Teaching of Elementary Mathematic

1. COURSE GUIDE
ix
COURSE GUIDE DESCRIPTION
You must read this Course Guide carefully from the beginning to the end. It tells
you briefly what the course is about and how you can work your way through the
course material. It also suggests the amount of time you are likely to spend in
order to complete the course successfully. Please keep on referring to the Course
Guide as you go through the course material as it will help you to clarify important
study components or points that you might miss or overlook.
INTRODUCTION
HBMT3103 Teaching of Elementary Mathematics Part III is one of the
courses offered by the Faculty of Education and Languages at Open University
Malaysia (OUM). This course is worth 3 credit hours and should be covered over
8 to 15 weeks.
COURSE AUDIENCE
This course is offered to students undertaking the Bachelor of Teaching (with
Honours) programme, majoring in Mathematics.
As an open and distance learner, you should be able to learn independently and
optimise the learning modes and environment available to you. Before you begin
this course, please ensure that you have the right course materials, understand the
course requirements, as well as know how the course is conducted.
STUDY SCHEDULE
It is a standard OUM practice that learners accumulate 40 study hours for every
credit hour. As such, for a three-credit hour course, you are expected to spend 120
study hours. Table 1 gives an estimation of how the 120 study hours could be
accumulated.

2. COURSE GUIDE
x
Table 1: Estimation of Time Accumulation of Study Hours
Study Activities Study
Hours
Briefly go through the course content and participate in initial discussion 3
Study the module 60
Attend 3 to 5 tutorial sessions 10
Online participation 12
Revision 15
Assignment(s), Test(s) and Examination(s) 20
Total Study Hours 120
COURSE OUTCOMES
By the end of this course, you should be able to:
1. Explain the concepts, definitions, rules and principles related to numbers,
operations, money, time, fractions, decimals, measurements and space;
2. Apply effective strategies in teaching the stipulated content area;
3. Use the language of mathematics effectively; and
4. Conclude on the importance and beauty of mathematics.
COURSE SYNOPSIS
This course consists of 10 topics which will assist you to achieve the identified
objectives. Each of these topics is described briefly as follows:
Topic 1 is a continuation of the same topic learned in Teaching of Elementary
Mathematics Part II. The operations cover the content area of whole numbers of
up to 100 000. This topic is presented in the simplest form. It begins with the
reading and writing of whole numbers followed by learning the place value of the
numbers within the same range. You are guided to learn place value and how to
round off whole numbers. The next part in this topic deals with addition and
subtraction operations of two to four numbers to the highest total of 100 000.
Mixed operations that involve addition and subtraction will also be introduced
here. Multiplication and division is the next topic of discussion. For these four

3. COURSE GUIDE
xi
basic operations, some real-life examples are shown to apply these concepts and
deliver them to your class efficiently.
Topic 2 discusses fraction. Fraction is used in almost every type of measurement –
time, weight, length, distance and others. Fraction, addition and subtraction of
fractions, and multiplication and division of fractions are presented in this topic.
Topic 3 demonstrates how to read and write a decimal number in words. You will
further learn how to convert fractions to decimals and vice versa, mixed numbers
to fractions and vice versa, comparing and arranging decimals numbers. This topic
also discusses the addition, subtraction, multiplication and division of two decimal
numbers. Lastly, you will learn how to write multiplication and division of
decimals in the standard written method.
Topic 4 illustrates how to read and write the value of money. We also discuss
addition, subtraction, multiplication and division involving money. Various
activities are planned for you to effectively teach mixed operations in solving
problems involving money.
Topic 5 demonstrates the basic operations of units of time. It is very important to
manage time so that we can schedule our time and plan our tasks properly and
effectively. This topic highlights how to teach reading and writing the time,
relationship between units of time, addition and subtraction involving time,
multiplication and subtraction involving time. Also included is understanding the
duration of time.
Topic 6 discusses units of length. You will learn about the measurements of
lengths in standard units and also the relationship between these units.
Mathematical operations such as addition, subtraction, multiplication and division
are applied on them. Lastly, we will look at how to use these skills in solving
everyday life problems.
Topic 7 explains the relationship between units of mass and how to convert the
units from one to another. Once you have gained the preliminary knowledge, you
will be able to do simple operations just like in the previous topic but now
involving mass. In the last part of this topic, you will see some examples of
everyday problems.
Topic 8 covers how to measure volume of liquid in standard units, understand the
relationship between units of volume of liquid and solving problems by using
addition, subtraction, multiplication and division.

4. COURSE GUIDE
xii
Topic 9 is devised for teachers to teach a lesson on object of two and three-dimensional
spaces. First, you will learn how to identify and measure two-dimensional.
Next, you will learn about perimeter and area and also to calculate
them. Lastly, you will learn how to identify three-dimensional spaces such as
cubes and cuboids. Finding volumes of cubes and cuboids are also covered in this
section.
Topic 10 discusses pictographs and bar graphs. You will learn how to describe
and interpret them and also to construct them to display data. The last section
shows some problem-solving exercise involving pictographs and bar graphs based
on real life situations.
TEXT ARRANGEMENT GUIDE
Before you go through this module, it is important that you note the text
arrangement. Understanding the text arrangement will help you to organise your
study of this course in a more objective and effective way. Generally, the text
arrangement for each topic is as follows:
Learning Outcomes: This section refers to what you should achieve after you
have completely covered a topic. As you go through each topic, you should
frequently refer to these learning outcomes. By doing this, you can continuously
gauge your understanding of the topic.
Self-Check: This component of the module is inserted at strategic locations
throughout the module. It may be inserted after one sub-section or a few sub-sections.
It usually comes in the form of a question. When you come across this
component, try to reflect on what you have already learnt thus far. By attempting
to answer the question, you should be able to gauge how well you have understood
the sub-section(s). Most of the time, the answers to the questions can be found
directly from the module itself.
Activity: Like Self-Check, the Activity component is also placed at various
locations or junctures throughout the module. This component may require you to
solve questions, explore short case studies, or conduct an observation or research. It
may even require you to evaluate a given scenario. When you come across an
Activity, you should try to reflect on what you have gathered from the module and
apply it to real situations. You should, at the same time, engage yourself in higher
order thinking where you might be required to analyse, synthesise and evaluate
instead of only having to recall and define.

5. COURSE GUIDE
xiii
Summary: You will find this component at the end of each topic. This component
helps you to recap the whole topic. By going through the summary, you should be
able to gauge your knowledge retention level. Should you find points in the
summary that you do not fully understand, it would be a good idea for you to
revisit the details in the module.
Key Terms: This component can be found at the end of each topic. You should go
through this component to remind yourself of important terms or jargon used
throughout the module. Should you find terms here that you are not able to
explain, you should look for the terms in the module.
References: The References section is where a list of relevant and useful
textbooks, journals, articles, electronic contents or sources can be found. The list
can appear in a few locations such as in the Course Guide (at the References
section), at the end of every topic or at the back of the module. You are
encouraged to read or refer to the suggested sources to obtain the additional
information needed and to enhance your overall understanding of the course.
PRIOR KNOWLEDGE
None.
ASSESSMENT METHOD
Please refer to myVLE.
REFERENCES
References are listed at the end of each topic.

6. COURSE GUIDE
xiv
TAN SRI DR ABDULLAH SANUSI (TSDAS) DIGITAL
LIBRARY
The TSDAS Digital Library has a wide range of print and online resources for the
use of its learners. This comprehensive digital library, which is accessible through
the OUM portal, provides access to more than 30 online databases comprising
e-journals, e-theses, e-books and more. Examples of databases available are
EBSCOhost, ProQuest, SpringerLink, Books24x7, InfoSci Books, Emerald
Management Plus and Ebrary Electronic Books. As an OUM learner, you are
encouraged to make full use of the resources available through this library.

7. HBMT3103
TEACHING OF
ELEMENTARY
MATHEMATICS
PART III
Mahmood Othman
Goh Thian Hee

8. Project Directors: Prof Dr Mansor Fadzil
Prof Dr Widad Othman
Open University Malaysia
Module Writers: Dr Mahmood Othman
Goh Thian Hee
Institut Pendidikan Guru
Kampus Pulau Pinang
Moderators: Siti Farina Sheikh Mohamed
Goh Thian Hee
Institut Pendidikan Guru
Kampus Pulau Pinan
Developed by: Centre for Instructional Design and Technology
Open University Malaysia
Printed by: Meteor Doc. Sdn. Bhd.
Lot 47-48, Jalan SR 1/9, Seksyen 9,
Jalan Serdang Raya, Taman Serdang Raya,
43300 Seri Kembangan, Selangor Darul Ehsan
First Edition, April 2008
Second Edition, August 2013
Copyright © Open University Malaysia (OUM), August 2013, HBMT3103
All rights reserved. No part of this work may be reproduced in any form or by any means
without the written permission of the President, Open University Malaysia (OUM).

9. Table of Contents
Course Guide ix- xiv
Topic 1 Whole Numbers 1
1.1 Reading and Writing Whole Numbers 2
1.2 Place Value 5
1.3 Rounding Off Whole Numbers 9
1.4 Addition and Subtraction within the Range of 100,000 11
1.4.1 Adding Numbers of Two or More Digits 12
1.4.2 Subtract One or Two Numbers 15
1.5 Multiplication and Division within the Range of 100,000 19
1.5.1 What is Multiplication? 19
1.5.2 Multiply Numbers with Two or More Digits 24
1.5.3 What is Division? 25
1.5.4 Divide by One, Two or Three Digit Numbers 26
1.6 Multiplication and Division in Everyday Life 29
1.7 Mixed Operations with Addition and Subtraction 31
Summary 35
Key Terms 35
References 36
Topic 2 Fractions 37
2.1 Idea of Fraction 38
2.1.1 Proper Fractions 38
2.1.2 Improper Fractions 40
2.1.3 Comparing and Arranging Fractions 40
2.1.4 Equivalent Fractions 42
2.2 Addition and Subtraction of Fractions 45
2.2.1 Adding and Subtracting Fractions with the Same
and Different Denominators 45
2.2.2 Solving Problems Involving Fractions 49
Summary 53
Key Terms 53
References 53

10. TABLE OF CONTENTS
iv
Topic 3 Decimals 54
3.1 Decimal Numbers 55
3.1.1 Converting Fractions to Decimals and Vice Versa 58
3.1.2 Converting Mixed Numbers to Fractions and
Vice Versa 60
3.2 Addition and Subtraction of Decimals 62
3.2.1 Addition of Decimal Numbers 62
3.2.2 Subtraction of Decimal Numbers 63
3.2.3 Addition and Subtraction of Three Decimal Numbers 64
3.3 Multiplication and Division of Decimals 66
3.3.1 Multiplication of Decimals 66
3.3.2 Division of Decimals 68
3.3.3 Multiplication and Division of Decimals in
Standard Written Method 69
Summary 73
Key Terms 73
References 73
Topic 4 Money 74
4.1 Reading and Writing the Value of Money 75
4.2 Addition and Subtraction Involving Money 78
4.3 Multiplication and Division Involving Money 80
4.3.1 Multiplication Involving Money 80
4.3.2 Division Involving Money 82
4.4 Mixed Operations Involving Money 85
4.5 Rounding Off Money to the Nearest Ringgit 87
Summary 89
Key Terms 90
References 90
Topic 5 Time 91
5.1 Minutes, Hours, Days, Months, Years and Decades 92
5.1.1 Relationship between Units of Time 93
5.1.2 Time Scheduling 94
5.1.3 Reading a Calendar 95
5.1.4 Converting Units of Time 97
5.2 Addition and Subtraction Involving Time 105
5.2.1 Addition Involving Units of Time 105
5.2.2 Subtraction Involving Units of Time 108

