The Whole

ADRIEL G. ROMAN
MYRICHEL ALVAREZ
AUTHORS
NOEL A. CASTRO
MODULE CONSULTANT
FOR-IAN V. SANDOVAL
MODULE ADVISER

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VISION
A premier university in CALABARZON,
offering academic programs and related
services designed to respond to the
requirements of the Philippines and the
.
global economy, particularly, Asian countries

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MISSION AND MAIN THRUST
The University shall primarily provide advanced
education, professional, technological and vocational
instruction in agriculture, fisheries, forestry, science,
engineering, industrial technologies, teacher education,
medicine, law, arts and sciences, information
technology and other related fields. It shall also
undertake research and extension services, and provide
a progressive leadership in its areas of specialization.

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GOALS
In pursuit of the college vision/mission the
College of Education is committed to develop the
full potentials of the individuals and equip them
with knowledge, skills and attitudes in Teacher
Education allied fields to effectively respond to
the increasing demands, challenges and
opportunities of changing time for global
competitiveness.

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OBJECTIVES OF BACHELOR OF SECONDARY
EDUCATION (BSEd)

Produce graduates who can demonstrate and practice the professional and
ethical requirements for the Bachelor of Secondary Education such as:

1. To serve as positive and powerful role models in the pursuit of learning
thereby maintaining high regards to professional growth.
2. Focus on the significance of providing wholesome and desirable learning
environment.
3. Facilitate learning process in diverse types of learners.
4. Use varied learning approaches and activities, instructional materials and
learning resources.
5. Use assessment data, plan and revise teaching-learning plans.
6. Direct and strengthen the links between school and community activities.
7. Conduct research and development in Teacher Education and other related
activities.

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This teacher’s guide Visual Presentation Hand-out entitled:
“MASTERING FUNDAMENTAL OPERATIONS AND INTEGERS
(MODULAR WORKBOOK FOR 1st YEAR HIGH SCHOOL)” is part of the
requirements in educational technology 2 under the revised
Education curriculum based on CHEd Memorandum Order (CMO)-
30, series of 2004. Educational technology 2 is a three (3) unit
course designed to introduce both traditional and innovative
technologies to facilitate and foster meaningful and effective
learning where students are expected to demonstrate a sound
understanding of the nature, application and production of the
various types of educational technologies.

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The students are provided with guidance and
assistance of selected faculty members of the college
through the selection, production and utilization of
appropriate technology tools in developing technology
based teacher support materials. Through the role and
functions of computers especially the internet, the
student researchers and the advisers are able to design
and develop various types of alternative delivery
systems. These kinds of activities offer a remarkable
learning experience for the education students as
future mentors especially in the preparation of
instructional materials.

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The output of the group’s effort may serve as an
educational research of the institution in providing effective and
quality education. The lessons and evaluations presented in this
module may also function as a supplementary reference for
secondary teachers and students.

FOR-IAN V. SANDOVAL
Computer Instructor/ Adviser/Dean CAS

NOEL A. CASTRO
Engineer/Mathematics Instructor

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PREFACE
This modular workbook entitled “Mastering
Fundamental Operations and Integers (modular workbook for
First Year High School)” aims you to become fluent in solving
any mathematical expressions and problems. This instructional
material will serve as your first step in entering to the world of
high school mathematics.
This modular workbook is divided into two units; the unit
I consist of four chapters which pertains to the four basic
operations in mathematics dealing with whole numbers and the
unit II which pertains to the use of four fundamental operations
in integers.
In mastering the four fundamental operations, you will
study the different parts of the four basic operations (addition,
subtraction, division and multiplication), and their uses and the
different shortcuts in using them. In this part, you will also learn
on how to check one’s operation using their inverse operation.

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In the unit II, you may apply here all the knowledge that you have gained
from the unit I. in this part, you may encounter several expressions where you
need to use all the knowledge that you have gained from the unit I. you will also
learn the nature of Integers, and also the Positive, Zero and Negative Integers.
This instructional material was designed for you to have a further
understanding about the four fundamental operations dealing with Whole
Numbers and Integers. It was also designed for you to have a deep interest in
exploring Mathematics.
The authors feel that after finishing this lesson, you should be able to feel
that EXPLORING MATHEMATICS IS INTERESTING AND FUN!!!

THE AUTHORS

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ACKNOWLEDGEMENT
The authors would like to give appreciation to the
following:

To Mr. For- Ian V. Sandoval, for his kind consideration
and for his advice to make this instructional material more
knowledgeable.
To Mrs. Corazon San Agustin, for her guidance to
finish this instructional modular workbook.
To Prof. Lydia R. Chavez for her wonderful advice to
make this instructional material becomes more
knowledgeable.
To Mrs. Evangeline Cruz for her kind consideration in
allowing us to borrow books from the library.

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To Mr. Noel Castro for giving his advice to make this
instructional material become knowledgeable.
To BSED Section 2 who gave the authors strength to finish
this instructional material.
To our Parents who support us morally and financially
while making this instructional material.
And to ALMIGHTY GOD who gave us knowledge, strength
and power to make and finish this modular workbook.

THE AUTHORS

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Table of Contents

VMGOs
Foreword
Preface
Acknowledgement
Table of Contents
UNIT I- MASTERING BASIC FUNDAMENTAL OPERATIONS
CHAPTER 1- ADDITION OF WHOLE NUMBERS
Lesson 1- What is Addition?
Lesson 2- Properties of Addition
Lesson 3- Mastering Skills in Adding Whole Numbers
Lesson 4- Different Methods in Adding Whole Numbers
Lesson 5- How to solve a word problem?
Lesson 6- Application of addition of whole numbers: WORD PROBLEM
CHAPTER 2- SUBTRACTION OF WHOLE NUMBERS

Lesson 7- What is Subtraction?
Lesson 8- Mastering Skills in Subtraction
Lesson 9- Problem Solving Involving Subtraction of whole numbers

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CHAPTER 3- MULTIPLICATION OF WHOLE
NUMBERS

Lesson 10- What is Multiplication?
Lesson 11- Properties of Multiplication
Lesson 12- Mastering Skills in Multiplying Whole Numbers
Lesson 13- “The 99 Multiplier” Shortcut in multiplying whole numbers
Lesson 14- “Power of Ten Multiplication” Shortcut In Multiplying Whole Numbers
Lesson 15- Problem solving involving Multiplication of Whole Numbers

CHAPTER 4- DIVISION OF WHOLE NUMBERS
Lesson 16- What is Division?
Lesson 17- Mastering Skills in Division of Whole Numbers
Lesson 18- “Cancellation of Insignificant Zeros” Easy ways in Dividing Whole Numbers
Lesson 19- Problem Solving Involving Division of Whole Numbers

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UNIT II- INTEGERS
CHAPTER 5- WORKING WITH INTEGERS
Lesson 20- What is Integer?
Lesson 21- Addition of Integers
Lesson 22- Subtraction of Integers
Lesson 23- Multiplication of Integer
Lesson 24- Division of Integers
Lesson 25- Punctuation and Precedence of Operation

MATH AND TECHNOLOGY
REFERENCES
About the Authors

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Overview

In this unit, you will understand the concept of the basic fundamental operations dealing
with whole numbers. This workbook will help you to master and to become skilled in the
fundamental operations.

