The document is a comprehensive overview of addition and subtraction of whole numbers, covering concepts such as reading, writing, and rounding whole numbers, as well as their properties and visual representation. It explains the Hindu-Arabic numeration system, the significance of digits, and methods for graphing and approximating whole numbers. Exercises are provided to reinforce understanding of these mathematical fundamentals.

1. Chapter 1
Addition and Subtraction of
Whole Numbers
FUNDAMENTAL OF MATHEMATICS

2. Chapter 1: Addition and Subtraction of
Whole Numbers
• 1.1 Reading and Writing Whole Numbers
• 1.2 Rounding Whole Numbers
• 1.3 Addition of Whole Numbers
• 1.4 Subtraction of Whole Numbers
• 1.5 Properties of Addition
Source:
Fundamental of Mathematics Denny Burzynski & Wade Ellis
https://cnx.org/contents/XeVIW7Iw@4.6:l0Q7pQNZ@5/Addition-of-Whole-Numbers

3. Chapter 1: Addition and Subtraction of
Whole Numbers
1.1 Reading and Writing Whole Numbers
Objectives
• know the difference between numbers and numerals
• know why our number system is called the Hindu-Arabic
numeration system
• understand the base ten positional number system
• be able to identify and graph whole numbers
• be able to read and write a whole number

4. Numbers and Numerals
• Number
A number is a concept. It exists only in the mind.
The earliest concept of a number was a thought that allowed
people to mentally picture the size of some collection of objects.
To write down the number being conceptualized, a numeral is
used.
• Numeral
A numeral is a symbol that represents a number.

5. Numbers and Numerals
• Sample Set A
The following are numerals. In each case, the first represents the
number four, the second represents the number one hundred
twenty-three, and the third, the number one thousand five. These
numbers are represented in different ways.

6. Numbers and Numerals
• Sample Set A
• Hindu-Arabic numerals
4, 123, 1005
• Roman numerals
IV, CXXIII, MV
• Egyptian numerals
• Do the phrases "four," "one hundred twenty-three," and "one
thousand five" qualify as numerals? Yes or no?

7. The Hindu-Arabic Numeration System
• Our society uses the Hindu-Arabic numeration system. This
system of numeration began shortly before the third century
when the Hindus invented the numerals.
0 1 2 3 4 5 6 7 8 9
Leonardo Fibonacci
About a thousand years later, in the thirteenth
century, a mathematician named Leonardo
Fibonacci of Pisa introduced the system into Europe.
It was then popularized by the Arabs. Thus, the name, Hindu-
Arabic numeration system.

8. The Base Ten Positional Number System
• Digits
The Hindu-Arabic numerals 0 1 2 3 4 5 6 7 8 9 are called digits.
We can form any number in the number system by selecting one
or more digits and placing them in certain positions. Each
position has a particular value. The Hindu mathematician who
devised the system about A.D. 500 stated that "from place to
place each is ten times the preceding."

9. The Base Ten Positional Number System
• Base Ten Positional Systems
It is for this reason that our number system is called
a positional number system with base ten.
• Commas
When numbers are composed of more than three
digits, commas are sometimes used to separate the digits into
groups of three.
• Periods
These groups of three are called periods and they greatly
simplify reading numbers.

10. The Base Ten Positional Number System
• In the Hindu-Arabic numeration system, a period has a value
assigned to each or its three positions, and the values are the
same for each period. The position values are
In our positional number system, the value of a digit is
determined by its position in the number.

11. The Base Ten Positional Number System
Sample Set B
1. Find the value of 6 in the number 7,261.
6 tens = 60
2. Find the value of 9 in the number 86,932,106,005.
9 hundred millions = 9 hundred million
3. Find the value of 2 in the number 102,001.
2 one thousands = 2 thousand

12. The Base Ten Positional Number System
Practice Set B
4. Find the value of 5 in the number 65,000.
5. Find the value of 4 in the number 439,997,007,010.
6. Find the value of 0 in the number 108.

13. Whole Numbers
• Whole Numbers
• Numbers that are formed using only the digits
0 1 2 3 4 5 6 7 8 9 are called whole numbers. They are
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …

14. Graphing Whole Numbers
• Number Line
Whole numbers may be visualized by constructing a number
line. To construct a number line, we simply draw a straight line
and choose any point on the line and label it 0.
• Origin
This point is called the origin. We then choose some
convenient length, and moving to the right, mark off consecutive
intervals (parts) along the line starting at 0. We label each new
interval endpoint with the next whole number.

15. Graphing Whole Numbers
• Graphing
We can visually display a whole number by drawing a closed
circle at the point labeled with that whole number. Another
phrase for visually displaying a whole number is graphing the
whole number. The word graph means to "visually display."

16. Graphing Whole Numbers
• Sample Set C
Graph the following whole numbers: 3, 5, 9.
Specify the whole numbers that are graphed on the following
number line.
The numbers that have been graphed are
0, 106, 873, 874

17. Exercises
1. What is a number?
2. What is a numeral?
3. Does the word "eleven" qualify as a numeral?
4. In our number system, each period has three values assigned
to it. These values are the same for each period. From right to left,
what are they?
5. In the number 841, how many tens are there?
6. In the number 3,392 how many ones are there?