11. TABLE OF CONTENTS
v
5.3 Multiplication and Division Involving Time 111
5.3.1 Multiplication Involving Units of Time 111
5.3.2 Division Involving Units of Time 112
5.3.3 Solving Problems Involving Time 114
5.3.4 Time Duration 116
Summary 120
Key Terms 121
References 121
Topic 6 Length 122
6.1 Measuring Lengths 123
6.2 Relationship between Units of Length 124
6.3 Convert Units of Length 126
6.4 Addition and Subtraction Involving Units of Length 130
6.5 Multiplication and Division Involving Units of Length 135
6.6 Solving Problems Involving Length 142
Summary 144
Key Terms 144
References 144
Topic 7 Mass 145
7.1 Measuring Mass 145
7.2 Relationship between Kilograms and Grams 147
7.3 Addition and Subtraction Involving Units of Mass 151
7.4 Multiplication and Division Involving Units of Mass 155
7.5 Solving Problems Involving Mass 160
Summary 163
Key Terms 164
References 164
Topic 8 Volume of Liquid 165
8.1 Measuring Volume of Liquid 166
8.2 Relationship between Units of Volume of Liquid 168
8.3 Addition and Subtraction Involving Units of Volume of
Liquid 171
8.4 Multiplication and Division Involving Units of Volume of
Liquid 178
8.5 Solving Problems Involving Units of Volume of Liquid 184
Summary 187
Key Terms 187
References 187

12. TABLE OF CONTENTS
vi
Topic 9 Shape and Space 188
9.1 Two-Dimensional Space 188
9.1.1 Identifying Two-Dimensional (2D) Shapes 189
9.1.2 Measuring and Identifying Dimensions of Two
Dimensional Shapes 192
9.2 Perimeter and Area 193
9.2.1 Understanding the Meaning of Perimeter 193
9.2.2 Understanding the Meaning of Area 197
9.2.3 Calculate the Area 198
9.3 Three-Dimensional Space 201
9.3.1 Identify Dimensions of Cubes and Cuboids 201
9.3.2 Unit Cubes 202
9.3.3 Volume of Cubes and Cuboids 203
Summary 207
Key Terms 207
References 208
Topic 10 Data Handling 209
10.1 Pictographs 210
10.1.1 Describing and Interpreting Pictographs 210
10.1.2 Constructing Pictographs 214
10.2 Bar Graphs 217
10.2.1 Describing and Interpreting Bar Graphs 217
10.2.2 Constructing Bar Graphs 220
10.3 Solving Problems Involving Pictographs and Bar Graphs 224
Summary 229
Key Terms 230
References 230

13. Topic
1
Whole
Numbers
LEARNING OUTCOMES
By the end of this topic, you should be able to:
1. Recognise whole numbers;
2. Identify place value of numbers up to 100,000;
3. Compare and round off numbers;
4. Add, subtract, multiply and divide within the range of 100,000;
5. Apply addition, subtraction, multiplication and division in everyday
life; and
6. Perform mixed operations involving addition and subtraction.
INTRODUCTION
Welcome to the first topic of this module. You will begin this topic with the
reading and writing of whole numbers within the range of 100,000. Next, you will
learn about place value of numbers and rounding off numbers.
The next part in this topic deals with addition and subtraction operations of two to
four numbers to the highest total of 100,000. Mixed operations that involve
addition and subtraction will be introduced here. Multiplication and division are
the next topics of discussion. You will find that multiplication is the repeated
addition of a unit. On the other hand, division involves determining how many
times one number is contained in another. Real-life examples of these four basic
operations are shown to enable you to apply these concepts and deliver them to
your class efficiently.

14. TOPIC 1 WHOLE NUMBERS
2
READING AND WRITING WHOLE
NUMBERS
1.1
Let us start off this module by looking at how to read and write whole numbers.
This involves reading and writing whole numbers from 1 up to 100,000. How do
you start off these lessons in your class? You explain to students the meaning of
whole numbers and ask them where they can see and experience numbers. Then
you can begin these lessons by doing some simple activities such as:
Counting the total number of thumb tacks in the classroom;
Counting the total number of pencils that pupils have; and
Counting the total number of books in the classroom.
(a) Recognising Whole Numbers
Based on the previous activities, we can conclude that the students are now
familiar with whole numbers. This will help them to read the numbers.
However, before they can read whole numbers, they have to recognise them.
Basically, recognising whole numbers is done through counting the numbers
in groups.
Let us look at a simple example of counting numbers in groups of ten
thousands.
(i) Show students a picture of ten baskets (refer to Figure 1.1), which
contain ten thousand rambutans each.
(ii) Ask students to count one by one until the tenth basket.

15. TOPIC 1 WHOLE NUMBERS
3
Figure 1.1: Sample exercise
(iii) Ask students to add up all the rambutans.
(iv) Tell them how ten baskets of ten thousand rambutans make a hundred
thousand.
Alternatively, you can explain that ten times ten thousand rambutans is
equal to one hundred thousand rambutans.
10,000 + 10,000 + 10,000 + 10,000 + 10,000 + 10,000 + 10,000 +
10,000 + 10,000 + 10,000 = 100,000
(v) Then, continue the exercise with different sets of number groups:
hundreds and thousands. Repeat the exercise until the students
understand the process of counting.
(b) Reading and Writing Whole Numbers up to 100,000
Now, how will you teach your students how to read and write whole
numbers up to 100,000? Start off by showing some examples of numbers
that appear in our daily lives such as postcodes in letters, receipts, bills and
etc. Let the students see and compare for themselves the differences in these
numbers by just looking at the number of digits. Then, give them a general
idea of how to read and write by providing suitable examples. Initially,

16. TOPIC 1 WHOLE NUMBERS
4
students may seem confused and find it difficult to understand. But go
through it anyway as the next topic on place values would be able to
enhance their skills in reading and writing.
Figure 1.2 (a): Example of postcode
Figure 1.2 (b): Example of a cheque

17. TOPIC 1 WHOLE NUMBERS
5
For example, how do we read the postcode in Figure 1.2 (a)? The postcode
is read as forty thousand four hundred and fifty On the other hand, the
amount on the cheque in Figure 1.2 (b) is read as Ringgit Malaysia twenty
one thousand three hundred and twenty three only.
Now that you have shown students some examples of reading numbers,
guide them in writing the numbers. Writing numbers means the changing of
words into numbers.
Try these activities in order to teach your students how to write numbers.
(i) Give your students a number in words: ninety five thousand, two
hundred and forty three. Explain in a simple way as follows:
Read the numbers until thousand, for example, ninety five
thousand. Write it in numbers and it will be 95,000. Then
Read the last few numbers, for example, two hundred and forty
three. Write it in numbers and it will be 243.
Add the two numbers: 95,000 + 243 = 95,243.
(ii) Give another example for the students to try out. Guide them through it
first and explain that this will be further explained later.
PLACE VALUE
Recognising the place value of a number is very important and is done by reading
the number. By knowing the place value of numbers, we are able to compare
them.
(a) Knowing Place Value of Numbers Up to 100,000
(i) Give your students a number in words such as sixty two thousand,
one hundred and thirty four. Ask them to read the number and show
them the way to write the number as illustrated in Table 1.1.
1.2

18. TOPIC 1 WHOLE NUMBERS
6
Table 1.1: Sample Exercise
Thousand Hundred Ten One
Ten One
6 2 1 3 4
(ii) Provide an empty table like the one above to the students. Read to the
students a number in words. For example, sixty two thousand, one
hundred and thirty four. Ask them to write the number in the table
provided.
(iii) Test their understanding again by writing the number 67,321 on the
board and reading it loudly as sixty seven thousand, three hundred
and twenty one. Then, fill up another table with the respective digits.
Lastly, ask the students to pronounce the number in words. The digit 6
has the value of 60,000 in number. It is spelt as sixty thousand. Next,
you can continue with thousands, hundreds, tens and ones. You can
check their answers by using these guidelines:
Combine all digits in words and add the word ‘and’ after hundred.
Hence, 67,321 is pronounced as sixty seven thousand, three
hundred and twenty one.
ACTIVITY 1.1
Convert the following words into numbers:
1. Seventeen thousand two hundred and twenty.
2. Nine thousand six hundred and fifty three.
(b) Comparing and Arranging Numbers
Before students can start to learn about arranging numbers, they need to
know how to compare a set of two or more numbers. When we compare
numbers, we want to know which number is bigger and which is smaller.
Once the values of bigger and smaller numbers are distinguished, they can
be arranged in ascending order from smaller to bigger values or in
descending order from bigger to smaller values. Comparison plays an
important role in arranging the numbers. There are two ways to arrange
numbers, as explained in Table 1.2.

19. TOPIC 1 WHOLE NUMBERS
7
Table 1.2: Two Methods of Arranging Numbers
Method Description
Ascending or Count On Arranging of numbers from small to big
Descending or Count Back Arranging of numbers from big to small
(i) Comparing Numbers
You can use the following algorithm as a guide to compare two
numbers.
Algorithm for Comparing the Digit Place Value (DPV)
IF DPV for both data is equal
Then bigger numbers = Number with bigger first digit number
(Compare from left to right)
Example 1: Comparing Numbers of Equal DPV
Compare these numbers:
87,423 79,324
Follow the steps below:
Step 1: Is Digit Place Value (DPV) for both data equal?
Answer is YES
Step 2: Compare DPV from left to right for both data (IF same DPV
move from left to right). DPV of first data, 8, is greater than first DPV
of second data, 7. Therefore, 87,423 is greater than 79,324.
Example 2: Comparing Numbers of NOT Equal DPV
Compare these numbers:
87,423 9,324
ELSE
IF digit place value for both data is NOT equal
Then bigger numbers = The number that has bigger DPV

20. TOPIC 1 WHOLE NUMBERS
8
Follow the steps below to get the answer:
Step 1: Is Digit Place Value for both data equal?
Answer is NO
87,423 has 5 DPV
9,324 has 4 DPV
Hence, 87,423 is greater than 9,324.
(ii) Arranging Numbers
Let us look at how numbers can be arranged. There are two ways of
arranging numbers – ascending and descending.
Arranging numbers in an ascending order is done by listing (count on)
in line numbers from smaller to bigger values. In contrast, when
arranging numbers in descending order, the numbers are (count back)
listed in line from bigger to smaller values. To visualise this, look at
Figure 1.3.
Figure 1.3: Ascending vs. Descending
Steps to follow for Count On
Step 1: Compare the numbers
Step 2: Select the smallest number
Step 3: Place the smallest number on the left
Step 4: Look at the other numbers and repeat Step 3 until ALL data
have been listed in Line

21. TOPIC 1 WHOLE NUMBERS
9
Example 3:
Count On
59,820 58,820 57,820 56,820 55,820 54,820
Counting in a descending order (count back) also involves four steps
as below:
Steps to follow for Count Back
Step 1: Compare the numbers
Step 2: Select the biggest number
Step 3: Place on the right a smaller number
Step 4: Look at the other numbers and repeat Step 3 until ALL data
have been listed in Line
Example 4:
28,982 28,972 28,962 28,952 28,942 28,932
Count Back
ROUNDING OFF WHOLE NUMBERS
1.3
Rounding off numbers is a way to estimate or approximate a whole number to the
nearest place digit. For example, you may need to round off the figure of today’s
total sales. Your mother may want to round off the figures of expenditure on
electricity bill, food, leisure and so on. Bear in mind that rounding off whole
numbers is not exact. It is a round number. When the actual number of objects is
not important, you can round off whole numbers to figure out an estimated
amount of the quantity.
Firstly, how can we describe rounding off numbers? Rounding off numbers means
you want to find the nearest approximation to a given number.
For example, you line up a list of numbers between 20 and 30. Now, you pick 27
as the number to be rounded off. Ask your students whether 27 is nearer to
20 or 30.