This modular workbook provides information about four operations and
how to perform such kind of operation in solving word problem. It also provides
exercises and activities that will help you become skilled and for you to master the
fundamental operations.

Objectives:
After studying this unit, you are expected to:

•discuss the four fundamental operations;
•perform the operations well;
•check the answers in addition and multiplication using their inverse operation.

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Introduction
In this chapter, you will learn deeply the addition operation, the different parts
of it, the different properties and the use of this operation in solving a word problem.
This chapter will serve as your first step in mastering the basic fundamental operations
for this chapter will discuss how to solve a word problem using systematic ways. All the
information you need to MASTER THE FUNDAMENTAL OPERATIONS DEALING
WITH WHOLE NUMBERS is provided in this chapter.

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Lesson 1
WHAT IS ADDITION?

Objectives:

After this lesson, the students are expected to:

• define what addition is;
• identify the different properties of addition;
• perform the operation (addition) correctly.

How well do you remember your basic addition facts? In addition sentence, 326 + 258 = 584 Sum
326 + 258 = 584, which are the addends and which is the sum?

Addition is a mathematical method on putting things together.
Adding whole numbers together is a method that requires
placing the numbers in column to get the answer.
Addition is represented by the plus sign (+). Addends
The addends and the sum are the two parts of addition.
The sum is the total and the addends are the numbers needed to add.

Examples:
1.27 +31=58 the addends are 27 and 31 and the sum is 58.
2.11+21=32 the sum is 32 and the addends are 11 and 21.

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WORKSHEET NO. 1
NAME: ___________________________________ DATE: _____________

YEAR & SECTION: ________________________ RATING: ___________

•Define the following terms

•ADDITION-
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_______________________________________________________________.
•ADDENDS-
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_______________________________________________________________.

•SUM-

________________________________________________________________
________________________________________________________________
________________________________________________________________
_______________________________________________________________.

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ADD THE FOLLOWING

SOLUTION

1. 31481+369=__________________

2. 23634+12438=________________

3. 3497+6826=__________________

4. 81650+3897601=______________

5. 7333+62766=_________________

6. 6. 178654321+236754=___________

7. 6585+8793=__________________

8. 4333+9586=__________________

9. 423381+46537=_______________

10. 546263+9520=________________

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Lesson 2
PROPERTIES OF ADDITION

Objectives:


•define the properties of addition;
•use the different properties of addition in solving;
•perform an operation using the properties of addition.

The 0 Property in Addition

This property states that any number added to 0 is
the number itself, that is, if “a” is any number, a +
0 = a.

Examples: 8 + 0 = 8 27 + 0 = 27
10 + 0 = 10 31 + 0 = 31

The Commutative Property of Addition

This property states that changing the order of the addends does not
change the sum. This means you need to remember only half of the basic facts.
In symbols, the property says that a + b = b + a, for any numbers a and b.:

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Examples:
6 + 8 = 14 8 + 6 = 14
11 + 27 = 38 27 + 11 = 3

Associative Property of Addition

This property states that changing the grouping of the addends does not
affect or change the sum, that is, if a, b and c are any numbers, (a + b) = c = a
+ (b + c).

Examples:
(4 + 3) + 8 = 4 + (3 = 8) = 15
9 + (8 + 6) = (9 + 8) + 6 = 23

Remember to work in the parenthesis first.

Summary:
The 0 Property in Addition
If “a” is any number, a + 0 = a.

The Commutative Property of Addition
If a + b = b + a, for any numbers a and b.

The Associative Property of Addition
If a, b and c are any numbers,
(a + b) = c = a + (b + c).

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WORKSHEET NO. 2
NAME: ___________________________________ DATE: _____________


Identify the properties of the following

1. 265 + 547 = 547 + 265___________________________

2. 85 + 78 = 78 + 85_______________________________

3. 15 + 0 = 15____________________________________

4. 3 + (5 + 9) = (3 + 5) + 9 =17______________________

5. 31+ (21+15) = (31+21) +15 = 67___________________

6. 59 + 0 = 59____________________________________

7. 100 + 0 = 100__________________________________

8. 65 + 498 = 498 + 65_____________________________

9. 9 + 5 = 5 + 9___________________________________

10. (10+10) + 10 = 10+ (10+10) =30___________________

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Lesson 3

MASTERING SKILLS IN ADDING WHOLE NUMBERS USING ADDITION TABLE

Objectives


•use the addition in table properly;
•mastering skills in addition using tables;
•discuss the use of addition table.

Addition Table
The Addition Table can help you to master the addition operation

+ 0 1 2 3 4 5 6 7 8 9 10 11 12
0 0 1 2 3 4 5 6 7 8 9 10 11 12
1 1 2 3 4 5 6 7 8 9 10 11 12 13
2 2 3 4 5 6 7 8 9 10 11 12 13 14
3 3 4 5 6 7 8 9 10 11 12 13 14 15
4 4 5 6 7 8 9 10 11 12 13 14 15 16
5 5 6 7 8 9 10 11 12 13 14 15 16 17
6 6 7 8 9 10 11 12 13 14 15 16 17 18
7 7 8 9 10 11 12 13 14 15 16 17 18 19
8 8 9 10 11 12 13 14 15 16 17 18 19 20
9 9 10 11 12 13 14 15 16 17 18 19 20 21
10 10 11 12 13 14 15 16 17 18 19 20 21 22

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How to use

Example: 3 + 5 + 1 2 3 4 5 6 7
Go down to the "3" row
1 2 3 4 5 6 7 8
then along to the "5" column,
and there is your answer! "8" 2 3 4 5 6 7 8 9
3 4 5 6 7 8 9 10
4 5 6 7 8 9 10 11
5 6 7 8 9 10 11 12

You could also go down
to "5" + 1 2 3 4 5 6 7
and along to "3", 1 2 3 4 5 6 7 8

or along to "3" and 2 3 4 5 6 7 8 9
down to "5" 3 4 5 6 7 8 9 10
4 5 6 7 8 9 10 11
to get your answer.
5 6 7 8 9 10 11 12

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WORKSHEET NO. 3
NAME: ___________________________________ DATE: _____________


•MOTHER OF ALL
SCIENCE!!!

