 1 Calculation 2
1 200 000 = 120 000
1 200 000
10 10
= (120 000. ÷ 1 000 000) million
= 120 000
= 0.12 million

1 200 000 ÷ 10 = 120 000 or 0.12 million
The number of plastic packages of gloves produced is 120 000 or 0.12 million.

2 8.25 million ÷ 3 = million

2 . 7 5 million State the answer in a whole number
and in fraction of a million.
3 8 . 2 5 million
−6
22
−2 1
15
− 15
0

8.25 million ÷ 3 = 2.75 million

1.2.1 €€Encourage pupils to use vertical form when dividing two numbers. 25

3 Divide 6 45 million by 8. Give the answer in a whole number.

6 45 million ÷ 8 =

Step 1 Step 2

6 54 × 2 million = 6 180 million 6 800 000 ÷ 8 =
× 2

= 6.8 million

= 6.800000 × 1 000 000

= 6 800 000

4 Find the quotient when 9 38 million is divided by 15.

9 38 million ÷ 15 = million Step 2
9.375
. million
Step 1 8 75.000 15 9.3 7 5 million

9 83 million = 75 million −72 −0
8 30 93

−2 4 −9 0
37
= 9.375 million 60
− 56 −
75
40
−
−40 0

0

7 million 62 500 625 000 5 million Complete the calculations
8 8 above. Which value is equal

to your answer in
example 4?

THINK Complete the number sentence
SMART
based on the given numbers.

6.23 8 7 6 41 ÷ = 0.89
million million million

€€Vary questions on division involving whole numbers, fraction of a million, and 1.2.1
26 decimal of a million to reinforce pupils' understanding and acquisition of skills.

€€Encourage pupils to solve division in vertical form.

LET’S DO IT

1 Find the sum.

a 38 075 + 991 002 + 75 600 = b 4 305 120 + 114 880 =
ii 4 225 965 + 899 035 =
c State the answer in fraction of a million.

i 1 720 900 + 1 079 100 =

d i 6 480 521 + 0.4 million = ii 1.53 million + 68 304 =

iii 320 159 + 3 million = iv 2 21 million + 470 000 =
4

e i 4.28 million + 3 51 million = ii 7 110 million + 370 000 + 0.83 million =

iii 0.93 million + 65 000 + 6 170 million =

2 Find the difference.

a i 6 732 189 – 5 401 207 = ii 7 982 000 – 2 483 000 =

b i 892 147 – 0.84 million = ii 5 54 million – 328 950 =

iii 3.98 million – 1 87 million = iv 5 330 472 – 0.9 million – 2 81 million =

v 6 45 million – 3 020 490 – 1. 45 million =

3 a Find the product.

i 6 × 230 000 = ii 3 × 385 000 = iii 25 × 276 000 =
iii 8 × 1 81 million =
b Calculate. Give the answer in whole numbers.

i 7 × 0.24 million = ii 9 × 3 million =
5

iv 32 × 0.002 million =

4 a Divide.

i 3 051 000 ÷ 5 = ii 1 071 000 ÷ 9 = iii 1 500 000 ÷ 12 =
iii 1 130 million ÷ 26 =
b Calculate. State quotients in whole numbers.

i 0.86 million ÷ 4 = ii 3 million ÷ 6 =
5

€€Encourage pupils to check answers using a calculator. 27
1.2.1

MIXED OPERATIONS

ADDITION AND SUBTRACTION

1 The following table shows the number of orders and sale of face shields.

Orders in 2019 0.4 million FACE SHIELD

FACE SHIELD

Sales in 2019 372 000 FACE SHIELD

Orders in 2020 5 41 million

Calculate the number of unsold face shields.