22. TOPIC 1 WHOLE NUMBERS
10
The students will notice that 30 is closer to 27 compared to 20. Therefore, 27
rounded off to the nearest ten is 30.
How about rounding off a whole number to a given place value? The following
steps may be used to round off a whole number to a specific place value. See
Table 1.3.
Table 1.3: Steps for Rounding Off
Step 1 Locate the digit in the rounding place. Look at the right digit.
Step 2 Is the digit greater or lesser than
5?
If greater than 5, then add 1 to the
rounding digit; otherwise, add 0.
Step 3 Replace all numbers by zeros to the right digit
Round Off Numbers to the Nearest Ten, Hundred, Thousand and Ten
Thousand
How do we round off 53 to the nearest ten? Follow the steps below:
(a) First, you have to locate the digit in the rounding place, that is, ten: 53.
Then, look at the digit at the right, 3.
(b) Digit 3 is less than 5, so we add 0 to 5 (rounding digit).
(c) Replace three with zero to the right.
The answer is 50.
Example 5:
Round off 452 to the nearest hundred.
(a) First, you have to locate the digit in the rounding place, that is, hundred: 4
52. Then, look at the digit at the right, 5.
(b) Digit 5 is equal to 5, then add 1 to 4 (rounding digit).
(c) Replace with the digits to the right with zeros (0).
The answer is 500.

23. TOPIC 1 WHOLE NUMBERS
11
Example 6:
Round off 94,851 to the nearest thousand.
(a) First, you have to locate the digit in the rounding place that is thousand: 94
851. Then, look at the digit at the right of 4, which is 8.
(b) Digit 8 is greater than 5, add 1 to 4 (rounding digit).
(c) Replace the digits to the right with zeros (0).
The answer is 95,000.
ACTIVITY 1.2
Round off to the nearest:
1. Ten 3. Thousand
56 5,236
644 32,644
9,878 90,878
2. Hundred 4. Ten Thousand
156 54,036
5,110 27,644
8,779 99,866
ADDITION AND SUBTRACTION WITHIN
THE RANGE OF 100,000
1.4
This section will begin with addition operations of two to four numbers up to the
highest total of 100,000. Next, you will perform subtraction of two numbers
within 100,000. Lastly, you will learn how to do subtraction in the range of
100,000. For each operation, there are some real-life examples to help you
understand and apply these concepts.

24. TOPIC 1 WHOLE NUMBERS
12
1.4.1 Adding Numbers of Two or More Digits
How do we add numbers of two or more digits? To add numbers of two or more
digits, follow these two steps:
Step 1: The numbers of place value are arranged in the same column.
Step 2: Add from the right to the left column. Leave one digit of the sum and
carry whatever number more than one digit to the left column.
Example 7:
A storekeeper needs to count the total number of oranges and grapes that he has.
There are 2,379 oranges and 23,034 grapes in his store. What is the total number
of fruits?
First, arrange the numbers in the same column so that the ones, tens, hundreds,
etc., place values are in the same column. Note that it does not matter which
number is above or below. Show the alternative way to the students.

25. TOPIC 1 WHOLE NUMBERS
13
Example 8:
Salim works in a bookstore. His boss needs to know the total number of items that
they have. The items that they have are 3,124 books, 13,824 magazines and
23,512 exercise books. Sum up the items that he has.
First, arrange the numbers in the same column so that all ones, tens, hundreds,
thousands and ten thousands place values are in the same column as shown below:
Addition is normally used in our daily life, like paying for the things that we buy
at the cashier counter. As a teacher, you should explain the importance of addition
in our real lives. By doing this, the pupils will understand better and appreciate the
importance of mathematics. The next example will illustrate this point.

26. TOPIC 1 WHOLE NUMBERS
14
Example 9:
In July 2007, 21,991 people visited Langkawi Island and 49,889 people visited
Padang Besar, Perlis. Find the total number of tourists in July 2007.
To guide pupils in answering this question, ask them to do some analysis as
follows:
What is given? Number of tourists visiting Langkawi Island (21,991) and
Padang Besar (49,889).
Next, what should be done? Find the total number of tourists in July 2007.
Operation:
You can solve this by writing the following: 21,991 + 49,889 = ?
Or
1 1 1 1
2 1 9 9 1
4 9 8 8 9
7 1 8 8 0
Checking the Answer:
To check the answer by approximation, you just round off each number to the
largest place value.
Example: 20,000 + 50,000 = 70,000, which is close to the actual answer.
SELF-CHECK 1.1
You are given RM17,577 and RM4,944. Find the total amount of money
and check your answer with your classmates.

27. TOPIC 1 WHOLE NUMBERS
15
ACTIVITY 1.3
1. Find the sum of
(a) 3,531 and 2,412
(b) 67,532 and 24,104
(c) 50,123 and 871 and 1,234
2. Based on the digits below, form the largest and the smallest numbers.
Hence, find the sum of the numbers formed.
8 9 0 5 1
3. Find the missing number: 32,010 + 51,000 + ? = 83,549
4. Johari is carrying out his daily inspection of inventory of certain
books. In all, there are 2,345 exercise books, 64,333 primary school
books and 56,879 secondary books. What is the total number of
books?
5. Putra Palace in Kangar, Perlis has 72 single rooms, 120 double
rooms and 30 suites. How many rooms are there altogether?
1.4.2 Subtract One or Two Numbers
This section shows subtraction of numbers within the range of 100,000. This is
done by subtracting the smaller number from a bigger number using the following
steps:
Step 1: Arrange the numbers according to the place value, with the bigger
number on top.
Step 2: Subtract digits from the right column to the left.
Step 3: To subtract a larger digit from a smaller digit in a column, borrow 1
from the left. This means borrowing one group of 10; thus, add 10 to the
top digit in the given column, then continue subtracting.

28. TOPIC 1 WHOLE NUMBERS
16
Example 10:
Subtract 65,425 from 94,568.
Arrange the numbers in columns. Start subtracting from right to left. If the lower
number is less than the upper number, subtract as usual.
8 14
9 4 5 6 8
6 5 4 2 5
2 9 1 4 3
After completing the subtraction, it is wise to check your answer using
approximation. Checking: Round up to the nearest thousands.
9 5 0 0 0
6 5 0 0 0
3 0 0 0 0
One of the most basic examples of subtraction is to know how much is left of your
salary after you have spent half of it. You can relate the use of subtraction to real-life
situations to help your students understand the concept better.
Example 11:
There are 69,000 football match tickets to be sold. Last week, 22,358 tickets were
already sold. How many tickets are left?
8 9 9 10
6 9 0 0 0
2 2 3 5 8
4 6 6 4 2
In the thousands, 4 is less than 5, borrow 1 from
group of 10 from 9, 9-1 = 8, so 10 + 4 = 14. Next
14 – 5 = 9. 1 has been taken away from 9 leaving
8, so 8 – 6 = 2.
The approximation value is 30,000 which is close
to the exact value 29,143. So the exact answer is
reasonable.
Arrange in columns. In column ones, tens and
thousands 3, 5 and 8 are greater than 0, so perform
the following steps. Borrow 1 group of 10 from 9,
9-1 = 8, add 10 + 0 = 10; borrow 1 group of 10
from this 10, hundreds column, 10-1 = 9, add to
tens column 10 + 0 = 10; borrow 1 group of 10
from this 10 tens column, 10-1 = 9, add to ones
column 10 + 0 = 10. Next 10 – 8 = 2.

29. TOPIC 1 WHOLE NUMBERS
17
Example 12:
Aminah runs a catering business. She bought plates, bowls and cups totalling 87
645 pieces. If there are 8 145 plates and 25 346 cups, how many bowls does she
have?
In this problem, you are given the total number of plates, bowls and cups. Then,
you are given also the total number of plates and cups respectively. To find the
number of bowls available, you have to subtract these numbers from the total.
7 17 5 13 15
8 7 6 4 5
8 1 4 5
2 5 3 4 5
5 4 1 5 5
So the number of bowls Aminah bought is 54 155.
Note: It is only critical that the biggest number
must be placed on top when you do the deduction
(shown in Example 12). The arrangement order of
the other two numbers which are deducted are not
of importance.
SELF-CHECK 1.2
1. Calculate 18,564 – 8,251 – 2,334 = _______________.
2. Azizah collected 2,855 seeds, Ramlah collected 2,624 seeds while
Jamnah collected 5,252 seeds. What is the difference in number of
seeds between:
(a) Azizah and Ramlah?
(b) Azizah and Jamnah?
(c) Jamnah and Ramlah?

30. TOPIC 1 WHOLE NUMBERS
18
ACTIVITY 1.4
1. Find the difference of:
(a) 23,000 – 2,924 = __________
(b) 99,089 – 26,866 = _________
(c) 70,000 – 9,318 = __________
2. Subtract:
(a) 37,156 – 6,963 = ________
(b) 31,350 – 8,905 = ________
(c) 100,000 – 65,000 – 15,000 = ________
3. Fill in the boxes with the correct numbers:
(a)
6 4 6
1 5 4 2 2
4 9 4 5
(b)
2 5 2 6 2
1 0 4 2 1
4 4 1
4. Solve the following problems:
(a) Mariam sells nasi lemak. In the first month, she obtained a
profit of RM1,520. In the second month, she made RM2,750
while in the third month she made RM152 less than in her
second month. What is the total profit she made within the
three months?
(b) Jason takes home a salary of RM5,630 a month. Each month,
he will spend RM500 on food, RM250 on petrol, RM480 on
utility bills and RM988 on miscellaneous items. How much
money has he left for his own savings?

31. TOPIC 1 WHOLE NUMBERS
19
MULTIPLICATION AND DIVISION WITHIN
THE RANGE OF 100,000
This section discusses multiplication and division involving whole numbers up to
100,000. Before you begin each part, explain in detail what multiplication and
division mean. Multiplication is the repeated addition of a unit. On the other hand,
division is how many times one number is contained in another.
Do you know that in mathematics, multiplication is a basic arithmetic operation?
If your students are good at multiplication, this will help them in their other
subjects. This topic will guide you to do multiplication by teaching you mental
multiplication, multiplication of two or more digits with one and two digit
numbers, and multiplication of numbers ending with zero(s). Next, you will be
taught how to do division of two and three digit numbers.
1.5.1 What is Multiplication?
Before you explain to students how to do multiplication, use a visual
representation to illustrate.
Let us take 4 8 as an example. So, what does 4 8 mean? It either means the
sum of eight 4s or the total of four 8s: 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32 or
8 + 8 + 8 + 8 = 32.
Let us visualise 4 8.
8 is the number of marbles placed in four containers. Ask your students to count
the marbles. The total number of marbles is:
8
4
3 2
1.5

32. TOPIC 1 WHOLE NUMBERS
20
(a) The Order Property
Let us look at the order property to do
multiplication. Can you write the multiplication for
the situation below? Visualise and use your
imagination. Teach your students how to do it too.
5 + 5 + 5
Let us say that there are three packs of biscuits. Each pack consists of five
biscuits. Count the total number of biscuits.
Answer:
There are 3 5 = 15 biscuits. In other words, five biscuits are added
repeatedly three times.
Give the students a few more situations to let them visualise and write the
multiplication. You may use items in the classroom to demonstrate this.
Do you know that multiplication has an order property? You can show this
by changing the order of multiplication as: 3 5 = 5 3 = 15
Three multiply by five means that we add three repeatedly five times.
3 + 3 + 3 + 3 + 3 = 15
Or, similarly like the first answer, you can tell your students that this
addition can also be done by adding five repeatedly three times.
5 + 5 + 5 = 15
Explain to your students that multiplication is very interesting and a
powerful tool in mathematics. The students are expected to memorise basic
multiplication from one until nine. Refresh their memory if they have
forgotten as this knowledge is required for use with other computational
skills.
(b) The Order of Factors
Now, let us look at the order of factors. Do you know that when numbers are
multiplied, they are called the factors of the product? Look at the following
example:
2 3 5

33. TOPIC 1 WHOLE NUMBERS
21
What are the factors of the product? The factors are 2, 3 and 5.
Here is an important fact about the order of factors. When doing
multiplication, the order of any number of factors does not count.
For example,
2 3 5 = 5 2 3 = 5 3 2
Show to the students that you can arrange the multiplication of two or more
numbers in various ways as shown above and still get the same answer, that
is 30.
Here is a tip you can give to your students:
When doing multiplication mentally, grouping the factors will help you.
Group the factors as you please in order to come out with an easy solution.
Doing multiplication mentally will help in speeding up the process of
problem solving.
Example 13:
Multiply this: 7 2 9 5
Solution:
There are many ways of solving this, but teach your students the easiest
method. This multiplication can be done easily if you know the right way of
grouping the factors. We can arrange the numbers in the order of your
preference because the order is not important here. Take advantage of
factors that produce a multiple of 10. So, you can group 2 5 and 7 9.
7 2 9 5 = (2 5) (7 9) You need to memorise simple 1 digit
multiplication to do this.
= 10 63 2 5 = 10 and 7 9 = 63
= 630 Multiply by 10, you just add 0 at the
right side of the number.