FOLLOW THE INSTRUCTION
1. Have your own addition table
2. With your addition table, add the following
1+4, 0+1, 3+4, 5+0, 5+4
6+4, 7+2, 8+0, 9+2, 10+4
1+6, 3+6, 5+6, 3+10
6+6, 10+6, 6+8, 10+10
3. After adding, try to put dots in every sum.
Try to connect the dots by a line in every number to find what the mother of all science is.

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Add the following numbers correctly. SOLUTION

1. 593423+4467=_____________________
2. 359+4843=________________________
3. 1297+4548=_______________________
4. 696493+266=______________________
5. 1898976+219876=__________________
6. 78589+66533=_____________________
7. 6485092+1764243=___________________
8. 828637+86464=______________________
9. 12379+2873=________________________
10. 53746+783579=_____________________
11. 642578+325646=_____________________
12. 12398+6327355=_____________________
13. 563745+654689=_____________________
14. 57684+8765358=_____________________
15. 425778+87654=______________________

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Lesson 4
DIFFERENT METHODS IN ADDING WHOLE NUMBERS

Objectives


solve addition using other methods;
discuss the different methods in adding whole numbers;
solve mathematical problems using the other method.

There are some easy ways in adding whole numbers.

Adding the column separately. Let 326+258 use as our illustrative example.
Adding in reverse order

326 300+20+6
+258 200+50+8 •Add the numbers in the hundreds
500 place.
•Add the numbers in the tens place.
300+20+6 •Add the numbers in the ones place.
200+50+8 •Then add their sum to get the total
500+70+14 sum.

500+70+14=584

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•Adding in column separately

EXAMPLE:

+ 526
278
14 1.Arrange the numbers vertically.
2.Add the numbers in the ones place.
+ 9 3.Then add the tens place and place the
sum under the tens place.
7 4.Then add the numbers in column.

804

To check;

•Add it upward.
•Subtract the sum to one of the addends.
•Add the numbers in the addends and in the sum if your answer in the
•sum is the same as in the addends, then your answer is correct.

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WORKSHEET NO. 4
NAME: ___________________________________ DATE: _____________


•Using any of the given ways, add the
following and write the answer in the
space provided. Show all your
solutions.

1. 39, 28_________________ 6. 343, 86________________
2. 43, 29_________________ 7. 987, 652_______________
3. 69, 51_________________ 8. 6232, 7434_____________
4. 70, 623________________ 9. 853 234, 578____________
5. 890, 431_______________ 10.6 754 236, 643 123_______

SOLUTION:

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B. Perform the operation using the procedure discussed.
Check your answer by using the short method.
WRITE YOUR SOLUTION

1. 642 890+57 829=______________________
2. 564 872 389+54 738=___________________
3. 12 345+42 321=________________________
4. 3255+6472865=________________________
5. 6437286+56387=_______________________
6. 54390+529=___________________________
7. 6348901+65890=_______________________
8. 7395+7598043=________________________
9. 225+264=____________________________
10. 367+201=____________________________
11. 9 632+2 330=_________________________
12. 1 423+54 673=________________________
13. 543 265+65 223=______________________
14. 673 895 462+54 289=___________________
15. 629 075+57823=_______________________

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Lesson 5

SOLVING WORD PROBLEM

Objectives

•discuss how to solve a word problem;
•solve any given problems systematically;
•use problem solving plan in solving any given word problem.

This problem solving plan should be
used every time we solve word problems.
Careful reading is an important step in
solving the problem. This lesson serves as an
introduction to the next chapter.
Throughout this lesson, we will be
solving problems that deal with real
numbers. In solving word problems, the
following plan is suggested:

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PROBLEM SOLVING PLAN

1. Understand the problem.
2. Devise a plan.
3. Carry out the plan. One harvest season, a farmer
4. Check the answer. harvested 531 sacks of rice.
This was 87 more than his
previous harvest. How many
sacks did he harvest during the
previous season?
Example:

PROBLEM SOLVING PLAN

1. UNDERSTAND THE PROBLEM
Understand the problem and get the general idea. Read the problem
•What is the problem about? one or more times. Each time you read ask:
•What information is given?
Represent what is asked with a symbol. {The problem is about the
•What is being asked?
number of sacks harvested. Let S be the number of sacks during the
previous harvest.}
2. DEVISE A PLAN
This is a key part in the 4 step plan for solving problems. Different
“87 more” suggests addition and we can problem solving strategies have to be applied. A figure, diagram, chart
write a formula: might help or a basic formula might be needed. It is also likely that a related
87+S=531. problem can be solved and can be used to solve the given problem. Another
devise is to use the “trial and learn from your errors” process. There is a lot
of problem solving strategies and every problem solver has own special
technique.

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3. CARRY OUT THE PLAN

If step two of the problem solving plan has been successfully completed in
detail, it would be easy to carry out the plan. It will involve organizing and doing the
necessary computations. Remember that confidence in the plan creates a better working
atmosphere in carrying it out
.
Solve the equations:
87+S=531
S=531-87
S=444 sack

4. CHECK THE ANSWER

This is an important but most often neglected part of problem solving.
There are several questions to consider in this phase. One is to ask if we use
another plan or solution to the problem do we arrive at the same answer.
.

It is reasonable that the
farmer harvested 444 sacks
during the previous harvest.
His harvest now which is 531
is more than the last harvest

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WORKSHEET NO. 5

NAME: ___________________________________ DATE: _____________


A. Discuss the different problem solving plan briefly.

1. Understand the problem
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
____________________________________________________________.
2. Devise a plan-
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_________________________________________________________.
3. Carry out the plan
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_________________________________________________________.
• Check the answer
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
_________________________________________________________.

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Lesson 6

APPLYING ADDITION OF WHOLE NUMBERS IN WORD PROBLEM

Objectives

•analyze the given problem;
•to develop the skills and knowledge in solving word problems;
•identify the different steps in word problems involving addition.