0.4 million – 372 000 + 5 41 million = million

Convert Step 1 Step 2
372 000 and
5 41  million 9
( 372 000. ÷ 1 000 000) million = 0.372 million 3 10 10

to decimal of a 5 41 million = 21 million 5 . 2 5 million 0 . 4 0 0 million
million first. 4 – 0 . 3 7 2 million

SUBTRACTION = 5.25 million 4 2 1 . 0 0 million 0 . 0 2 8 million

−2 0 0 . 0 2 8 million
+ 5 . 2 5 0 million
10
5 . 2 7 8 million
−8

20

− 20

0

0.4 million – 372 000 + 5 41 million = 5.278 million
The number of unsold face shields is 5.278 million.

2 6 21 million + 2 501 479 – 3.008 million =
Give the answer in a whole number.

Step 1 Step 2

6 21 million = 6.5 × 1 000 000 1 99
= 6 500 000 8 10 10 11
6 500 000
9 001 479
3.008 million = 3.008 × 1 000 000 +2 501 479 – 3 008 000

= 3 008 000 9 001 479 5 993 479

6 21 million + 2 501 479 – 3.008 million = 5 993 479

€€Emphasise working from left to right for mixed operations of addition and 1.2.1
28 subtraction.

3 5 120 900 – (2.65 million + 1 25 million) =
State the answer in a whole number.

Step 1 1 . 4 million

1 25 million = 7 million 5 7 . 0 million
5 −5
20
= 1.4 million −2 0
0

Step 2 Step 3 Solve the TIPS
operations in
1 0 12 brackets first.

2 . 6 5 million 5 120 900
+ 1 . 4 0 million −4 050 000

4 . 0 5 million 1 070 900

4.050000 × 1 000 000
= 4 050 000

5 120 900 – (2.65 million + 1 25 million) = 1 070 900

4 6.4 million + (3.9 million – 1 21 million) =
Give the answer in fraction of a million.

Step 1 Step 3 Step 4
1 21 million = 1.5 million
6 . 4 million million =   million
Step 2 + million
3 . 9 million =   ÷ million
− 1 . 5 million million ÷

million =   million

Complete steps 2 until 4 to get the answer.

€€Provide additional exercises on mixed operations as reinforcement activities. 29
1.2.1 €€Emphasise that operations in brackets must be solved first.

MULTIPLICATION AND DIVISION

1 There are Distribute the
A container has 7 similar face masks equally
81 million pieces of containers.
face masks. to 5 hospitals.

How many face masks are received by each hospital?

1 million × 7 ÷ 5 =
8

Step 1 Step 2 Step 3
0.175 million
1 million × 7 0 . 8 7 5 million 0 . 1 7 5 million = 0.175000 × 1 000 000
8 8 7 . 0 0 0 million = 175 000
5 0 . 8 7 5 million
= 7 million −0 −0 Solve the TIPS
8 70 08
−5 operations from
= 0.875 million −64 37 left to right.
− 35
60 25
−25
− 56 0

40

−40

0

1 million × 7 ÷ 5 = 175 000
8

The number of face masks received by each hospital is 175 000.

2 0.02 million ÷ 8 × 24 3 4 51 million ÷ (20 × 3) = million

= million 4 51 21
5
0.02 million ÷ 8 × 24 million = million 4 . 2 million

= 0.02 million 3 = 4.2 million 5 2 1 .0million
8 −20
× 24 10
−1 0
1 4.2 million ÷ (20 × 3) 0

= 0.02 million × 3 = 4.2 million ÷ 60

= 0.06 million = 0.07 million

0.02 million ÷ 8 × 24 4 51 million ÷ (20 × 3) = 0.07 million
= 0.06 million

€€Vary questions on multiplication and division to reinforce pupils' understanding. 1.2.1
30 €€Guide pupils to calculate using strategies suited to their abilities.

ADDITION AND MULTIPLICATION We still have 12 boxes of vitamin
1 pills in our stock. Each box

contains 15 bottles of vitamin pills.

I just received
0.46 million bottles

of vitamin pills.

Calculate the current number of bottles of vitamin pills.
0.46 million + 12 × 15 =

Step 1 Step 2

1 0.46 million = 0.460000 × 1 000 000 TIPS
= 460 000
12
× 15 Step 3 Order of operation
460 000 + 180 = 460 180 × first, then +.
60
+1 20

1 80

0.46 million + 12 × 15 = 460 180

The current number of bottles of vitamin pills is 460 180 bottles.