34. TOPIC 1 WHOLE NUMBERS
22
Here are some guidelines for you to improve the skill of multiplication
mentally with whole numbers that end in 0s. Let us try the following:
200 30
You can ignore those 0s and multiply the numbers that remain. Then, put
back all the 0s that you ignored.
Example 14:
200 30 = 6,000
How do we get the answer? Follow these steps:
(i) Ignore all the 0s and simply multiply: 2 3 = 6.
(ii) Since we ignored the three 0s, we must put back these three 0s in the
answer. Count the total number of zeros for the two numbers (in this
case 3 zeros), then put it behind 6: 200 30 = 6.
SELF-CHECK 1.3
Calculate 9 20.
Example 15:
Calculate 16 5 mentally.
Can we calculate this mentally? The answer is yes. The multiplication of the
numbers without any ending 0s can be done mentally. How do we show this?
First, divide 16 into two groups (any ending numbers 0s) which are 10 and 6
(16 = 10 + 6). Then, multiply each of them by 5.
Therefore 16 5 = (10 5) + (6 5)
= 50 + 30 = 80

35. TOPIC 1 WHOLE NUMBERS
23
Example 16:
What is the answer for 11 65?
Multiplication of any two numbers by 11 is particularly easy, because we can split
11 into 10 and 1. Therefore, 11 65 is equal to (10 65) + (1 65).
650 + 65 = 715
Example 17:
How much is 13 12?
Because multiplication is a repeated addition, you can do multiplication easily if
you know the trick. Consider the above example, remember that 12 12 = 144.
Separate 13 into 12 and 1: 13 = 12 + 1.
Therefore, 13 12 = (12 12) + (1 12)
= 144 + 12 = 156
SELF-CHECK 1.4
Solve the following:
(a) 26 6 (d) 15 26
(b) 11 25 (e) 11 6
(c) 23 12 (f) 24 34

36. TOPIC 1 WHOLE NUMBERS
24
1.5.2 Multiply Numbers with Two or More Digits
Your students should be able to multiply single digit numbers mentally. This will
help them and serve as a basis for them to learn multiplication of numbers with
more than two digits. Now, how do we deal with the multiplication of numbers
with two or more digits? These three steps are provided as guidelines:
Step1: Arrange each digit of the number under the other and draw a line
beneath these numbers.
Step 2: Begin multiplying each of the digits in the number above with each of
the digit in the number below from right to left.
Step 3: The products of multiplying each number above by each number below
are arranged under the other line from left to right.
We shall apply these steps in the next few examples.
(a) Multiplying Two Digit Numbers with One Digit Numbers
Example 18:
Multiply 89 9.
Follow the steps below:
Hence, 89 9 is 801.
(b) Multiplying Two Digit Numbers with Two Digit Numbers
Example 19:
Multiply 84 98.
Use similar steps as in Example 18.

37. TOPIC 1 WHOLE NUMBERS
25
Step1: Arrange by placing number 84 above and
98 below. Align digit ones, tens, hundred.
Step2: Multiply first by 8, 84 × 8 = 672. Next
multiply by 9, 84 × 90 = 7,560. Then,
arrange the partial products.
Step3: Add all the partial products to get the total
8,232.
3
3
8 4
× 9 8
}
}
1 61 7 2
7 5 6 0 +
8 2 3 2
So, the answer for 84 98 is 8 232.
(c) Multiplying Numbers Ending with Zero(s)
Let us look now at multiplication of numbers ending with zero(s). This kind
of multiplication can be solved easily and more quickly than others. Explain
to the students the following steps:
Step 1: Multiply only the digits.
Step 2: Attach the total number of zeros to the product obtained from the
multiplication.
Example 20:
Multiply 3,500 80
4
3 5 0 0
8 0
2 8 0
Step 1: Multiply the digits, 35 x 8 = 280.
Step 2: Add three zeros to the product, 28,000.
As an educator, you have to show more examples to your students to let them
fully understand the techniques of multiplication. Guide students through the steps
so that they will be confident enough to attempt to answer questions on their own.
1.5.3 What is Division?
When do we use division? We use division when we want to separate a quantity
equally. Use some items in the classroom to show how things can be divided into
groups. Give students a rough idea about the process of division.

38. TOPIC 1 WHOLE NUMBERS
26
Let us say we have 3 3 matches. They
are equal to nine and hence, 9 3 = 3.
This means we can divide nine matches
equally into three groups. Thus, we
obtain three sticks of matches per group.
Do note that the process of dividing two to five digit numbers by two or three
digit numbers are basically the same. Remind your students of this regularly.
1.5.4 Divide by One, Two or Three Digit Numbers
(a) Dividing by a One Digit Number
Example 21:
You want to divide 20 cans of Coca-Cola into four packages. How many
cans of Coca-Cola are there in each package?
To solve this problem, first, show students that you can form the operation
using the symbol: 20 4. Second, write the division using a long-division
symbol ( ).
5
4 20
-20
0
Start dividing the digits of the numbers from left to right by four.
The first digit two is less than four, so you should choose two
digits (20) which is bigger than four. Next, you can ask your
students for a number when multiplied by four will result in an
answer less or equal to 20. The answer is 4 5 = 20. Place 5 on
top ( ) and 20 below 20. Then, subtract 20 – 20 = 0. This
means that there are no remainders and 20 can be exactly divided
by 4. Therefore, 20 4 = 5.

39. TOPIC 1 WHOLE NUMBERS
27
Example 22:
Calculate 57 000 8.
7 125
8 57000
56
10
8
20
16
40
40
0
Start dividing the digits of the numbers from left to right by
eight. The first digit five is less than eight, so you should
choose two digits (57) which are bigger than eight. Next, ask
your students for a number when multiplied by eight will
result in an answer less or equal to 57, which is 8 7 = 56.
Place seven on top and 56 below 57. Then, subtract
57 – 56 = 1. The difference is less than eight. Bring down the
digit zero next to one to become 10.
Again, ask for a number when multiplied by eight will result
in an answer less or equal to 10. The answer is 8 1 = 8, so
put one on top of division and then subtract 10 – 8 = 2. The
difference is less than eight. Bring down the digit zero next to
two to get 20, for a number when multiplied by eight will
result in an answer less or equal to 20. The answer is 8 2 =
16. Put two on top of the division. Then, subtract 20 – 16 = 4.
Bring down the digit zero to make 40. Finally, find a number
when multiplied by eight will result in an answer less or equal
to 40. Therefore, 8 5 = 40. Put five on top of the division
symbol. Subtract 40 – 40 = 0. Hence, 57,000 8 = 7,125.
Example 23:
524 6
87
6 524
48
44
42
2
Hence, 524 6 = 87, remainder 2.
Example 24:
3,568 6
594
6 3568
30
56
54
28
24
4
Hence, 3,568 6 = 594, remainder 4.

40. TOPIC 1 WHOLE NUMBERS
28
(b) Dividing by Two or Three Digit Numbers
In this section, you will see an example of the division of numbers by two or
three digits numbers. Follow the guidelines in Example 25.
Example 25:
78 35
2
35 78
70
8
Start dividing the digits of the numbers from left to right by
35. The first digit seven is less than 35, so you should choose
two digits (78) which are bigger than 35. Next, ask your
students whether 35 ? is less than or equal to 78. The answer
is 35 2 = 70. Place two on top and 70 below 78.
Then, subtract 78 – 70 = 8.
Hence, 78 35 = 2, remainder 8.
The next few examples will further illustrate this method.
Example 26:
564 35
16
25 564
- 35
214
- 210
4
Hence, 564 35 = 16, remainder 4.
Example 27:
9,578 35
273
35 9578
70
257
245
128
105
23
Hence, 9,578 35 = 273, remainder
23.

41. TOPIC 1 WHOLE NUMBERS
29
MULTIPLICATION AND DIVISION
IN EVERYDAY LIFE
1.6
Multiplication and division are used regularly in our daily life. Below are some
examples which can be used to guide students.
Example 28:
3,550 sweets are to be divided into 25 packages. How many sweets are there in
each package?
First, you have to write the division operation: 3,550 25
142
25 3550
- 25
105
- 100
50
50
0
Start dividing the digits of the numbers from left to right by 25.
The first digit three is less than 25, so you should choose two
digit (35) which is bigger than 25. Next, ask your students
whether 25 ? is less than or equal to 35. That is 1. Place one
on top and 25 below 35. Then subtract 35 – 25 = 10.
The difference is less than 25. Bring down the digit five and
place it behind 10 to become 105.
Again, ask your students whether 25 ? is less than or equal to
105. The answer is 25 4 = 100. Then, subtract 105 – 100 = 5.
The difference is less than 25. Bring down the digit zero to add
and become 50. Finally, ask them whether 25 ? is less than or
equal to 50. The answer is 25 2 = 50. Subtract 50 by 50 and
you will get 0. Hence, 3 568 25 = 142.
Example 29:
Sarimah runs a photocopying business. She earns RM12,250 per week. Her
business operates five days a week and the machine can operate for 10 hours per
day. How much does she earn per hour?
To solve this question it will be wise to do some analysis like what is shown.
Once students have understood the question properly, it will be easier for them to
solve it.

42. TOPIC 1 WHOLE NUMBERS
30
(a) What is given? Earns RM12,250 per week.
Operates five days a week. Machine can
operate for 10 hours a day.
(b) What is asked? Earning per hour.
(c) How much RM is earned? Use division
First, divide amount earned by working hours: 12,250 5 10.
Next, simplify 5 10 = 50 and the problem becomes 12,250 50.
245
50 12250
- 100
225
200
250
250
0
12 is less than 50. So choose 122. 50 2 = 100 is less than 122.
Subtract 122 – 100 = 22. Bring down five and it becomes 225.
50 4 = 200. Subtract 225 – 200 = 25. Since 25 is less than 50.
Bring down zero to become 250. 50 5 = 250. Subtract
250 – 250 = 0.
SELF-CHECK 1.5
1. Salim is a hotel manager who wants to set all the tables with six
special cups each in an executive dining room. He needs 252 cups.
Calculate how many tables are there in the executive dining room.
2. Calculate the following:
(a) 5 2565 (b) 7 5279
(b) 7 6680 (d) 28 4884
3. A father of four children has 2,458 stamps. He wants to distribute
the stamps equally among his four children. How many stamps will
each child get?