LOOK AT THE EXAMPLE

A farmer gathered 875 eggs from one poultry house and 648 from another. How many eggs did he gather?
We want the answer to 875 + 648 =?
Add the ones: 5 + 8 = 13 ones = 1 ten + 3 ones.
• Write 3 in the ones column and bring the 1 ten to
11 the tens column.
• Add the tens: 1 +7 +2 = 12 tens = 1 hundred + 2
875 tens.
• Write 2 under the tens column and bring the 1
+648 hundred to the hundreds column.
•
1 523 Add the hundreds: 1 + 8 + 6 = 15 hundreds = 1
thousand + h hundreds. Write 15 to the left of 2.
The farmer gathered 1 523 eggs.
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Here is another example:

Add: 5 326 + 1 456 =?
•6 + 6 = 12 =10 + 2
•1 ten + 2 tens + 5 tens = 8 tens
Add: 5 986 + 3 759 =? •3 hundred + 4 hundreds=7 hundreds
•6 + 9 = 15 =10 + 5 5 thousand +1 thousands= 6 thousands.
1 11 •1 ten + 8 tens + 5 tens = 14 tens = 1 hundred + 4 tens. Thus, 5 326 + 1 456 =6782
•1 hundred + 9 hundreds +7 hundreds = 17 hundreds = 1
5 986 thousand + 7 hundreds.
+3 759 1 thousand +5 thousands + 3 thousands = 9 thousands. 1
9 745
Thus, 5 986 + 3 759 = 9 745
5 326
+ 1 456

6782
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WORKSHEET NO. 6
NAME: ___________________________________ DATE: _____________


Answer the following problem solving

1. Mr. Parma spent Php.260 for a shirt and Php.750for a pair of shoes. How much did he pay in all?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
______________________________________________________________.

2. Miss Callanta drove her car 15 287 kilometers and 15 896 kilometers the next year. How many
kilometers did she drive her car in two years?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
______________________________________________________________.

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3. Four performances of a play had attendance figures of 235, 368, 234, and 295. How many
people saw the play during the period?
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_____________________________________________________________________________.

4. The monthly production of cars as follows: January-4,356, February- 4,252, and March- 4425,
June-4456, July-4287, August-4223, September-4265, October-4365, November-4109, and
December- 4270. How many cars were produced in the whole year?

_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_____________________________________________________________________________.

5. If a sheetrock mechanic has 3 jobs that require 120 4x8 sheets, 115 4x8 sheets, and 130 4x8
sheets of sheetrock respectively. How many 4x8 sheets of sheetrock are needed to complete the 3
jobs?
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
__________________________________________________________________________

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Introduction
In this chapter, you will learn the subtraction operation,
the different parts of it and the use of this operation in solving
word problem. You will also learn the different ways on how
to solve and check the answer or the difference which you can
use in your everyday life. This chapter provides the
information that will help you master the subtraction as one of
the fundamental operation in Mathematics.

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Lesson 7

WHAT IS SUBTRACTION?

Objectives


define what is subtraction;
identify the parts in subtraction;
differentiate the subtraction from addition.

What is Subtraction?

After learning and describing addition as a process of
combining two or more groups of objects, we can now
consider its opposite operation --- Subtraction. If addition is
combining of group of object, subtraction is the process of
taking away or of removing something. The symbol used for
subtraction is the minus sign (-).

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When we write 12 – 6, we wish to subtract 6 from 12 or to
take away 6 from 12. To find the difference between two numbers, we
have to look for a number which when added to the subtrahend, will
give the minuend. The table shows the relation between addition and
subtraction. One undoes the work of the other.

Let us consider the notation below.

+ 6 addend
12 addend
18 sum Minuend 18
Subtrahend -6

Difference 12

Difficulties may arise in subtraction when a digit of the subtrahend is
larger than the corresponding digit in the minuend. The process of doing a
subtraction of this type is called barrowing or regrouping

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WORKSHEET NO. 7
NAME: ___________________________________ DATE: _____________


A. Give the meaning of the following words.

1. Subtraction-________________________________________________
2. Minuend-__________________________________________________
3. Subtrahend-________________________________________________
4. Difference-_________________________________________________

B. Name the following parts of the mathematical expression given below.

12638 _____
- 3630 _____
9008 _____
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D. Solve the following to get the difference
WRITE YOUR SOLUTION HERE:

1. 349 2. 1243 3. 5428 4. 10,000
-265 -360 -2001 -6,543

1. 5637584-43675=________________
2. 5389-782=_____________________
3. 43674-768=____________________
4. 376598-5281=__________________
5. 67396-683=____________________
6. 57290-7849=___________________
7. 56284-6847=___________________
8. 683963-68363=_________________
9. 6254-978=_____________________
10. 654-87=______________________

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Lesson 8
MASTERING SKILLS IN SUBTRACTING WHOLE NUMBERS

Objectives


•enhance the knowledge in terms of subtracting whole numbers;
•develop the speed in solving subtraction;
•perform the steps in subtracting whole numbers.

Cain kiblah type his report in physics at the computer shop for about
5 hours and 17 minutes while Lane Margaret types her report for only 3
hours and 28 minutes. How fast does Lane Margaret type her report than
Cain kiblah?

To make the subtraction convenient, we borrow 1 minute so we have:

5 hrs + 17 mins 5 hrs + 17 mins
- 3 hrs + 28 mins 77mins
1 hr + 49mins - 3 hrs + 28 mins

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WORKSHEET NO. 8
NAME: ___________________________________ DATE: _____________


Solve and get the difference Simplify the following numbers

1.10327-1685=____________
•Subtract 381 from 1895
2.74577-7658=____________
3.9443-99195=____________
4.14652-9195=____________
Subtract 443 from 1084
5.19919-8881=____________
6.8322-4909=____________
7.8851-8453=____________
8.7609-6957=____________
•Subtract670 from 2064
9.8858-182=_____________
10. 8905-18=___________
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Lesson 9
PROBLEM SOLVING INVOLVING SUBTRACTION
Objectives


follow the steps correctly in problem solving involving subtraction;
discuss the different steps in problem solving;
develop the knowledge in problem solving.

To master the application of
subtraction in problem solving,
here are some examples:

Pedro had marbles. He gave away two of his marbles to Juan. If Pedro had
twelve marbles, how many marbles left to Pedro after he gave two to Juan?
We can use the problem solving plan:
1.
Know what the problem is.
a.
What is asked? How many marbles left to Pedro?
b.
What are given? 12 marbles of Pedro and 2 to Juan
c.
What operation to be used? Subtraction
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12 – 2 = n 12 – 2 = 10

N = 10 marbles left to Pedro.

Checking:
2 + 10 = n 2 + 10 = 12

Another example:
Mt. Everest, is 29 028 ft. high, while the Mt. McKinley is 20 320 ft. high. How much is Mt. Everest
higher than Mt. McKinley?

