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WHOLE
NUMBERS
Concept of whole
numbers

MATHEMATICS FORM 1
WHOLE NUMBERS
COUNTING
PLACE VALUE
WRITING &
READING

CONCEPT OF
WHOLE NUMBER
 WRITING AND
READING WHOLE
NUMBERS
 COUNTING WHOLE
NUMBERS
 IDENTIFY PLACE
VALUE

Whole numbers are used
in currency.

WHOLE NUMBERS
Whole numbers are a
set of counting
numbers that starts
with 0, 1, 2, 3, 4, 5,
….
The smallest whole
number is zero (0)

WRITING AND READING WHOLE
NUMBERS
ONE SIXTY
FOURTY-
THREE
ONE
HUNDREDS
TWENTY-ONE
FOUR THOUSAND
AND TEN

COUNTING WHOLE NUMBERS
Count on in
tens from
30 to 100.
Count back
in
hundreds
from 1500
to 700.
30, 40, 50,
60, 70, 80,
90, 100.
1500, 1400,
1300, 1200,
1100, 1000,
900, 800,
700.

PLACE VALUE
The value of a digit
depends on its place
in the whole number.
Each place has a
different value which
is known as the
place value.

What is the number
represented by the diagram?
100
HUNDREDS
30
TENS
6
UNITS

Activity 1: What is the place
value
of 9?
The number of
students in the
school:
1 389
students

Answer:
THOUSANDS HUNDREDS TENS UNITS
1 3 8 9

Activity 2: What is the place
value
of 3?
The numbers of
butterfly in the
garden :
3 291 butterflies

Answer:
THOUSANDS HUNDREDS TENS UNITS
3 2 9 1
Exercises

SYSTEM OF WRITING
WHOLE NUMBERS
Million Thousand Hundred
Hundred
Million
Ten
Million
Unit Hundred
Thousand
Ten
Thousand
Unit Hundred Ten Unit

Understanding
Whole Numbers
Lesson 1-1

Vocabulary
standard form – a number is written using digits and
place value (the regular way to write numbers).
expanded form – a number is written as a sum using
the place and value of each digit.

How To Read a Large
Number
•Numbers are grouped in sets of
three (each set is called a period).
•Only read three numbers at a time.
•Say the name of the period that
the numbers are in.
•Say “and” for the decimal, but do
not say “and” if there isn’t a
decimal.

Example
4,658,089
Millions period Thousands period Ones period
Four million, six hundred fifty-eight thousand,
eighty-nine.

Comparing
Numbers
• Line up the numbers vertically (up
and down) by the ones place (or the
decimal, if there is one).
• Start at the left and compare the
digits.
• Move towards the right until you
find a difference.

Just a Reminder…
< means “less than.”
> means “greater than.”
= means “equal to.”

Example
45,312 45,321
45,312
45,321
1 is less than
2
<

Example 2 – Put the numbers in
order from least to greatest.
321; 345; 354; 29; 1,013; 312; 332
321
345
354
29
1013
312
332
largest
smallest
29
1,013
312 321 332
345 354
< < <
< <

Rounding Whole Numbers
Rounding to a specific place:
 Identify the place
(“nearest hundred”, for example)
 Look at the number immediately to th
right.
 Is it 5 or higher? Round up.
 Is it 4 or lower? It stays the same.
 All digits to the right of the specified
become zeros.

Try these examples
Round to the nearest hundred:
4,856 10,527 234,567 8,648,078
And the answers are…
4,900 10,500 234,600
8,648,100

Key Terms
 Addends: numbers being added
 Sum or total: The answer or result of
addition.
 Commutative property of addition: two
or more numbers can be added in either
order without changing the sum
 Associative property of addition: When
more than two numbers are being added, the
addends can be grouped by two at a time in
any way.