43. TOPIC 1 WHOLE NUMBERS
31
ACTIVITY 1.5
1. The pupils at Sekolah Kebangsaan Abi in Perlis are having a co-curricular
activity in Danga Bay, Johor Baru. The organiser needs to
hire enough buses to take the 253 teachers and pupils. If each bus
can acccommodate 45 people, how many buses will he need to rent?
2. Abu buys Utusan Malaysia and The Star newspapers every day. He
needs to pay RM40 and RM36 for each newspaper respectively.
How much must he pay for both newspapers in three months?
3. 12 watermelons weigh an average of 354g. What is the weight of
each watermelon on average?
4. 2,200 cards were put into packs of 10. How many cards are there in
each pack?
5. Half an hour = ____ minutes.
MIXED OPERATIONS WITH ADDITION
AND SUBTRACTION
1.7
How do we calculate problems with mixed operations? In mixed operations, we
start calculating from left to right. Let us look at the following examples.
Example 30:
55 + 29 – 34 =
For the above problem, add the
two numbers first as:
5 5
+ 2 9
8 4
Then, subtract 34 from the total:
8 4
3 4
5 0
Hence, 55 + 29 – 34 = 50.

44. TOPIC 1 WHOLE NUMBERS
32
Example 31:
567 + 154 – 152 =
Add the two numbers first as:
5 6 7
1 5 4 +
7 2 1
Then, subtract 152 from the total:
7 2 1
1 5 2
5 6 9
So the answer for 567 + 154 –152 is 569.
You can also do the mixed operations involving addition and subtraction in
another way. Do the subtraction first, followed by the addition. But make sure that
when you give examples of this kind, the first subtraction must not be negative as
the students are not up to this level yet.
Example 32:
53 – 28 + 56 =
Subtract the two numbers first as:
5 3
2 8
2 5
Add 25 with 56:
2 5
5 6 +
8 1
The final answer for 53 – 28 + 56 is 81.
Do you know that there is a checking strategy to check whether the answer to the
mixed operations involving addition and subtraction problem is correct? Here is
the strategy:
(a) Bring the negative number to the right hand side value. When you move the
number to the other side of the ‘=’ sign, the negative sign will change to
positive.
(b) Add the right hand side value.
(c) Next add the left hand side value.
(d) The right hand side value must be equal to the left hand side value.

45. TOPIC 1 WHOLE NUMBERS
33
Let us consider Example 30 to apply this strategy.
55 + 29 – 34 = 50
55 + 29 = 50 + 34
Add the right hand side value:
5 5
2 9 +
8 4
Add left hand side value:
5 0
3 4 +
8 4
Hence, 55 + 29 – 34 = 50 is correct.
Let us look at how to solve some problems involving addition and subtraction.
First, you should understand the problem thoroughly so that you can arrange the
strategy to solve the problem.
Example 33:
Aminah has RM50 and her mother gives her RM20. She buys a book at a cost of
RM55. What is the amount of money left?
From the problem stated, you can do the following:
You have to understand the question thoroughly. Use the questions in the left column
as a guideline. Ask the same questions to the students.
What information is given? Group the information into two
Amount she has Amount she pays
RM55 and RM20 RM55
What is asked? Amount of money she has
left.
What operations are needed? Addition Subtraction
Solve:
5 0
2 0 +
7 0
Hence, the solution RM50 + RM20 – RM55 = RM15.
7 0
5 5
1 5

46. TOPIC 1 WHOLE NUMBERS
34
Now, to check that the answer is correct, you should do the opposite. Move the
negative sign to the right hand side. Then it becomes:
RM50 + RM20 = RM55 + RM15
The left hand side and the right hand side have the same value, which is RM70.
ACTIVITY 1.6
Give these pictures to your students to have a look at them. Then, ask the
students to write THREE problems involving addition and subtraction for
any pictures that they like. Collect all the problems and solve them together.
ACTIVITY 1.7
1. Mega Hotel has 82 single rooms, some double rooms and 35 suites.
There are 250 rooms in total. How many double rooms are there in
the hotel?
2. There are 15 boys and 18 girls in a class. The following day, three
boys and two girls were transferred to another school. How many
children are left in the school?
3. Amran has 35 stamps. His dad gives him another 10 stamps but then
he misplaces 13 of the stamps. Find the number of stamps left.
4. Ah Chong bought three books at a price of RM35 each. The price of
each book was reduced to RM25. How much money does he save?

47. TOPIC 1 WHOLE NUMBERS
35
In this topic, we have learned about:
Recognising whole numbers;
Identifying place value of numbers;
Comparing and arranging two or more numbers;
Rounding off whole numbers;
Addition and subtraction within the range of 100,000;
Multiplication and division within the range of 100,000;
Multiplication and division to solve problems in daily life; and
Mixed operations involving addition and subtraction.
Addition
Approximation
Arrange
Ascending
Borrowed
Count back
Count on
Descending
Division
Estimation
Left hand side
Mixed operation
Multiplication
Ones
Order property
Place value
Repeated addition
Right hand side
Round off
Subtraction
Symbol of division, or long-division
symbol
Symbol of multiplication, ×
Tens
Thousands

48. TOPIC 1 WHOLE NUMBERS
36
Cardanha, J. M. (1993). Career math skills. Columbus, Ohio: McGraw-Hill
School Education Group.
edHelper.com. (n.d.). Grade four math worksheets. Retrieved from http://www.
edhelper.com/math_ grade4.htm
Ministry of Education Malaysia. (2009). Integrated curriculum for primary schools
mathematics Year 4. Kuala Lumpur: Curriculum Development Centre.
Shum, K. W., Chan, S.H. (2004). Reference text series KBSR Year 4. Kuala
Lumpur: Pearson.

49. Topic
2
Fractions
LEARNING OUTCOMES
By the end of this topic, you should be able to:
1. Identify proper and improper fractions;
2. Compare and arrange fractions;
3. Write equivalent fractions;
4. Perform addition and subtraction of fractions; and
5. Solve problems involving addition and subtraction of proper fractions.
INTRODUCTION
Fractions are used in almost every type of measurement such as time, weight,
length and distance. For example, things that we buy and share with others are
measured in fractions. You will learn about proper and improper fractions, the
operations of fractions, and addition and subtraction involving fractions. These
operations involve proper fractions with denominators of up to 10.

50. TOPIC 2 FRACTIONS
38
IDEA OF FRACTION
2.1
Let us compare and arrange proper fractions and improper fractions.
2.1.1 Proper Fractions
First of all, let us look at the meaning of fraction. If a whole quantity or object is
divided into several equal parts, one or more of these parts from the whole object
is called a fraction.
In any fraction, for example,
2
3
, the number 2 at the top is denoted as the
Numerator and the bottom number, 3, is the Denominator. The fraction can also
be written as:
Fraction = Numerator
Denominator
Example 1:
Let us say that you are given a cake. You want to share it equally among six
people. How do you do that?
Solution:
Explain to students that we can divide the cake into six parts. Each part of the
cake is
1
6
. Each person can have
1
6
of the cake. Illustrate this on the board,
showing the division of the cake.

51. TOPIC 2 FRACTIONS
39
Write down the fractions for the shaded parts:
1.
2.
3.
4.
5.
ACTIVITY 2.1

52. TOPIC 2 FRACTIONS
40
2.1.2 Improper Fractions
A fraction in which the numerator is greater than the denominator is called an
improper fraction.
An example of an improper fraction is 7 .
2
Example 2:
Each circle is divided into three equal parts in Figure 2.1. The shaded areas are 8
3
.
Figure 2.1: Example of improper fraction
Thus, the numerator is greater than the denominator. Hence,
8
3
is an improper
fraction.
2.1.3 Comparing and Arranging Fractions
A cake is to be shared among eight pupils. What fraction of the cake will each
pupil get?
Each pupil 1
of the cake.
8
Say that the cake can be divided into eight equal parts. When half of the cake has
been eaten, there are still four pieces left.

53. TOPIC 2 FRACTIONS
41
So, 4 1
. This means that although four pieces of cake have been eaten, we can
8 2
say that half of the cake is still available. Show the students in pictorial form, so
that they can understand easily. You can also prepare a circular cutout in eight
equal parts to represent the cake slices. Teach them the fractions involved by
asking them to colour the parts accordingly. This is a good way to visualise
fractions as well as to stimulate an enjoyable learning experience.
Now, let us compare which fraction is bigger or smaller by looking at these two
rulers in Figure 2.2.
Figure 2.2: Comparing fractions using rulers
Ask your students which ruler has a longer shaded region.
When the denominators are equal, you can decide which fraction is bigger by
comparing the numerator value. You can explain this by using fractions.
The fraction of the first ruler: 6
10
The fraction of the second ruler: 8
10
Therefore,
8
10
is bigger than 6
10
because 8 is bigger than 6.

54. TOPIC 2 FRACTIONS
42
When the denominators are not equal, then you can compare certain fractions by
looking at a simple chart as shown below (Figure 2.3). This is not the best way as
a better way would be using equivalent fractions to compare.
Figure 2.3: Fraction wall
So, 1 is bigger than 1 ; 1 is bigger than 1 ; 1 is bigger than 1 .
2 2 5 5 10
2.1.4 Equivalent Fractions
If the denominators are not equal, it will be hard for students to compare fractions.
Teach them how to express and write equivalent fractions. Equivalent fractions
are not only useful in comparing the size of fractions but they are also needed
when we use operations such as addition and subtraction to solve questions.
So what does an equivalent fraction mean? An equivalent fraction is defined as a
fraction that has the same value.
Let us look at the following examples in Figure 2.4. You can use these examples
to explain the concept of fractions to your students.

55. TOPIC 2 FRACTIONS
43
Figure 2.4: Equivalent fractions
Equivalent fractions have the same value. To obtain the equivalent fraction, you
have to multiply or divide both the numerator and denominator by the same
number.
2 2
2
4
4 4
2 8
Now, let us try some examples. Fill in the blank spaces in the fractions below.
(i) 3 3 ? 6 (ii) 2 2
?
4
4 4 ? 8 5 5
? 10
Students should now be able to make comparisons among fractions. These
comparisons can be done by following the steps below:
Steps to compare fractions:
(a) Find the least common denominator.
(b) Change each fraction to an equivalent fraction with the least common
denominator as its denominator.
(c) Compare the numerator.

56. TOPIC 2 FRACTIONS
44
Let us apply these steps for the following examples.
Example 3:
Compare 1 and 3
5 5
.
Look at the denominator – are they equal? Yes
If equal, then compare the numerator: 1 and 3
5 5
.
3 is greater than 1: So, 3
5
is greater than 1
5
.
Example 4:
Compare 3 and 7
4 8
.
Look at the denominator – are they equal? No
If not equal, find the least common denominator 4: 4, 8, 12, 16,..
8: 8, 16, ...
Change each fraction to an equivalent fraction with the least common
denominator as its denominator:
3
3 2
6
4 4
2 8
Compare the numerators: 6 and 7
8 8
7 is greater than 6: So, 7 is greater than 6
8 8
.