1. What is asked?
How much Mt. Everest higher than Mt. McKinley?

2. What are given?
Mt. Everest, is 29 028 ft. high and Mt. McKinley is 20 320 ft. high.

3. What operation to be used?
Subtraction
29 028 – 20 320 = n
29 028 – 20 320 = 8 708 ft.
Checking:
8 708 + 20 320 = n
8 708 + 20 320 = 29 028

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WORKSHEET NO. 9
NAME: ___________________________________ DATE: _____________


A. Get one whole sheet of
paper and solve the following problem.

1. In 1992, William Clinton got 44 908 254 votes as the president of USA while George Bush got 39 10 343 votes
and Foss Perot got 19 741 65 votes. How many more votes did Clinton have than Bush? Bush than Foss?

____________________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.

2. In May of 1994, there were 42 518 000 beneficiaries in the social security program while there were
41 784 000 beneficiaries on May 1993. How much was the increase of beneficiaries from 1993 to 1994?

____________________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.

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3. In 1998, a school had an enrollment of 5908 pupils while there are 6519 pupils enrolled in
1999. How much more pupils enrolled in 1999 than in 1998?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
________________________________.
4. Martial law was declared in 1972. Now, it is 2009, how many years ago it was?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
________________________________.
5. If Clark was born on December 31 2009, how old is he now?
________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________.
6. What number will make 2 816 to become 5229?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
____________________________.
7. A philanthropist donated P850 765 to an orphanage. The amount was used for some repairs and
the purchase of some equipment worth P519 800. How much money was left for other projects?

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______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
_________________.

8. If you born on 1953, how old are you now?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
_________________.

9. Mr. Fabre exported to other Asian countries P2 759 000 worth of furniture while Mr. Co exported P5 016
298 worth. How much more where Mr. Co’s exports than those of Mr. Fabre?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
________________.

10. The total number of eggs produced in the United States in 1993 was 71, 391, 000,000. The total
number of eggs produced in 1992 was 70,541,000,000. How many more eggs were produced in the United
States in 1993 than in 1992?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
_________________.

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Introduction

In this chapter, you will learn about the multiplication
operation, its different parts and ways in solving it and the use of this
operation in word problem. This chapter provides lessons and exercises
that will help you to master the multiplication of whole numbers.

Contents Back Next

Lesson 10
WHAT IS MULTIPLICATION?

Objectives

After this lesson, the students are expected to;

•define what multiplication is.
•identify the part of multiplication.
•perform the multiplication operation properly.

Multiplication is a repeated addition. It can be thought of as
addition repeated a given number of times.

For example, 3 x 5 = 15 can be solving as 5 + 5 + 5 =15. 3 mean that the 5 is to be used three times. The same problem
can also be thought of as 5x 3, or 3 + 3 +3 + 3 + 3 =15. Written this way, the three is used as a total of five times in either case
is 15.

The number in the upper part is called the
multiplicand and in the lower position is called the
3 multiplicand multiplier. The answer in the multiplication is called product.
5 multiplier
15 product

Contents Back Next

WORKSHEET NO. 10
NAME: ___________________________________ DATE: _____________


A. Identify the following.
7 __________
2 __________
14 ___________

B. Get the product of the following.

1.32 x 25= 6. 14 x 193=

2. 10 x10 = 7. 66 x 15=

3.25 x 68= 8. 157 x 11=

4.31 x1545= 9. 655 x 8=

5.27 x 17781= 10. 856 x 18=

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Lesson 11
PROPERTIES OF MULTIPLICATION
Objectives


oreview the different properties of multiplication;
odevelop the knowledge in the properties of multiplication;
oapply the properties of multiplication in solving problem.

1. IDENTITY PROPERTY
The product of the 1 and any number a is a, that is, 1 x a = a for any number.

Example:

21 x a = 21 27 x a =27 31 x a = 31
11 x a = 11 5xa=5 13 x a = 13

2. ZERO PROPERTY
The product of 0 and any number a is 0, that is a x 0 = 0 for any number a.

Example:

0 x 87 = 0 0 x 98 = 0 15 x 0 = 0
45 x 0 = 0 14 x 0 = 0 58 x 0 = 0
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3. COMMUTATIVE PROPERTY

Changing the order of the factors does not change the product, that is, a x b = b x a for any
number of a and b.

Example:

7 x 4 = 28 = 4 x 7 5 x 12 = 60 = 12 x 5
5 x 6 = 30 = 6 x 5 4 x 11 = 44 = 11 x 4

4. ASSOCIATIVE PROPERTY

Changing the grouping of the factors does not affect the product, that is, a x (b x c) = (a x b) x c for
any number of a, b, and c.

Example:

(7 x 4) x 5 = 140 = 7 x (4 x 5)
(4 x 6) x 8 = 192 = 4 x (6 x 8)

5. DISTRIBUTIVE PROPERTY

If one factor is a sum of two numbers, multiply the addends to the multiplier before adding will not
change the answer, that is a x (b + c) = (a x b) + (a x c).

Example:

5 x (6 + 7) = 30 + 35 = 65
6 x (7 + 9) = 42 + 54 = 9 Back Next

WORKSHEET NO. 11
NAME: ___________________________________ DATE: _____________


AFill on the blank and identify the
property of each.

1. (8 x 4) + (8 x 6) = 8 x (__ + 6) = ______

2. (7 x 5) x 2 = 7 x (__ x __) = ______

3. (9 x 5) = 25 x__ = _______

4.8 x 0 = ______

5. (12 x 3) + (12 x 7) = _____

B. Fill the missing number. Use the property of multiplication to get product

1. 6 x 7 = __ x 6 6. (7 x __) + (__ x 6) = 7 x (3 +6)

2. 5 x 0 = __ 7. 27 x __ = 27

3. 8 x 1 __ 8. 8 x __ = 0

4. (4 x 5) x 7 = 4 x (__ x 7) 9. 6 x (3 x 4) = (6 x __) x 4

5. 8 x (2 + __) = (8 x 2) + (8 x __) 10. 4 x 9 =__ x 4

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Lesson 12
MASTERING SKILLS IN MULTIPLYING WHOLE NUMBERS
Objectives


multiply whole numbers in easy way;
develop the speed in multiplying whole numbers;
perform multiplication correctly.

Since multiplication is a shortcut for
1 1 Carries repeated addition, we can get the product of a
2 4 two factors without the use of a two factors
without the use of repeated addition. Take a look
3 5 8 Multiplicand
at the example:
x 2 5 Multiplier

1 7 9 0 1st partial product
+7 1 6 2nd partial product

8 9 5 0 Product

Contents Back Next

In mastering the multiplication operation, knowing how
to multiply using multiplication table helps you to become
fluent in multiplying numbers.

How to use multiplication table?