Addition
 Addition occurs when you
join two numbers together.
These numbers are called
addends.
4 + 2 = ?
Addends

You add the two addends
together to get a sum.
4 + 2 = 6
Sum

Let’s add large numbers.
12 and 34 Line up numbers
12
+ 34
Line up the
digits on
top of each
other
starting with
the number

12
+ 34
6
Line up the digits on top
of each other starting
with the number on the
right (the rightmost digit,
which is called the
“ones” place.)
Then add the numbers that
are on top of each other like
you normally would add
numbers.

12
+ 34
6
Line up the digits on
top of each other
starting with the
number on the right
(the rightmost digit,
which is called the
“ones” place.)
Then add the numbers
that are on top of each
other like you normally
would add numbers.

12
+ 34
46
Line up the digits on
top of each other
starting with the
number on the right
(the rightmost digit,
which is called the
“ones” place.)
And do the same for
the other column of
numbers.

Adding larger numbers...
You may have to “carry” numbers
to the next column of numbers
being added if the first column is
over 9.
2 3 1
+ 4 5 9

over 9.
2 3 1
+ 4 5 9
0
Since
9+1=10, we
will write
the last
digit of 10

over 9.
2 3 1
+ 4 5 9
0
Since
9+1=10, we
will write
the last
digit of 10
1

over 9.
2 3 1
+ 4 5 9
0
Now we will
add the 3
and 5, and
also the 1
since it was
1

over 9.
2 3 1
+ 4 5 9
9 0
Now we will
add the 3
and 5, and
also the 1
since it was
1

over 9.
2 3 1
+ 4 5 9
9 0
Now we will
add the 2
and 4 that
in the far
left column.
1

over 9.
2 3 1
+ 4 5 9
6 9 0
Now we will
add the 2
and 4 that
in the far
left column.
1

With some practice, you will be able
to successfully add positive whole
numbers!
This will be useful in all aspects of
this class AND in your everyday life.
Let’s look at a real-world example...

You graduated from Islamic College!!!!
As some of your
graduation gifts, you
receive gifts from
family and friends with the values
of
$50, $129, $78, and $23.

You will simply need to ADD all of those
numbers up to get the total.
5 0
1 2 9
7 8
+ 2 3

5 0
1 2 9
7 8
+ 2 3
0
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
0+9+8+3=20
2

5 0
1 2 9
7 8
+ 2 3
8 0
Keep in mind to line up
he places, add each column,
and carry if the number
has more than one digit!
2+5+2+7+2=18
2
1

5 0
1 2 9
7 8
+ 2 3
2 8 0
eep in mind to line up
aces, add each column,
d carry if the number
s more than one digit!
1+1=2
2
1

5 0
1 2 9
7 8
+ 2 3
2 8 0
You got $280
in gifts!
Congratulations!!!
2
1

• Adding in columns - Uses no equal sign
5
+ 5
10
897
+ 368
1265
Simple
Complex
Answer is called “sum
Table of Digits

What is Subtraction?
Subtracting whole
numbers is the inverse
operation of adding
whole numbers.

Subtraction
 Subtraction occurs when you
take one number away from
another number.
5 - 2 = ?

When you subtract the
numbers, you end up with
the difference.
5 - 2 = 3
Difference

Subtractions with one digit
are usually fairly easy.
Things start getting
complicated when you have
more than one digit and you
cannot remove the number
at the bottom from the
number on top such as
when doing 85 − 8

Example
Since you could
not remove 8
from 5, you

You can also write the problem without the tens and
the ones to make it look simpler as illustrated below

Another example
Always start
with the ones.
5424
- 756

Step #1
Borrow a 10 from 2 tens
The problem becomes

Step #2
Borrow 1 hundred from 4
hundreds. 1 hundred = 10 tens.
Then add 10 tens to 1 ten to make
it 11 tens

Step #3
Borrow 1 thousand from 5 thousands. 1 thousand
= 10 hundreds. Then add 10 hundreds to 3
hundreds to make it 13 hundreds
Then, just subtract now since all numbers at the
bottom are smaller than the number on top

Let’s Try Some!
4,987
- 2,158
3,230
- 320
17
7 212
9
2
8
2, 1,9 1 0

onclusion
 Now you should be able to
add and subtract single
digit numbers by using
pictures to solve the
problems given to you.
You should also understand
what an addend, sum, and
difference is.