57. TOPIC 2 FRACTIONS
45
ADDITION AND SUBTRACTION OF
FRACTIONS
2.2
Keep in mind that adding fractions is not the same as adding whole numbers. To
add fractions, the fractions must look alike.
2.2.1 Adding and Subtracting Fractions with the
Same and Different Denominators
To add fractions, the fractions must look alike. This means that they must have the
same denominators. When adding fractions, you have to follow this general rule.
General rule:
a b
a b
c c c
Example 5:
5 1 5
1
6
8 8 8 8
Then, if possible you should reduce the fraction to its simplest form. To express
fractions in the simplest form, divide the numerator and denominator of the
fractions by the same number. Show some examples to your students.
Example 6:
Simplify:
6 6
2 3
8 8 2 4
Thus, 6 is equivalent to 3 .
8 4
Example 7:
Find the sum of
3 2 3 2
2
8 4 8 4
2
3 4
7
8 8 8
Change
2
4
to an equivalent fraction with a
common denominator.
2
4
is equivalent to
.
4
8

58. TOPIC 2 FRACTIONS
46
Figure 2.5: Example of sum of fractions
Example 8:
Find the sum of
3 + 2 = 3×2 + 2
5 10 5×2 10
6 + 2 = 8
10 10 10
Note that after the fractions are added, if possible, you should make the final
result in a smaller or reduced fraction form. You have seen this in Example 6
where we divide both the numerator and denominator by the same number. Some
guidelines below serve as an alternative method which may help you explain the
steps to the students on simplifying fractions.
Steps to reduce a fraction to its simplest form:
(a) Factorise the numerator.
(b) Factorise the denominator.
(c) Find the fraction mix that equals 1.
Example 9:
Reduce the fraction 8
10
.
Find the equivalent fraction for
3
5
. The answer is
6
10
.
First and second steps: Factorise the numerator and denominator.
4×2
5×2
Note that all factors in the numerator and denominator are separated by
multiplication signs.

59. TOPIC 2 FRACTIONS
47
Third step: Find the fraction that equals 1.
4×2
5×2
can be written as 4 2
5 2
which
in turn can be written as 4
5
1 or similarly 4
5
.
8 = 4
10 5
(This is the simplest form)
Example 10:
Reduce the fraction 15
6
.
First and second steps: Rewrite the fraction with both the numerator and the
denominator factorised.
5
3
2
3
Third step: Find the fraction that equals 1.
5
3
2
3
can be written as 5 3
which in
2 3
turn can be written as 5
2
1 or similarly 5
2
.
15 = 5
6 2
(This is the simplest form)
1. 1 + 1
5 5
2. 1 + 2
5 5
3. 3 + 1
5 5
4. 3 + 2
10 10
5. 3 + 2
8 8
6. 2 + 3
7 7
7. 2 + 1
9 9
8. 1 + 5
8 8
9. 3 + 1
10 5
10. 2 + 5
3 6
11. 3 + 2
6 6
12. 3 + 6
4 8
ACTIVITY 2.2

60. TOPIC 2 FRACTIONS
48
Keep in mind that subtracting fractions is done the same way as adding fractions.
To subtract fractions, they must look alike.
The general rule for subtraction of fractions is:
a - b = a - b
c c c
Let us try this:
(i)
5 - 2 = 5- 2 = 3
8 8 8 8
(ii)
1 - 1 =
4 8
1 - 1 = 2 - 1
4 8 8 8
= 2 -1 = 1
4 8
(iii)
2 - 2
3 6
2 - 2 = 4 - 2
3 6 6 6
= 4 - 2 = 2
6 6
Reduce to = 2 ÷ 2
6÷ 2
= 1
3
Change
1
4
to its equivalent fraction
1× 2 2
=
4×2 8
Change
2
3
to its equivalent
fraction
2×2 4
=
3×2 6

61. TOPIC 2 FRACTIONS
49
In summary, adding and subtracting like fractions can be done in the following
way:
(a) Add or subtract the numerators.
(b) Keep the like denominators.
(c) Reduce to the simplest fraction.
a ± b = a ± b
c c c
2.2.2 Solving Problems Involving Fractions
We often encounter problems involving fractions in our daily life. How do we
solve these problems? Tell your students to do the following in order to help solve
these problems:
(a) Understand the problem thoroughly.
(b) Identify what information has been given.
(c) Identify what the question asks for.
(d) Identify what operations are needed.
(e) Work out the solution.
Let us see some examples that demonstrate problem solving involving fractions.

62. TOPIC 2 FRACTIONS
50
Example 11:
You have to understand the question thoroughly
What information is given? Water melon is cut into
eight slices.
8 slices
Aminah ate three slices. 3 slices eaten
Halim ate two slices. 2 slices eaten
What does the question ask? How many slices of
watermelon are left?
What fractions are involved? 3
8
and
2
8
What operations are needed? Subtraction
Solve: 3 2
1- -
8 8
8 3 2 3
- - =
8 8 8 8
Change one into a
fraction with the same
8
denominator:
1=
8
.
Hence the solution 8 - 3 - 2 = 3
8 8 8 8
Example 12:
A primary school has a building which is two storeys high. Each floor has five
classes. Year 1 pupils occupy three classes on the ground level and Year 2 pupils
occupy two classes on the first floor. How many classes are occupied by Year 1
and Year 2 pupils?

63. TOPIC 2 FRACTIONS
51
You have to understand the question thoroughly
What information is given? Two-storeys-high building.
Each floor has five classes.
Year 1 pupils occupy three
classes at ground level.
Year 2 pupils occupy two
classes at the first floor.
What does the question ask? How many classes are
occupied?
What fractions are involved?
Year 1 pupils: 3
10
Total classes =
2 5 = 10
Year 2 pupils: 2
10
What operations are needed? Addition
Solve: 3 2 5
+ =
10 10 10
5 5÷5 1
= =
10 10 ÷ 5 2
Reduce the
fraction
1. 3 - 1
5 5
2. 3 - 1
4 4
3. 8 - 2
9 3
4. 2 - 2
5 10
5. 7 - 2
8 4
6. 3 - 2
7 7
7. 2 - 1
9 9
8. 5 - 2
8 4
9. 3 - 5
4 8
10. 5 - 4
10 10
11. 5 - 3
6 8
12. 9 - 3
10 4
ACTIVITY 2.3

64. TOPIC 2 FRACTIONS
52
ACTIVITY 2.4
Problem 1:
Simplify the following fractions.
1. 18
24
2. 6
8
3. 9
15
4. 18
32
5. 6
4
6. 18
9
7. 4
10
8. 10
12
9. 2 4
6
Problem 2:
Jackson read 1
4
of a novel on Sunday. He continued to read another 1
4
of
the novel the next day. What fraction of the book has he read?
Problem 3:
Sue and some friends helped to paint a wall. They painted one third of the
wall pink. What fraction of the wall is not painted?
ACTIVITY 2.5
You are given some strings, paper, scissors and a pen. Discuss how you
can demonstrate and explain to your students the fractions 5 , 2
8 5
and the
operation 1 1
.
3 6

65. TOPIC 2 FRACTIONS
53
In this topic, we have learned about:
The idea of fraction – proper fractions, improper fractions, comparing and
arranging fractions and expressing equivalent fractions.
Addition and subtraction of fractions.
Addition
Common multiple
Denominator
Equivalent
Improper fraction
Least common denominator
Numerator
Proper fraction
Simplest fraction
Subtraction
Cleaves, C., Hobbs, M. (2003). Reference to mathematics: A guide for every
math. New Jersey: Prentice Hall.
Ministry of Education Malaysia (2004). Integrated curriculum for primary schools
mathematics Year 3. Kuala Lumpur: Curriculum Development Centre.
Shum, K. W., Chan, S. H. (2004). Reference text series KBSR Year 3. Kuala
Lumpur: Pearson.

66. Topic
3
Decimals
LEARNING OUTCOMES
By the end of this topic, you should be able to:
1. Write decimal numbers in words;
2. Convert fractions to decimals and vice versa;
3. Perform addition and subtraction of decimals up to two decimal
places;
4. Perform multiplication and division of decimals up to two decimal
places by a whole number; and
5. Show multiplication and division of decimals in standard written
method; and
6. Solve problems related to multiplication and division of decimals.
INTRODUCTION
It is common to see numbers that have decimals in them. Decimals are points
which are located in between the digits in the numbers. A decimal point in a
number shows the accuracy of the number value. The location of the decimal
point (in between digits) indicates the size of the number.
We will learn how to write decimal numbers in words. Later, we will also learn
how to convert fractions to decimals and vice versa followed by how to convert
mixed numbers to fractions and vice versa. Then, we will arrange decimal
numbers. After that, we will do some calculations as we learn how to do addition,
subtraction, multiplication and division involving decimal numbers. Lastly, we
will multiply and divide decimals in the standard written method.

67. TOPIC 3 DECIMALS
55
Figure 3.1: Decimals
Source: www.CartoonStock.com
DECIMAL NUMBERS
3.1
Let us recall the first topic of this module. In Topic 1, you have learnt about place
value. You can refresh your students’ memories about place value by presenting
the place value chart as shown in Table 3.1.
Table 3.1: Place Value Chart
Hundred
Thousands
Ten
Thousands Thousands Hundreds Tens Ones
Based on the chart, your students can see that the place value starts with ones at
the right followed by tens, hundreds, thousands, ten thousands and hundred
thousands. Ones is the basic unit and the next place value is multiplied by 10.

68. TOPIC 3 DECIMALS
56
Tens: 10 1 = 10
Hundreds: 10 10 = 100
Thousands: 10 100 = 1,000
And so on.
Now, you can tell your students about decimals. Tell them that decimal is the
moving to the right after the ones. Start with 1,000 and move to the place value to
the right.
1,000 10 = 100
100 10 = 10
10 10 = 1
You can get the value to the right of each place value by dividing by 10. Suppose
you divide 1 by 10:
1÷10 = 1
10
, this is a fraction and you read it as “one tenth”.
The value to the right of ones is called decimal point. The decimal (base ten)
shows where the whole number ends and the fraction begins. The decimal place
value chart is just the opposite of the place value chart. The decimal place value
chart is shown below in Table 3.2. The shaded grey area is not needed for your
students at this level of study.
Table 3.2: Decimal Place Value Chart
Ones Tenths Hundredths Thousandths Ten
Thousandths
1 1/ 10 1/100 1/1,000 1/ 10,000
Now, how do we read and write a decimal number in words? Let us follow the
following four guidelines in order to teach your students how to read and write
decimal numbers.

69. TOPIC 3 DECIMALS
57
Four Guidelines to Read and Write a Decimal Number:
(a) Mentally align the whole numbers in the place value chart and the
decimal numbers in the decimal place chart.
(b) Read the whole number.
(c) Use decimal point and read the decimal place value as you read the
whole number.
(d) End by reading the last decimal place value where the numbers end.
Let us go through the following examples.
Example 1:
Read 35.63.
Solution:
(a) Mentally align the numbers.
Hundred
Thousands
Ten
Thousands Thousands Hundreds Tens Ones
3 5
and
Tenths Hundredths
1/ 10 1/100
6 3
(b) You read it as thirty five and sixty three hundredths.

70. TOPIC 3 DECIMALS
58
Example 2:
Write
18
100
as a decimal.
Solution:
If any whole number is divided by a denominator with the power of ten, you can
do it quickly as shown below:
(a) Write the numerator. 18
(b) Count how many zeros there are at the denominator. 2
(c) Move the decimal point two places from right to left.
Attach zeros on the left end of decimal point. 0.18
Hence
18
100
= 0.18.
Note:
Zeros attached to the end of a decimal number do not change the value of the
numbers. Look at the example below. The zero(s) attached to the end of a decimal
number does not affect its value.
0.3 = 0.30 3
10
= 30
100
In the next two subtopics, you will learn about converting fractions and mixed
numbers to decimals and vice versa. This skill is important in mathematics as we
need it to help us solve problems involving decimals. Therefore, you need to have
a good grasp of decimal conversion.
3.1.1 Converting Fractions to Decimals and Vice Versa
This section explains how you can convert fractions to decimals and decimals to
fractions.
When converting fractions to decimals, you can tell your students to follow these
three steps:
(a) Place the decimal point after the number of the numerator.
(b) Attach the zeros as needed after the decimal point.
(c) Divide the numerator by the denominator using long division.