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Multiplication Table

X 0 1 2 3 4 5 6 7 8 9 10 11 12

0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9 10 11 12

2 0 2 4 6 8 10 12 14 16 18 20 22 24

3 0 3 6 9 12 15 18 21 24 27 30 33 36

4 0 4 8 12 16 20 24 28 32 36 40 44 48

5 0 5 10 15 20 25 30 35 40 45 50 55 60

6 0 6 12 18 24 30 36 42 48 54 60 66 72

7 0 7 14 21 28 35 42 49 56 63 70 77 84

8 0 8 16 24 32 40 48 56 64 72 80 88 96

9 0 9 18 27 36 45 54 63 72 81 90 99 108

10 0 10 20 30 40 50 60 70 80 90 100 110 120

11 0 11 22 33 44 55 66 77 88 99 110 121 132

12 0 12 24 36 48 60 72 84 96 108 120 132 144
Example:
Remembering 9's
What's 9 x 7? Use the 9-method! Hold out all 10 fingers,
and lower the 7th finger.

There are 6 fingers to the left and 3 fingers on the right.
The answer is 6.

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WORKSHEET NO. 12
NAME: ___________________________________ DATE: _____________


• Find the product of the following. (You may use a multiplication table if you want).

WRITE YOUR SOLUTION HERE:

1. 59x 8 =________________
2. 48 x 3 =_______________
3. 31 x 6 =_______________
4. 27 x 21 =______________
5. 11 x 15 =_______________
6. 21 x 27 =_______________
7. 14 x 17 =_______________
8. 8 x 32 = ________________
9. 78 x 45 =_______________
10. 11 x 23 =_____________

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Lesson 13
“THE 99 MULTIPLIER” SHORTCUT IN MULTIPLYING WHOLE NUMBER

Objectives

multiply whole numbers mentally;
appreciate exploring the world of multiplication;
appreciate the multiplication operation.

This lesson is concern in one of the easy ways in
getting the product in multiplication. If the digits in the
multiplier (or even multiplicand) are all 9 such as 9, 99, 999…,
annex to the multiplicand as many zeros as there are 9’s in the
multiplier and from it, subtract the multiplicand.

Here some examples:

999 364= 364 000-364= 369 636 Why?

2834 99= 283 400-2834= 280566 Why?

31×999= 31 000-31= 30 969 Why?
Contents Back Next

WORKSHEET NO. 13
NAME: ___________________________________ DATE: _____________


•Multiply the following using the “99 multiplier” method.
•99×99=________________________
•33×99=________________________
•47x99=________________________
•65x9=_________________________
•21x99=________________________
•81x99=________________________
•72x999=_______________________
•56x9999=______________________
•34x9=_________________________
•8x9=__________________________

B. Solve the following
•Find the product of 873 and 9999=________________________
•Find the product of 132 and 999=_________________________
•Find the product of 665 and 99=__________________________
•Find the product of 670 and 9=___________________________
•Find the product of 493 and 999=_________________________

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Lesson 14
“THE POWER OF TEN” MULTIPLICATION

Objectives

specializing skills in multiplication;
perform multiplication easily;
develop the speed in multiplying numbers.

When the factors are in the power of ten such as 10, 100, 1000, 10 000, 100 000 and so on
and so fort, just multiply the digit that is form 1 to 9 and add the number of zeros.

Example:

31 x 100 = 3 100
270 x 10 = 2 700
15 000 x 100 = 1 500 000

When the factors are end in both zero, multiply the significant number and used the number of zeros
in both factors to the product.

Example:

2 380 x 40 = 95 200
2 380 x 400 = 952 000
Contents Back Next

WORSHEET NO. 14
NAME: ___________________________________ DATE: _____________


A. Based to the power of ten, multiply the following.

1. 100 x 320 =_________ 6. 75 x 100 =_________
2. 10 x 27 = __________ 7. 56 x 10 = __________
3. 100 x 414 = ________ 8. 38 x 100 =__________
4. 176 x 100 = ________ 9. 68 x 10 000 =________
5. 39 x 1 000 = ________ 10. 59 x 1 000 =________

B. Find the product of the following.

1. 2 080 x 30 =____________ 6. 720 x 40 =____________
2. 3 150 x 60 =____________ 7. 7 230 x 50 =___________
3. 1 470 x 20 =____________ 8. 2 030 x 60=___________
4. 30 x 90 =____________ 9. 456 x 70=____________
5. 30 x 80 =____________ 10. 86 x 690=____________

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Lesson 15
PROBLEM SOLVING INVOLVING MULTIPLICATION
Objectives

•describe how to use the multiplication in problem solving;
•follow the steps correctly in multiplication of word problem;
•discuss the use of multiplication in problem solving.

A screw machine can produce
95 screws in one minute. How many
screws it can produce in one hour?

1. What is asked?
How many screws a screw machine can produce in one hour?

2. What are given?
Screw machine can produce 95 screws in a minute.

Multiplication

Contents Back Next

Solution:
60 minutes = 1 hour
95 crews x 60 minutes = n

Therefore, the screw machine can produce 5 700 crews in one hour.

N = 5 700 screws.

Here is another example,
A department store bought 32 crates of portable radios. Each crate contains 50 radios.

How many portable radios does the store have?
1. What is asked?
How many portable radios does the store have?
2. What are given?
50 portable radios in 1 crate and 32 crates
Multiplication
Solution:
1 crate = 50 radios
32 crates x 50 radios = n
N = 1 600 portable radios

Therefore, there are 1 600 portable radios does the store
have.

Back
Back Next
Next

WORKSHEET NO. 15
NAME: ___________________________________ DATE: _____________


Answer the following word problem.

1. Victoria and her brother, Daniel, deliver Sunday papers together. She delivers 58 papers and he delivers 49
papers. Each earns 75 cents for each paper delivered. How much more does Victoria earn than Daniel each
Sunday?
________________________________________________________________________________________
________________________________________________________________________________________
_______________________________________________________________________________________.

2. In one basketball stadium, a section contains 32 rows and each row contains 25 seats. If the stadium has 4
sections, how many seats it has?
________________________________________________________________________________________
________________________________________________________________________________________
_______________________________________________________________________________________.

3. Season tickets for 45 home games cost P789. Single tickets cost P15 each. How much more does a season
ticket cost than individual tickets bought of each game?
________________________________________________________________________________________
________________________________________________________________________________________
_______________________________________________________________________________________.

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4. A store has 124 boxes of pencils with 144 pencils in each box. How many pencils they have?
_________________________________________________________________________________________
_________________________________________________________________________________________
_____________________________________________________________________________________.

5. An eagle flies 70 miles per hour. How far can an eagle fly in 15 hours?
_________________________________________________________________________________________
_________________________________________________________________________________________
_____________________________________________________________________________________.