2 130 million + 0.48 million × 6 = million Which card
shows

3 million + 0.48 million × 6 3 million + 0.48 million × 6 the correct
10 10 calculations?

Card A = 0.3 million + 0.48 million × 6 Card B = 0.3 million + 0.48 million × 6
= 0.78 million × 6 = 0.3 million + 2.88 million

= 4.68 million = 3.18 million

3 14 × (0.001 million + 1 million) = Complete this.
2
+ 500 000)
14 × (0.001 million + 1 million) = 14 × ( 
2

= 14 ×

=

€€Encourage pupils to create questions on mixed operations of addition and 31
1.2.1 multiplication. Then, solve and check answers using a calculator.

SUBTRACTION AND MULTIPLICATION Our charity organisation received
1
3 million pieces of blankets.
4

1 000 boxes of blankets

have been distributed

to victims of COVID-19.

Each box has 40 pieces

of blankets.

Calculate the remaining number of blankets after distribution.

3 million – 1 000 × 40 =
4

Step 1 Step 2

1 000 4 0 . 7 5 million 0.75 million
× 40 3 . 0 0 million = 0.750000 × 1 000 000

40 000 − 0 = 750 000

30 Step 3 TIPS
−2 8

20 750 000 Order of operation
− 20 − 40 000 × first, then –.

0 7 1 0 000

3 million – 1 000 × 40 = 710 000
4

The remaining number of blankets is 710 000.

2 1.4 million × 6 – 5 110 million = million

2 8.4 million Convert the answer to
− 5. 1 million
1 .4 million million a whole number.
×6 3.3 million

8.4 million

1.4 million × 6 – 5 110 million = 3.3

3 (4 52 million – 4.1 million) × 25 = million

4 52 million = 22 million 4 . 4 million 4.4 million 1
5 − 4. 1 million
5 2 2 . 0 million 0 . 3 million
= 4.4 million −20 0.3 million × 25
20
−2 0 15
+0 6 0
0
0 7 . 5 million

(4 25 million – 4.1 million) × 25 = 7.5 million

32 €€Emphasise that the operations in the brackets must be solved first. 1.2.1
€€In example 3, guide pupils to convert 4 25 million to 4.4 million.

ADDITION AND DIVISION

1 Alpha Company received

1 53 million pieces of tiles.

Our factory will distribute
4.9 million more tiles to
Alpha Company and 6 other

companies equally.

How many tiles will Alpha Company receive after the distribution?

1 53 million + 4.9 million ÷ 7 = million

Step 1 Step 2 Step 3

0 . 7 million 1 53 million = 8 million 1
5
7 4 . 9 million 1 .6 million
−0 1 . 6 million + 0.7 million TIPS
49
−4 9 5 8 . 0 million 2.3 million
0 −5
30 Order of operation
−3 0 ÷ first, then +.
0

1 35 million + 4.9 million ÷ 7 = 2.3 million
Alpha Company received 2.3 million tiles.

2 0.072 million ÷ 24 + 1 190 million = million 3 (2.08 million + 4 41 million) ÷ 40
=
0 . 0 0 3 million

24 0 . 0 7 2 million 1 190 million = 19 million (2.08 million + 4 41 million) ÷ 40
−0 10

0 0 = 1.9 million = (2.08 million +  ) ÷ 40

−0 = million ÷ 40

07

−0 0.0 0 3 million = ÷ 40
72 + 1 .9 0 0 million
=
−72 1 .9 0 3 million
0

0.072 million ÷ 24 + 1 190 million = 1.903 million

€€Encourage pupils to solve basic operations using vertical form. 33
1.2.1 €€Vary questions so that pupils are proficient in converting fraction of a million

and decimal of a million to solve number sentences.

SUBTRACTION AND DIVISION

1 Distribution of flags in conjunction with National Day celebration.
6 53 million flags are distributed equally

State A State B State C State D State E

City Rural areas
1.07 million

How many flags are distributed to the rural areas?