71. TOPIC 3 DECIMALS
59
Example 3:
Convert 6
8
to decimal number.
Solution:
0.75
8 6.00
- 5.6
40
- 40
0
Place a decimal after six. Attach zeros as needed. Divide as usual.
How about converting decimals to fractions? To convert decimals to fractions,
follow the three steps below:
(a) Write the numerator as a whole number.
(b) Write the denominator as power of tens with the number of zeros depending
on how many places there are after the decimal point.
(c) Reduce the fraction to its simplest form.
Let us demonstrate these steps in Example 4.
Example 4:
Convert 0.5 and 0.85 to fractions.
Solution:
Move one decimal place to the right The denominator is 10 (one zero)
0.5 = 5
10
Write in fraction, the numerator should
be in whole number
= 1
2
Reduce the fraction
Move two decimal places to the right The denominator is 100 (two zeros)
0.85 = 85
100
Write in fraction form, the denominator
should be in whole numbers.
= 17
20
Reduce the fraction by dividing both
numerator and denominator by 5.

72. TOPIC 3 DECIMALS
60
3.1.2 Converting Mixed Numbers to Fractions and
Vice Versa
In this section, whole numbers are seen to be combined with fractions. These are
called mixed numbers. You will learn how to convert them to fractions and vice
versa.
Introduce the steps below to convert mixed numbers to fractions.
(a) Write the mixed number as a whole number and decimal number.
(b) Convert decimal number to fraction.
(c) Convert fraction to mixed number fraction.
Example 5:
Convert 17.3 to mixed number fractions.
Solution:
17.3 = 17 and 0.3 Write as whole numbers and decimal numbers.
0.3 = 3
10
Convert decimal numbers to fraction and
reduce the fraction whenever possible.
17 3
10
Write the mixed fractions.
Conversely, the steps below show the conversion of mixed number fractions to
decimals.
(a) Write the mixed number fractions as whole numbers and fractions.
(b) Use long division to convert the fraction to decimal number.
(c) Write the mixed number fraction.

73. TOPIC 3 DECIMALS
61
Example 6:
Convert 13 3
4
to decimal number.
Solution:
13 3
4
= 13 and 3
4
Write as whole numbers and fractions.
0.7 5
4 3.00 G
- 2 8
20
- 20
0
Use long division to convert the fraction to decimal
numbers.
13 3
4
= 13.75 Write the decimal numbers.
SELF-CHECK 3.1
Solve the following problems:
1. Read 53.86.
2. Write 81
100
as a decimal.
3. Convert 3
5
to decimal number.
4. Convert 0.6 and 0.05 to fractions.
5. Convert 12.5 to mixed number fraction.
6. Convert 111
4
to decimal number.

74. TOPIC 3 DECIMALS
62
ADDITION AND SUBTRACTION OF
DECIMALS
3.2
Now, we will learn how to do addition and subtraction of simple decimals. You
will learn how to teach addition and subtraction of one and two decimal place
numbers.
3.2.1 Addition of Decimal Numbers
Adding decimal numbers is just like adding whole numbers. However, in adding
the decimal numbers, you have to line up the decimal points and add the numbers
accordingly. Follow the three steps below in order to add decimal numbers:
(a) Arrange the decimal numbers so that the decimal points are in a vertical line.
(b) Add the numbers of the same digit place from right to left.
(c) Place the answers in the same place.
Let us go through the following examples in class. Example 7 shows addition of
one decimal place numbers and Example 8 shows addition of two decimal place
numbers.
Example 7:
Add 13.4 + 45.1
Solution:
1 3 . 4
4 5 . 1 +
5 8 . 5

75. TOPIC 3 DECIMALS
63
Example 8:
Add 2.61 + 56.79
Solution:
(a) Arrange the decimal numbers so that the
decimal points are in a vertical line.
5 6 . 7 9
2 . 6 1 +
(b) Add the numbers in the same column. 1 1
5 6 . 7 9
2 . 6 1 +
5 9 . 4 0
2.61 + 56.79 = 59.40
3.2.2 Subtraction of Decimal Numbers
How about the subtraction of decimal numbers? The steps are quite similar to
addition. You can explain the three steps below to your students to show them
how to subtract decimal numbers:
(a) Arrange the decimal numbers so that the decimal points are in a vertical line.
(b) Subtract each number from right to left.
(c) Place the answer in the same place.
Let us go through the following examples.
Example 9:
Subtract 7.9 from 12.7
11 1
1 2 . 7
7 . 9 –
4 . 8
Hence, 12.7 – 7.9 = 4.8.

76. TOPIC 3 DECIMALS
64
Example 10:
Subtract 9.28 from 16
Solution:
(a) Arrange the decimal numbers so that the decimal
points are in a vertical line.
1 6 . 0 0
9 . 2 8 –
(b) Subtract the numbers in the same column. 15 9 1
1 6 . 0 0
9 . 2 8 –
6 . 7 2
16 – 9.28 = 6.72.
3.2.3 Addition and Subtraction of Three Decimal
Numbers
Now, we will learn about the addition and subtraction of three decimal numbers.
For your information, adding and subtracting three decimal numbers is just like
adding and subtracting two decimal numbers. Again, you have to guide your
students in performing these operations. Let us follow the steps below:
(a) Arrange the decimal numbers so that the decimal points are in a vertical line.
(b) Add the numbers in the same digit – placed from right to left.
(c) Place the answers in the same places.
You can demonstrate these steps by using the following example in class.

77. TOPIC 3 DECIMALS
65
Example 11:
Add 65.00 + 42.56 + 55.12
Solution:
1
6 5 . 0 0
4 2 . 5 6
5 5 . 1 2 +
1 6 2 . 6 8
65.00 + 42.56 + 55.12 = 162.68.
Next is the subtraction of three decimal numbers. There are four steps involved in
the subtraction of three decimal numbers:
(a) Arrange the decimal numbers so that the decimal points are in a vertical line.
(b) Subtract the first two decimal numbers starting from right to left.
(c) Subtract the remaining decimal number from the result in Step 2.
(d) Place the decimal in the same place.
Let us do the following examples to show how to apply these steps.
Example 12:
Subtract 52.97 – 17.33 – 10.58
Solution:
4 1
5 2 . 9 7
1 7 . 3 3 –
5 1
3 5 6 4
1 0 . 5 8 –
2 5 . 0 6
Hence, 52.97 – 17.33 – 10.58 = 25.06

78. TOPIC 3 DECIMALS
66
SELF-CHECK 3.2
Solve the following problems and show how you can explain the steps to
your students:
1. 23.45 + 5.23
2. 12.32 – 9.43 – 1.20
3. 10 – 1.6
MULTIPLICATION AND DIVISION OF
DECIMALS
3.3
Previously, you have learned multiplication involving whole numbers. Now, you
will learn multiplication and division of decimals. This section begins by
describing the multiplication of decimals, followed by division of decimals with
whole numbers.
3.3.1 Multiplication of Decimals
The multiplication of decimals is the same as the multiplication of the whole
numbers, except at the end of the operations you need to take into consideration
the decimal places. Now, let us look at the steps to teach students how to multiply
decimals. There are four steps to do multiplication of decimals:
(a) Place the decimal number above the other number (whole number) so that
they are lined up vertically.
(b) Disregard the decimal points and multiply the numbers.
(c) Count the total number of digits to the right of the decimal point to
determine the decimal number.
(d) Place the decimal point in the product by moving the decimal point from
right to left of the digits according to number of digits counted in Step (c).
Now, let us demonstrate how to use these steps by showing the following
examples in class.

79. TOPIC 3 DECIMALS
67
Example 13:
Multiply 1.63 5
Solution:
(a) Place the Decimal Above the Other Number 1 . 6 3
5
(b) Multiply the Numbers
Multiply the two numbers on the right side
(5 3 = 15). This number is larger than nine, so
place one above the number six and place five
below the line in the right column.
Multiply the digits (5 6 = 30) and add the total
to one above the column to produce 31. The
number one from the total of 31 is placed below
the line and the three of the 31 is placed above
the digit one.
The one of the top number is multiplied by five
of the lower multiplier (5 1= 5) and added to
the number three that was previously carried,
5 + 3 = 8 and the total eight is placed below the
line.
In the beginning, you disregarded the decimal
point. Now, you must consider the decimal
point. Count the decimal places and move the
decimal point to its proper location. There are
two decimal places in the decimal number 1.63.
So we move the decimal point two places to the
left of 815 to get the answer 8.15.
3 1
1 . 6 3
5
8 1 5
1.63 5 = 8.15

80. TOPIC 3 DECIMALS
68
Example 14:
Multiply 1.39 57
Solution:
(a) Place One Decimal Above the Other 1 . 3 9
5 7
(b) Multiply the Numbers
Multiply the 1.39 by seven and then by five and
place the products of the first above the other.
Add the products from right to left.
Placing the decimal point: The decimal number
1.39 has two decimal places, so we move the
decimal two places to the left of 7923 to produce
the answer 79.23.
1 4
2 6
1 . 3 9
5 7 G
9 7 3G
6 9 5 +
7 9 2 3
1.639 57 = 79.23
3.3.2 Division of Decimals
Now, let us learn how to divide decimals. Division involving decimals is done
using the steps below:
(a) Write the division using a long-division symbol ( ).
(b) Insert the decimal point above the decimal in the dividend.
(c) Proceed with division of the whole number.

81. TOPIC 3 DECIMALS
69
Example 15:
Divide 8.4 6
Solution:
(a) Insert the decimal point above the decimal in the dividend. .
6 8.4
(b) Proceed with the division. 1.4
6 8.4
- 6
2.4
- 2.4
0
Example 16:
Divide 16.08 24
Solution:
(a) Insert the decimal point above the decimal in the dividend. .
24 16.08
(b) Proceed with the division as before. 0.67
24 16.08
- 144
16 8
- 16 8
0
3.3.3 Multiplication and Division of Decimals in
Standard Written Method
Last but not least, let us look at multiplication and division of decimals in
standard written method. What is the standard written method in multiplying and
dividing of decimals? The standard written method is a way of locating correctly
the decimal points of 10, 100 and 1,000 or the quotient.

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First, let us look at multiplication. To multiply the decimal by a factor 10, 100 or
1,000, just move the decimal point to the right of the decimal numbers as many
times as the number of 0s (see Example 17 and Example 18).
Example 17:
Multiply 19.15 100
Solution:
Move the decimal point to two places to the right 19.15 100 = 1915
Example 18:
Multiply 9.18 1,000
Solution:
Move the decimal point three places to the right. Attach a zero to the end of the
numbers. 9.18 1 000 = 9180
How about division? To divide the decimal by a factor 10, 100 or 1,000, move the
decimal point to the left of the decimal numbers as many times as the number of
0s.
Let us look at Example 19 and Example 20 for further clarification.
Example 19:
Divide 89 100
Solution:
Move the decimal point two places to the left. 89 100 = 0.89
Example 20:
Divide 271.2 1 000
Solution:
Move the decimal point three places to the left. Attach a zero in front of the
numbers. 271.2 1 000 = 0.2712

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SELF-CHECK 3.3
Solve the following problems and write down how you can explain your
working to your students:
1. 50.45 52
2. 112.5 9
ACTIVITY 3.1
1. Discuss how to compare the decimal numbers 22.36 and 22.31.
2. To convert decimal to fraction, write the numerator as ______
number and denominator as _______. Then ________the fraction.
3. When converting mixed number to fractions, separate the number
into _________and __________.
4. Adding decimal numbers is just like adding whole numbers.
True or False?
5. The standard written method in multiplying the decimal by a factor
10, 100, or 1,000 is by moving the decimal point to the right of the
decimal number as the number of 0s. True or False?
6. Discuss how to multiply 2.93 15.
7. Solve the following:
(a) 43.43 + 54.11
(b) 45.54 – 13.58
(c) 63.79 – 18.33 – 9.89
(d) 89.32 – 31.08 – 38.21