6. Mandy can laid 65 bricks in 30 minutes. How many bricks can Mandy lay in 5 hours?
_________________________________________________________________________________________
_________________________________________________________________________________________
_____________________________________________________________________________________.

7. Sound waves travels approximately 1 100 ft. per sec. in air. How far will the sound waves travel in 3 hours?
_________________________________________________________________________________________
_________________________________________________________________________________________
_____________________________________________________________________________________.

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8. One cassette seller sold 650 cassettes. The cassettes cost her P15.00 each and sold them for P29.00 each. What
was her total profit?
____________________________________________________________________________________________
____________________________________________________________________________________________
_______________________________________________________________________________.

9. If a worker can make 357 bolts in one hour, how many bolts he can make in eight hours?
____________________________________________________________________________________________
____________________________________________________________________________________________
_______________________________________________________________________________.
10. If 1cubic yard of concrete costs P55.00, how much would 13cubic yards cost?
____________________________________________________________________________________________
____________________________________________________________________________________________
_______________________________________________________________________________.

SOLUTION:

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Introduction
In this chapter, you will learn about the division operation
its different parts and uses in solving word problem. This chapter
provides you the information you need to master one of the fundamental
operations in mathematics which is division.

Contents Back Next

Lesson 16

WHAT IS DIVISION?

Objectives

 define division;
 identify the parts of division;
 discuss the division operation.

In mathematics, especially in elementary arithmetic, division ( ) is the
arithmetic operation that is the inverse of multiplication. Division can be
described as repeated subtraction whereas multiplication is repeated addition.
Division is defined as this reverse of multiplication. In high school, the process is
also the same.

64 8=8
since since
8 X 8=64

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In the above expression, a is called the dividend, b the divisor and c the
quotient.

Example:

Suppose that we have twelve students in the class and we want to divide the class into three equal groups.
How many should be in each group?

Solution:

We can ask the alternative question, "Three times what number equals twelve?"
The answer to this question is four.

We write

4
3 12 or 12 3=4

we call the number 12 the dividend, the number 3 the divisor, and the number 4 the quotient.

quotient
divisor dividend or dividend divisor = quotient

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Example •Division by Oneself

Suppose that you had $100 and had to distribute all the money to 100 people so that each person
received the same amount of money. How much would each person get?

Solution

If you gave each person $1 you would achieve your goal. This comes directly from the identity property of one. Since
the questions asks what number times 100 equals 100.

In general we conclude,

Any number divided by itself equals 1
Example

100 100 = 1 38 38 = 1 15 15 = 1

B. Division by 1

Example
Now let’s suppose that you have twelve pieces of paper and need to give them to exactly one
person. How many pieces of paper does that person receive?

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Solution

Since the only person to collect the paper is the receiver, that person gets all twelve pieces. This also comes
directly from the identity property of one, since one times twelve equals one.

Examples

12 1 = 12 42 1 = 42 33 1 = 33

When Zero is the Dividend

Any number divided by 1 equals itself

Example

Now lets suppose that you have zero pieces of pizza and need to distribute your pizza to four friends so that each
person receives the same number of pieces. How many pieces of pizza does that person receive?

Solution

Since you have no pizza to give, you give zero slices of pizza to each person. This comes directly from the
multiplicative property of zero, since zero times four equals zero.

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Zero divided by any nonzero number equals zero

Examples

0 4=0 0 1 = 0 0 24 = 0

The Problem with Dividing by Zero

Example

Finally lets suppose that you have five bags of garbage and you have to get rid of all the garbage,
but have no places to put the garbage. How can you distribute your garbage to no places and still get rid of it all?
Solution

You can't! This is an impossible problem. There is no way to divide by zero.

Dividing by zero is impossible

Examples
5 0 = undefined 0 0 = undefined 1 0 = undefined

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WORKSHEET NO. 16
NAME: ___________________________________ DATE: _____________


A. Give the name of the following unknown parts of division.

___________ 56 8=7 _________

_______________

B. As far as you remember, try to divide the following.

1.56 7=
2.54 6=
3.900 100=
4.64 16=
5.56 8=
6.122 11=
7.144 12=
8.256 16=
9.180 9=
10.360 4=
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Lesson 17
MASTERING SKILLS IN DIVISION OF WHOLE NUMBERS

Objectives

•develop knowledge in dividing whole numbers;
•follow the steps in dividing whole numbers;
•master the division of whole numbers.

In mastering the division operation, you should need to know all the things
in this operation. When dividing numbers, it has not always given an exact
quotient. This process is what we called division with remainder.

Division with Remainder

Often when we work out a division problem, the answer is not a whole number.
We can then write the answer as a whole number plus a remainder that is less than the divisor.
Example
34 5
Solution
Since there is no whole number when multiplied by five produces 34, we find the nearest number
without going over. Notice that

5 x 6 = 30 and 5 x 7 = 35
Hence 6 is the nearest number without going over. Now notice that 30 is 4 short of 34. We write
34 5 = 6 R 4 "6 with a remainder of 4“0
Contents Back Next

Example
4321 6

Solution
720
6 | 4321
42 6 x 7 = 42
12 43 - 42 = 1 and drop down the 2
12 6 x 2 = 12
0 6x0 = 0
We can conclude that 4321 6 = 720 R1 1 1-0 = 1
In general we write
(Divisor x quotient) + Remainder = dividend

Example 511
37 18932
185 37 x 5 = 185
43 189 - 185 = 4 and drop down the 3
37 37 x 1 = 37
37 37 x 1 = 37
25 62 - 37 = 25
We can conclude that
18932 37 = 511 R25

Take note: the remainder may also be expressed in decimals.

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(SPECIAL TOPIC)

Mental Division of Whole Numbers

The process of division is just multiplication in reverse.

This means that if 4 3 = 12 then 12 3 = 4 and 12 4=3

If you know your multiplication tables well, you should find it reasonably easy to do simple divisions in your head

.
For example: you want to work out 42 7, and you remember that 6 7 = 42,
• Brackets first
so the answer is 6.
• O
• Divide
When there is more than one operation in a question, you need to remember the order in
• Multiply
which operations are carried out. This can be summarized by BODMAS:
• Add
• Subtract

If you see two of the same operation you just do them in the order they appear (left to right).
Below are three examples of BODMAS used in a question.

(a) 3 + 4 5 = 3 + 20 = 23 (Multiply before Add)

(b) 10 ( 2 + 3 ) = 10 5=2 (Brackets before Division)

(c) 20 2 2 = 10 2=5 (do operations left to right)

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WORKSHEET NO. 17
NAME: ___________________________________ DATE: _____________


Work out the answers to the questions below and fill in the boxes.