6 53 million ÷ 5 – 1.07 million = million Which value is the same as

6 53 million = 33 million 1 . 3 2 million 2 12 the answer,
5 6 . 6 0 million
5 1 . 3 2 million 1 million or 21  million?
− 1 . 0 7 million 4
6 . 6 million − 5

5 3 3 . 0 million 16 0 . 2 5 million

−30 −1 5

3 0 10

−3 0 − 10

00
6 35 million ÷ 5 – 1.07 million = 0.25 million

The number of flags distributed to the rural areas is 0.25 million.

2 9.9 million – 6 21 million ÷ 13 =
9.9 million – 6 21 million ÷ 13 = 9.9 million – 6.5 million ÷ 13
= 9.9 million –

=

3 (8.04 million – 3 52 million) ÷ 16 = Between calculation 1 and
calculation 2, which is easier?

Calculation 1 (8.04 million – 3 52 million) ÷ 16 = (8 040 000 – 3 400 000) ÷ 16
= 4 640 000 ÷ 16
= 290 000

Calculation 2 (8.04 million – 3 52 million) ÷ 16 = (8.04 million – 3.4 million) ÷ 16
= 4.64 million ÷ 16

= 0.29 million

(8.04 million – 3 52 million) ÷ 16 = 290 000 or 0.29 million

34 €€Emphasise that division must be solved first for questions which 1.2.1
do not involve brackets.

BASIC OPERATIONS AND MIXED OPERATIONS INVOLVING UNKNOWN

1 Clothes Manufactured by Factory T

Type of clothes Total clothes manufactured

Long-sleeved 0.6 million

Short-sleeved x

Total 1.3 million

How many short-sleeved clothes are manufactured by Factory T?

0.6 million + x = 1.3 million

0.6 million + x = 1.3 million APPLICATION
x = 1.3 million – 0.6 million OF THE
2Sim+ pxle=e5xample . x = 0.7 million
x=5–2 CONCEPT OF
0 13 EQUALITY

1 . 3 million
− 0 . 6 million

0.6 million + 0.7 million = 1.3 million 0 . 7 million

SCAN ME

The number of short-sleeved clothes manufactured by Factory T is 0.7 million.

2 y – 1 million = 3 million y – 1 million = 3 million
8 4 8 4

What is the value of y? y = 3 million + 1 million
4 8

Simple example. y = 3 × 2 million + 1 million
4 × 2 8
y–3=4
y = 4 + 3 y = 6 million + 1 million
8 8

y = 7 million
8

7 million – 1 million = 3 million The value of y is 7 million.
8 8 4 8

THINK Given x – 0.92 million = 1.67 million and 1 200 000 – y = 0.35 million.
SMART Find the value of x – y in decimal of a million.

1.2.1 35

3 3 × h = 1 500 000
Find the value of h.

Simple example. 8 ÷ 4 can be written as 84.
4 × k = 6 800 000.
4 × h = 8 Find the value of k.
h = 8 ÷ 4

3 × h = 1 500 000
5
1 500 000
h = 3

1
h = 500 000

3 × 500 000 = 1 500 000

The value of h is 500 000.

4 g ÷ 7 = 0.04 million
Find the value of g.

Simple example. r ÷ 6 = 1 million Complete
2 these.
g ÷ 2 = 3
g = 3 × 2 r = 1 million ×
2
g ÷ 7 = 0.04 million
g = 0.04 million × 7 r =

= 0.28 million The value of r is .

0.28 million ÷ 7 = 0.04 million

The value of g is 0.28 million.

THINK Given 8 × g = 9.6 million and g ÷ 4 = m.
SMART Find the value of m.

36 1.2.1

5 First football Second football
match match

There are k number of 0.1 million spectators left and
0.04 million entered. The total number
spectators for the
of spectators is 40 200 people.
first match.