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8. Multiply the following:
(a) 8 . 1 (b) 4 . 6
5 3
_______ _______
(c) 0 . 8 6 (d) 3 . 0 6
8 4
__________ __________
(e) 5 . 8 1 (f) 2 . 0 6
9 8
__________ __________
(g) 6 . 2 6 (h) 5 . 9 3
2 2 9
__________ __________
(i) 2 . 7 0 (j) 2 5 . 6
5 4 3 6
__________ __________
(k) 0 . 5 6 (l) 0 . 6 3
1 4 4 2
__________ __________
9. Divide the following:
(a) 172.5 100
(b) 305.35 10
(c) 76 100
(d) 12. 1 000
(e) 2.94 10
(f) 777.7 10
(g) 31.9 100
(h) 0.8 10
(i) 64.31 100

85. TOPIC 3 DECIMALS
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In this topic, we have learned how to:
Write decimal numbers in words;
Convert fractions to decimal and vice versa;
Convert mixed numbers to fractions and vice versa;
Perform addition and subtraction on two and three decimal numbers;
Solve multiplication and division on two and three decimal numbers; and
Perform multiplication and division of decimals in standard written method.
Addition
Basic unit
Decimal point
Denominator
Descending
Division
Long-division symbol
Multiplication
Numerator
Place value
Standard written method
Subtraction
Vertical line
Whole numbers
Banfill, J. (2006). Comparing decimals. Retrieved on from http://www.aaaknow.
com/dec52_x2.htm
Ministry of Education Malaysia. (2004). Integrated curriculum for primary schools
mathematics Year 4. Kuala Lumpur: Curriculum Development Centre.
Wikimedia Foundation, Inc. (2007). Primary mathematics/decimals. Retrieved
from http://en.wikibooks.org

86. Topic
4
Money
LEARNING OUTCOMES
By the end of this topic, you should be able to:
1. Read the value of money up to RM10,000;
2. Perform addition and subtraction involving money;
3. Perform multiplication and division involving money;
4. Perform mixed operations involving money;
5. Round off money to the nearest ringgit; and
6. Solve problems involving money.
INTRODUCTION
Can you imagine living without money? I am sure this can be very difficult to
imagine as money is very important in our everyday life. We use money to buy
things – clothes, groceries, fuel, houses and so on. Money is also used to pay for
the services given to us, for example, to pay for transport services – bus, taxi, train
and so on. Therefore, it is important for you to understand the mathematical
calculation involving money and how to apply it in your daily life. As for your
students, they are at a stage where they need to use money to buy lunch or
stationery. This topic will be able to help them.
The topic begins with how to read and write the value of money. Then, you will
learn to perform addition and subtraction involving money. After that, you will
learn how to perform multiplication and division involving money. Rounding off
money is also very useful to learn because sometimes we need to estimate the
total amount we have. Lastly, you will learn how to perform mixed operations

87. TOPIC 4 MONEY
75
involving money so that you can do calculations to solve problems in everyday
life.
ACTIVITY 4.1
Ask your students to count how many coins they have.
READING AND WRITING THE VALUE OF
MONEY
4.1
Being able to read and write the value of money will help your students in
everyday life. This knowledge is very useful when you go shopping, save or
withdraw money or do other transactions. The section below will discuss how to
teach reading and writing the value of money up to RM10,000.
Activity 1: Reading and Writing the Value of Money
Objective:
By the end of this activity, your students will be able to read and write the value
of money.
Material:
Savings account book.
Example 1:
(a) The teacher begins this activity by showing the account as shown in the
picture (Figure 4.1).

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Figure 4.1: Read the value of money in a savings account book
(b) Ask them, how many transactions have been made in the account during the
latest month: (i) How much are the deposits? and (ii) How much are the
withdrawals?
(c) Now, look at the arrangement of money given, then read and write the
amount of money. See Figure 4.2.
Figure 4.2: Money
Source: http://www.bnm.gov.my

89. TOPIC 4 MONEY
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ACTIVITY 4.2
1. Read the following amounts:
(a) RM3 126.20 (b) RM5 215.10
2. Write the amount in numbers: Seven thousand eight hundred and
fifty two ringgit.
ACTIVITY 4.3
1. How much are these amounts?
2. Read and write the following amounts in words:
(a) RM48.50 (b) RM895.30
(c) RM995.35 (d) RM5 323.00
(e) RM8 546.15 (f) RM9 876. 86

90. TOPIC 4 MONEY
78
ADDITION AND SUBTRACTION
INVOLVING MONEY
4.2
We use money to pay bills and buy things such as food and tickets. Also, we save
our money in the bank, exchange money and so on. These activities require
knowledge – a very basic knowledge which is addition and subtraction of money.
Let us look at Activity 2 to learn how to add and subtract money.
Activity 2: Addition and Subtraction Involving Money
Objectives:
By the end of this activity, your students will be able to:
(a) Add money.
(b) Subtract money.
Example 2:
(a) Teacher says, “If you go to the electrical shop, you will see some of these
items”. See Figure 4.3.
Figure 4.3: Items and prices in an electrical shop
(b) Ask students to add all the prices of the items above.
(c) Then, tell them that the addition can also be written as:
RM5 995.50 + RM3 677.99 + RM299.99 =

91. TOPIC 4 MONEY
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(d) Next, you align the numbers to be added from the right and add the column
of the digits.
1 2 2 2 1
RM 5 9 9 5 . 5 0
RM 3 6 7 7 . 9 9
+ RM 2 9 9 . 9 9
RM 9 9 7 3 . 4 8
Example 3:
Compare the prices of cameras in Figure 4.4:
Figure 4.4: Cameras
Source: http://www.dcresource.com/reviews/canon/
http://electronics.howstuffworks.com/camera.htm
(a) Tell your students to compare the different prices. Next, tell them to use
subtraction. Subtract the smaller money value from the larger money value.
(b) Then, you write the subtraction in equation form as follows:
RM3,500.90 – RM2,355.89 =

92. TOPIC 4 MONEY
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(c) Show them the subtraction
RM 3 5 0 0 . 9 0
– RM 2 3 5 5 . 8 9
RM 1 1 4 5 . 0 1
Hence, RM3,500.90 – RM2,355.89 = RM1,145.01.
ACTIVITY 4.4
1. What is the total amount of money in ringgit and sen?
(a) RM995.50 + RM3,677.99 + RM2,899.99 =
(b) 515 sen + 6485 sen + 2058 sen =
2. Subtract the amount of money:
(a) RM8,858.20 – RM5,635.25 =
(b) RM3,113.30 – RM110.25 =
MULTIPLICATION AND DIVISION
INVOLVING MONEY
4.3
This section demonstrates to you the multiplication and division of money by a
single digit number. Let us start the lesson!
4.3.1 Multiplication Involving Money
The multiplication of money involves multiplying a decimal number by a single
digit number. The following steps will guide you to do multiplication involving
money:
In your answer, place the decimal point according to the money being multiplied.
Since you are multiplying money, remember to add the RM sign to your answer.

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Activity 3: Multiplication of Money
Objective:
By the end of this activity, your students will be able to multiply money.
Example 4:
Multiply the following: RM0.58 4 =
Solution:
(a) Ask your students to multiply the numbers only.
(b) RM0.58 The number being multiplied has two decimal places.
4
RM232 The answer must also have two decimal places.
(c) Now, ask them where the decimal point for the number 232 should be
placed.
(d) After you get the answer, explain to them that to place the decimal number
they just count the decimal places for the number being multiplied. Since,
the number being multiplied has two decimal places, place two decimal
places counting from right, RM2.32
Hence, RM0.58 4 = RM2.32.
In Example 5, ask all your students to do the multiplication of RM570.35 8 and
guide them using the multiplication steps above. The answer for the multiplication
is as follows.
Example 5:
RM570.35 The number being multiplied has two decimal places.
8
RM4562.80 The answer must also have two decimal places.
This technique can also be called short multiplication. What does it mean?

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You can use the short multiplication technique with a series of simple
multiplication problems. How do you do that? You can do it by multiplying from
right to left and carrying any product of 10 or more to the next column.
4.3.2 Division Involving Money
Division involving money requires the division of a decimal number by a single
digit number. The following steps will guide you in teaching this subject:
(a) Use long division ( ) and start dividing the digits from left to right.
(b) Place the decimal point according to the money being divided.
Again, since you are dividing money, remember to add the RM sign to your
answer.
Activity 4: Division of Money
Objective:
By the end of this activity, your students will be able to divide money.
Let us look at Example 6.

95. TOPIC 4 MONEY
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Example 6:
RM855.30 10 =
Procedure:
(a) For the example above, ask one student to write the division using long
division symbol on the blackboard.
The students should write: 10
(b) Then, ask them whether the number 855.30 can be divided by 10. You know
that 8 multiplied by 10 is equal to 80. Place 8 on top of the division and 80
below 85.
(c) Next, subtract 85 – 80 = 5.
(d)
85.53
10 855.30
- 80
55
50
53
50
30
30
Ask them what number can produce the nearest
value to 55 when multiplied by 10. The answer is 5
(5 50 = 50). Put 5 on top of the division and place
50 below 55 and subtract them. Place the remaining
number below. As 5 is smaller than 10, to divide 5
by 10 you have to bring down 3 to make 53. (There
is decimal point before 3, so place the decimal point
on top of the division). Again, ask for a number
which when multiplied by 10 will result in an
answer less or equal to 53. The answer is 5 (10 5 =
50). So put 5 on top of the division. Then subtract:
53 – 50 = 3. Bring down the digit 0 to make 30.
Finally, ask for a number which when multiplied by
10 will result in an answer less or equal to 30. Since
the answer is 3 (310=30), put 3 on top of the
division. Subtract 30 - 30 = 0. Hence 855.30 10 =
85.53.
Hence, RM855.30 10 = RM85.53.
Next, ask the students to do Example 7 by themselves and guide them as they do
the exercise to make sure they follow the steps above. The answer is given as
follows.

96. TOPIC 4 MONEY
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Example 7:
Divide RM45.05 5 =
Solution:
Divide the digits from left to right, divide 45 5 = 9, then, 5 5 = 1.
9.01 Next, place the decimal point.
5 45.05
- 45.0
5
- 5
0 Hence, RM45.05 5 = RM9.01.
ACTIVITY 4.5
1. Find the multiplication of:
(a) 2 RM156 = (b) 7 RM644.50 =
(c) 5 RM987.80 = (d) 9 RM156 =
2. Calculate:
(a) RM56 6 =
(b) RM2 622 8 =
3. Find the multiplication of:
(a) 4 RM516 = (b) 5 RM106.30 =
(c) 8 RM89 = (d) 3 RM1 156.60 =
4. Solve the division of:
(a) RM55 5 = (b) RM660 6 =
(c) RM3 814 8 = (d) RM5 056 7 =

97. TOPIC 4 MONEY
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5. Do the following multiplication:
(a) 2 RM156 = (b) 7 RM644.50 =
(c) 5 RM987.80 = (d) 9 RM156 =
6. Divide the values below:
(a) RM5,805 5 = (b) RM9,668 6 =
(c) RM5,616 8 = (d) RM3,056 7 =
7. Fill in the blanks:
(a) 7 _________ = RM106.30
(b) 8 RM989.00 = ________
(c) 9 RM156.60 = _______
MIXED OPERATIONS INVOLVING MONEY
4.4
Let us look at mixed operations involving money. I am sure we have to deal with
a lot of calculations every day involving money. To calculate the problems
involving money, you must be familiar with the addition, subtraction,
multiplication and division of money. The following questions are needed to do
operations involving money:
(a) How to write the problem in mathematical symbols?
(b) How to add or subtract the number?
Let us look at Activity 5 that shows you how to perform this kind of calculation.
Activity 5: Mixed Operations Problem Involving Money
Objective:
By the end of this activity, your students will be able to use any of the mixed
operations to solve problems involving money.
Let us look at Example 8 to solve a mixed operation problem involving money.