Question 1 (a) 16 4 _________
(b) 12 6 _________
(c) 15 5 _________
(d) 20 4 _________
(e) 18 9 _________
(f) 40 8 _________

Use mental arithmetic to answer these questions (g) 36 9 _________
(do not use a calculator). Then check.
(h) 15 3 _________
(i) 64 8 _________
(j) 42 7 _________
(k) 24 6 _________

(l) 32 8 _________

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Use BODMAS to work out
whether these statements
are TRUE or FALSE.

(a) 10 2=2 10
__________

(b) 12 + 8 2 = 10 __________

(c) 3 + 12 4=6 __________

(d) 6 2+3=6 __________
Work out the answers to the following questions (without a calculator).

(a) 3 + 4 8
__________

(b) 8 + 3 6 __________

(c) 8 6-4 __________

(d) 12 2+5 __________

(e) 5 - 12 3 __________

(f) 14 2+8 __________

(g) 3 2+8 4 __________

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Lesson 18
“CANCELLATION OF INSIGNIFICANT ZEROS “EASY WAYS IN DIVIDING WHOLE NUMBERS

Objectives
divide whole numbers using other method;
perform division of whole numbers mentally;
define “ cancellation of insignificant zeros.”

The cancellation of Insignificant Zeros is one of
the easy ways in performing division of whole numbers.
It is done by cancelling the insignificant zeros in both the
divisor and the dividend.

Contents Back Next

101
50 5050 505 5=101 ( both dividend and divisor)
50
050
050
0

210
2. 5 1050 105 5=21(10) =210 (the insignificant zero in
-10 dividend was cancelled)
-50 To check multiply the quotient to the divisor then
50 multiply also the place value of the removed zeros
0 Remember that in
cancelling both the
dividend and divisor, the
insignificant zeros are
Examples needed to be the same. If
you cancelled 3 zeros in
the dividend, you need
300÷10=30 also to cancel 3 zeros
50÷50=1 from the divisor.
1000÷10=100

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WORKSHEET NO. 18
NAME: ___________________________________ DATE: _____________


•Divide the following using the Cancellation of Insignificant Method.

1. 640 80=___________________

2. 140 20=___________________

3. 36000 600=________________

4. 700 350=__________________

5. 3500 70=__________________

6. 350 100=__________________

7. 5600 800=_________________

8. 600 30=___________________

9. 100 50=____________________

10. 800 40=___________________

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11. 1000 100=_________________ WRITE YOUR SOLUTION HERE:

12. 140 70=___________________
13. 420 20=____________________
14. 14000 70=_________________
15. 36000 180=_________________
16. 4800 240=_________________
17. 99000 330=________________
18. 860 20=___________________
19. 770 770=__________________
20. 630 30=___________________

Draw a 2 dimensional clock.
Then draw a line across the clock so that the sum of the numbers in each group is the same.

B. CHALLENGE!!!
• Copy the figure. Show how to divide it into 2 equal parts.
Each part must have the same size and shape.
• Copy the figure again. Show how to divide it in 3 equal parts.
• Copy the figure again. Show how to divide it in 4 equal parts.

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Lesson 19
PROBLEM SOLVING INVOLVING DIVISION OF WHOLE NUMBERS

Objectives

• solve the given problem critically;
• follow the steps in problem solving ;
• apply the division of whole numbers in solving mathematical problem.

Like the first three operations, the division operation is very usable to
our daily lives. We use also this operation to solve some problems. Take a
look and study the examples given below

Example

You are the manager of a ski resort and noticed that during the month of January you sold a total of 111,359 day ski
tickets. What was the average number of tickets that were sold that month?

Contents Back Next

Solution
Since there are 31 days in January, we need to divide the total number of tickets by 31

3589
31 | 111259
93 31 x 3 = 93
182 111 - 93 = 18 and drop down the 2 Answer: The ski resort
155 31 x 5 = 155 averaged 3,589 ticket sales
275 182 - 155 = 27 and drop down the 5 per day in the month of
248 31 x 8 = 248 January.
279 275 - 248 = 27
279 31 x 9 = 279
0
Another example
Courtney is hanging glow in the dark stars in each room of his house. If there are 160 stars
in the box and she wants 16 in each room, how many rooms can she hang stars?

Solution
Since there are 160 stars in the box and she wants 16 in each room. And the problem is
asking for how many stars in each room will be?

10
16 160 16x1=16 Answer: Courtney can hang
16 16-16=0 her 160 stars in 10 rooms
00 16x0=0
00
0

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WORKSHEET NO. 19
NAME: ___________________________________ DATE: _____________


A. Analyze and solve the following problems.

1. Jacinta has 5 pennies in a jar. If she divides it into 2 stacks of 50, how many stacks does she have now?
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
________________.

2. Harry has 300 pieces of chalk with the same amount in each box. There are 20 boxes how many pieces of chalk
in EACH box?
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________.

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3. The surface area of a floor is 150 square feet. How many 10 ft. square tiles will be needed (inside of 150
feet) to cover the floor? (How many 10's are inside of 150?)
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
_____________________________________________.
4. Billy was offered a job at the nearby golf course. The owner offered him $500.00 per seven day week or
$50. the first day and agreed to double it for each following day. How could Billy make the most amount of
money? Which deal should he accept and why?
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_________________________________________.

5. Sally is having a birthday party with 10 people. When everyone gets there she asks everyone to introduce
themselves and shake everyone's hand. How many handshakes will there be? How do you know?
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_________________________________________.

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Overview
In UNIT II, you will expect the concept of the basic fundamental operations
dealing with the integers the concept, the nature and the difference between them.
Likewise, the lessons provided in this unit will enable you to perform skillfully
the four fundamental operations with integers.
You will think much critically to perform the activities and to
solve the exercises that will be given to you in this unit. This unit also contains
precedence of operations which you can use in Algebra II.
Objectives:
After studying this unit, you are expected to:
1. discuss the integers;
2. use the fundamental operations in solving integers;
3. appreciate the integers as a part of your discussion;
4. gain more knowledge about integers that will guide you in the world of
algebra;
5. discuss the order of operation.

Contents Back Next

Introduction
You have finished Unit 1 of this modular workbook. You now
already reviewed what you have taken in your Elementary level .
Now, you are ready to proceed to the next chapter of this modular
workbook, the INTEGERS. This chapter will give you a deep
understanding about integers, the different kinds of integers, the uses of
integers in Mathematics and the functions of integers in our real world.
In studying high school math, integers are always present. It seems
that you have already mastered the fundamental operations in whole
numbers you may now proceed to the next chapter which is the application
of the four fundamental operations that you have mastered.

Contents Back Next

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