Calculate the value of k.

k – 0.1 million + 0.04 million = 40 200

Simple example. k – 0.1 million + 0.04 million = 40 200
k = 40 200 + 0.1 million – 0.04 million
k – 5 + 3 = 4 k = 40 200 + 100 000 – 40 000
k = 4 + 5 – 3 k = 140 200 – 40 000

k = 100 200

100 200 – 0.1 million + 0.04 million = 40 200

The value of k is 100 200.

6 p ÷ 2 × 3 = 750 000
Calculate the value of p in fraction of a million.

Simple example. p ÷ 2 × 3 = 750 000
p = 750 000 ÷ 3 × 2
p ÷ 4 × 5 = 10 p = 250 000 × 2
p = 10 ÷ 5 × 4 p = 500 000

p = 500 000 million
1 000 000

p = 5 ÷ 5 million
10 ÷ 5

p = 1 million
2

1 million ÷ 2 × 3 = 750 000
2

The value of p is 1 million.
2

€€Use small number values to explain how to solve mixed operations involving
1.2.1 unknown. 37

7 y + 3 × 0.2 million = 900 000 Simple example. First, multiply.
What is the value of y? y + 2 × 3 = 7 Then, relate
y + 6 = 7 addition with
y + 3 × 0.2 million = 900 000 y = 7 − 6 subtraction to

y + 0.6 million = 0.9 million solve.

y = 0.9 million – 0.6 million Simple example.
m − 2 × 4 = 5
y = 0.3 million m − 8 = 5
m = 5 + 8
0.3 million + 3 × 0.2 million = 900 000
×
The value of y is 0.3 million.

8 m – 1 million × 2 = 0.5 million
10

What is the value of m?

m – 1 million × 2 = 0.5 million
10

m – 2 million = 5 million
10 10

m = 5 million + 2 million
10 10

m = 7 million
10

7 million – 1 million × 2 = 0.5 million
10 10

The value of m is 7 million.
10

Solve this.

s × 6 ÷ 7 = 0.24 million
s = 0.24 million ÷

s = million

THINK Given p × q = 7 83 million and w + p × q = 9.09 million.
SMART Find the value of w.

€€Carry out suitable simulation to reinforce pupils' understanding 1.2.1
38 in finding unknown.

9 k − 2.86 million ÷ 22 = 0.37 million
What is the value of k in fraction of a million?

Step 1 Step 2

0 . 1 3 million k − 0.13 million = 0.37 million

22 2 . 8 6 million k = 0.37 million + 0.13 million
−0
28 = 0.50 million 1
−2 2
66 Step 3 0 . 3 7 million
− 66 + 0 . 1 3 million
0
0.5 million = 50 million 0 . 5 0 million
100

= 5 ÷ 5 million
10 ÷ 5

= 1 million
2

1 million − 2.86 million ÷ 22 = 0.37 million
2

The value of k is 1 million.
2

10 4.3 million + h ÷ 3 = 5.99 million Step 2
What is the value of h ?
h ÷ 3 = 1.69 million
Step 1 h = 1.69 million × 3
h = 5.07 million
4.3 million + h ÷ 3 = 5.99 million
h ÷ 3 = 5.99 million − 4.3 million
h ÷ 3 = 1.69 million

5. 9 9 million 22
– 4. 3 0 million
1 .6 9 million
1 . 6 9 million ×3

5.0 7 million

4.3 million + 5.07 million ÷ 3 = 5.99 million 39

The value of h is 5.07 million.

€€Encourage pupils to use different ways to solve mixed operations
1.2.1 involving unknown.

11 ( p + 0.006 million) × 4 = 36 000 Relate multiplication with division.
Calculate the value of p. Relate addition with subtraction.

Step 1 Step 2

0.006 million = 0.006000 × 1 000 00 0 (p + 0.006 million) × 4 = 36 000

= 6 000 p + 0.006 million = 36 000 ÷ 4

p + 6 000 = 9 000

p = 9 000 − 6 000

p = 3 000

( 3 000 + 0.006 million) × 4 = 36 000

The value of p is 3 000.