18. Exercises
7. In the number 10,046, how many thousands are there?
8. In the number 779,844,205, how many ten millions are there?
9. In the number 65,021, how many hundred thousands are
there?
10. For following problems, give the value of the indicated digit in
the given number.
a. 5 in 599 c. 9 in 29,827
b. 1 in 310,406 d. 6 in 52,561,001,100
11. Is there a smallest whole number? If so, what is it?

19. Exercises
11. Construct a number line in the space provided below and
graph (visually display) the following whole numbers: 84, 85,
901, 1006, 1007.
12. Specify, if any, the whole numbers that are graphed on the
following number line.

20. 1.1 Reading and Writing Whole Numbers
• Reading Whole Numbers
• To convert a number that is formed by digits into a verbal
phrase, use the following method:
Beginning at the right and working right to left, separate the
number into distinct periods by inserting commas every three
digits.
Beginning at the left, read each period individually, saying
the period name.

21. 1.1 Reading and Writing Whole Numbers
• Sample Set A
• Write the following numbers as words.
1) Read 42958.
Forty-two thousand, nine hundred fifty-eight.
2) Read 307991343.
Three hundred seven million, nine hundred ninety-one
thousand, three hundred forty-three.
3) Read 36000000000001.
Thirty-six trillion, one.

22. 1.1 Reading and Writing Whole Numbers
• Writing Whole Numbers
• To express a number in digits that is expressed in words, use
the following method:
Notice first that a number expressed as a verbal phrase will
have its periods set off by commas.
Starting at the beginning of the phrase, write each period of
numbers individually.
Using commas to separate periods, combine the periods to
form one number.

23. Writing Whole Numbers
• Sample Set B
• Write each number using digits.
1) Seven thousand, ninety-two.
7,092
2) Fifty billion, one million, two hundred thousand, fourteen.
50,001,200,014
3) Ten million, five hundred twelve.
10,000,512

24. Exercises
1-3) For the following problems, write all numbers in words.
1. A person who watches 4 hours of television a day spends 1460
hours a year watching T.V.
2. Astronomers believe that the age of the universe is about
20,000,000,000 years.
3. If a 412 page book has about 52 sentences per page, it will contain
about 21,424 sentences.
4-5) For the following problems, write each number using digits.
4. Thirty-five million, seven thousand, one hundred one
5. One hundred trillion, one

25. 1.2 Rounding Whole Numbers
• Objectives
1. understand that rounding is a method of approximation
2. be able to round a whole number to a specified position

26. Rounding as an Approximation
• A primary use of whole numbers is to keep count of how many
objects there are in a collection. Sometimes we're only
interested in the approximate number of objects in the
collection rather than the precise number. For
example, there are approxi
mately 20 symbols in the
collection.
The precise number of
symbols in the collection is
18.

27. Rounding
• We often approximate the number of objects in a collection by
mentally seeing the collection as occurring in groups of tens,
hundreds, thousands, etc. This process of approximation is
called rounding. Rounding is very useful in estimation.

28. 1.2 Rounding Whole Numbers
• The process of rounding whole numbers is illustrated in the
following examples.
1) Round 67 to the nearest ten.
• On the number line, 67 is more than halfway from 60 to 70.
The digit immediately to the right of the tens digit, the round-
off digit, is the indicator for this.
Thus, 67,
rounded to the
nearest ten, is 70.

29. 1.2 Rounding Whole Numbers
2) Round 4,329 to the nearest hundred.
On the number line, 4,329 is less than halfway from 4,300 to
4,400. The digit to the immediate right of the hundreds digit,
the round-off digit, is the indicator.
Thus, 4,329, rounded
to the nearest hundred
is 4,300.

30. 1.2 Rounding Whole Numbers
3) Round 16,500 to the nearest thousand.
On the number line, 16,500 is exactly halfway from 16,000 to
17,000.
By convention, when the number to be rounded is exactly
halfway between two numbers, it is rounded to
the higher number. Thus, 16,500, rounded to the nearest
thousand, is 17,000.

31. 1.2 Rounding Whole Numbers
4) A person whose salary is Php 41,450 per month might tell a
friend that she makes Php 41,000 per month. She has rounded
41,450 to the nearest thousand.

32. The Method of Rounding Whole Numbers
From the observations made in the preceding examples, we can
use the following method to round a whole number to a
particular position.
Mark the position of the round-off digit.
Note the digit to the immediate right of the round-off digit.
• If it is less than 5, replace it and all the digits to its right with zeros.
Leave the round-off digit unchanged.
• If it is 5 or larger, replace it and all the digits to its right with zeros.
Increase the round-off digit by 1.

33. The Method of Rounding Whole Numbers
• Sample Set A
Use the method of rounding whole numbers to solve the
following problems.
1) Round 3,426 to the nearest ten.
2) Round 9,614,018,007 to the nearest ten million.
3) Round 148,422 to the nearest million.
4) Round 397,000 to the nearest ten thousand.
5) Round 30,852,900 to the nearest million.

34.  end 
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