63
Multiplication
• In Arithmetic - Indicated by “times” sign (x).
Learn “Times” Table
6 x 8 = 48
In Arithmetic

• Complex Multiplication - Carry result to next column.
64
Complex Multiplication
Problem: 48 x 23
48
X 23
4
+ 2
48
X 23
144
+ 2
48
X 23
144
+ 1
6
48
X 23
144
+ 1
960
1104
Same process is used when multiplying
three or four-digit problems.

65
MULTIPLICATION PRACTICE EXERCISES
1. a. 21
x 4
b. 81
x 9
c. 64
x 5
d. 36
x 3
2. a. 87
x 7
b. 43
x 2
c. 56
x 0
d. 99
x 6
3. a. 24
x 13
b. 53
x 15
c. 49
x 26
d. 55
x 37
84 729 320 108
609 86 0 594
312 795 1274 2035

66
MULTIPLICATION PRACTICE EXERCISES (con’t)
4. a. 94
x 73
b. 99
x 27
c. 34
x 32
d. 83
x 69
5. a. 347
x 21
b. 843
x 34
c. 966
x 46
6. a. 360
x 37
b. 884
x 63
c. 111
x 19
6862 2673 1088 5727
7287 28,662 44,436
13,320 55,692 2109
7. a. 493
x 216
b. 568
x 432
c. 987
x 654
106,488 245,376 645,498

67
Finding out how many times a divider “goes into” a
whole number.
• Finding out how many times a divider “goes into” a
whole number.
Division
15 5 = 3 15 3 = 5

68
Shown by using a straight bar “ “ or “ “ sign.
• Shown by using a straight bar “ “ or “ “ sign.
48 5040
1 48 “goes into” 50 one time.
48 1 times 48 = 48
2 50 minus 48 = 2 & bring down the 4
4
0
48 goes into 24 zero times.
0
Bring down other 0.
48 goes into 240, five times
5
240
0
5 times 48 = 240
240 minus 240 = 0 remainder
So, 5040 divided by 48 = 105 w/no remainder.
Or it can be stated:
48 “goes into” 5040, “105 times”

69
DIVISION PRACTICE EXERCISES
1. a. b. c.
2. a. b. c.
3. a. b.
211 62 92
13 310 101
256 687
4. a. b.
98 67
48 5040 7 434 9 828
9 117 12 3720 10 1010
23 5888 56 38472
98 9604 13 871
5. a. b.
50 123
50 2500 789 97047

70
DIVISION PRACTICE EXERCISES (con’t)
6. a. b.
7. a. b.
8. a. b.
7 9000
61 101
67 r 19 858 r 13
9. a. b.
12 r 955 22 r 329
21 147 3 27000
32 1952 88 8888
87 5848 15 12883
994 12883 352 8073

COMBINED
OPERATIONS
+ –
x
÷

Problem: Evaluate the following arithmetic expression:
3 + 4 x 2
Solution: Student 1 Student 2
3 + 4 x 2 3 + 4 x 2
= 7 x 2 = 3 + 8
= 14 = 11

To add and to subtract:
we do the operations
from left to right

To multiply and to divide:
do the operation from left to
right

To perform computation involving
combined operations,
a)first, multiply or divide from
left to right
b)then, add or subtract from left
to right

To perform computations involving
combined operations that include brackets ( ),
work that brackets first
then, multiply or divide from left to right
lastly, add or subtract from left to right

SUMMARY
COMBINED OPERATIONS
To perform computations involving combined operations:
1.Work the brackets ( ) first.
2.Then, multiply or divide.
3.Finally add or subtract from left to right.

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