12 (2 190 million – m ) ÷ 1 000 = 500 Step 2

Find the value of m.

Step 1

2 190 million = 2.9 million (2 190 million – m) ÷ 1 000 = 500

= 2.900000 × 1 000 000 2 190 million – m = 500 × 1 000
= 2 900 000 2 190 million – m = 500 000



Relate division with 2 190 million – 500 000 = m
multiplication.

2 900 000 – 500 000 = m

2 400 000 = m

(2 190 million – 2 400 000 ) ÷ 1 000 = 500 1.2.1

The value of m is 2 400 000.

€€Guide pupils to understand how to solve unknown involving brackets.
40

LET’S DO IT

1 Solve and write answers in whole numbers.

a 0.9 million – 800 000 + 1.7 million = b 2.5 million + 500 000 – 1.3 million =

c 9 000 000 – 3 54 million + 1.3 million = d 3 700 000 + 5 21 million – 7.375 million =

e 0.3 million + 1 900 × 6 = f 1.2 million + 1.08 million × 3 =

g 3 million + 2.07 million ÷ 3 = h 3 million ÷ 2 + 4 110 million =
5
4
j 9.825 million – 5 × 1.94 million =
i 1.09 million – 324 000 × 2 =

k 81514 41m×mil(li0ioll.in4on×m–3ill1i÷o.6n5m+=il1l3i0onm÷illi5 on=) = l 0.2 million – 0.875 million ÷ 8 =
m
o n 19 × 0.028 million ÷ 4 =
p (3 25 million – 2.84 million) × 10 =
q (480 000 – 2 million) ÷ 20 = r (6.904 million + 2 190 million) ÷ 15 =
5

2 Solve and write answers in decimal of a million.

a 4.7 million – 100 000 + 2 110 million = b 0.8 million + 900 000 × 6 =

c 2 51 million + 4.02 million ÷ 6 = d 8.071 million – 2 × 0.92 million =

e 5 1 million – 3.003 million ÷ 3= f 3 million × 4 ÷ 5 =
g (0.75 million + = 4
4 3 h (4 83 million – 1.9 million) ÷ 9 =
5 million)
7×

3 Solve and write answers in fraction of a million.

a 8.1 million + 0.9 million – 3 51 million = b 0.03 million × 12 + 0.14 million =

c 6 45 million + 5.6 million ÷ 7 = d 5.14 million – 5 × 0.488 million =

e 3.51 million – 1.21 million ÷ 11 = f 3 million ÷ 8 × 24 =
4
g (3 87 million – 3.85 million) × 100 = h (0.8 million + 2 52 million) ÷ 32 =

4 Find the values of p. b p – 6 41 million = 1 21 million
a p + 0.35 million = 1.4 million d p ÷ 2 = 5 000 000
c 9 × p = 0.027 million

e p – 3 million + 0.08 million = 115 096 f p ÷ 7 × 4 = 0.065 million
5
g p + 4 × 0.3 million = 1 85 million 4
h p – 5 million × 6 = 2.09 million

i p + 1.04 million ÷ 16 = 1 000 000 j (1 170 million – p) ÷ 10 = 0.081 million

1.2.1 41

PRIME NUMBERS AND COMPOSITE NUMBERS

1

1 2 3 4 5 6 7 8 9 10

I use yellow for prime numbers. 11 12 13 14 15 16 17 18 19 20
A prime number is only divisible by 21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
itself and number 1.

41 42 43 44 45 46 47 48 49 50

What about numbers Those are composite numbers
that are not coloured? except number 1.

2 9 Number 9 is a composite
9÷1=9 number because it is
7 9÷9=1
7÷1=7 9÷3=3 divisible by number 1, itself,
7÷7=1 and other numbers without

any remainder.

I am a prime number. Composite numbers TIPS
I can only be divided are numbers that are
by the number 1 and not prime numbers,

myself. 0, and number 1.

€€Recall pupils' previous knowledge on prime numbers before introducing 1.3.1
42 composite numbers.