304127466-Whole-Numbers_for class 6-ppt.ppt

whole number

1. Chapter 1
Whole Numbers
1

2. WHOLE
NUMBERS
Concept of whole
numbers

3. MATHEMATICS FORM 1
WHOLE NUMBERS
COUNTING
PLACE VALUE
WRITING &
READING

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

5. Whole numbers are used
in currency.

6. 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)

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

8. 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.

9. 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.

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

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

12. Answer:
THOUSANDS HUNDREDS TENS UNITS
1389

13. Activity 2: What is the place
value
of 3?
The numbers of
butterfly in the
garden :
3291butterflies

14. Answer:
THOUSANDS HUNDREDS TENS UNITS
3291
Exercises

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

16. THANK TOU

17. Understanding
Whole Numbers
Lesson 1-1

18. 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.

19. Place Value Chart

20. 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.

21. Example
4,658,089
Millions period Thousands period
Ones period
Fourmillion, six hundred fifty-eightthousand,
eighty-nine.

22. 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.

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

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

25. Example2 –Put the numbersin
orderfromleast to greatest.
321; 345; 354; 29; 1,013; 312; 332
321
345
354
29
1013
312
332
largest
smallest
29
1,013
312321332
345354
< < <
< <

26. Rounding Whole Numbers
Rounding to a specific place:
Identify the place
(“nearest hundred”, for example)
Look at the number immediately to the
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 place
become zeros.

27. 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

28. Key Terms
Addends: numbers being added
Sumor 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.

29. Addition &
Subtraction

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

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

32. 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
on the right

33. Let’s add large numbers.
12 and 34 Line up 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.

34. Let’s add large numbers.
12 and 34 Line up 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.

35. Let’s add large numbers.
12 and 34 Line up 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.

36. 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

37. 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
0
Since
9+1=10, we
will write
the last
digit of 10
(the zero)

38. 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
0
Since
9+1=10, we
will write
the last
digit of 10
(the zero)
and “carry”
1

39. 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
0
Now we will
add the 3
and 5, and
also the 1
since it was
carried
over.
1

40. 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 31
+ 4 59
90
Now we will
add the 3
and 5, and
also the 1
since it was
carried
over.
1

41. Adding larger numbers...
You may have to “carry” numbers
to the next column of numbers
being added if the first column is
over 9.
23 1
+ 45 9
9 0
Now we will
add the 2
and 4 that
in the far
left column.
1

42. Adding larger numbers...
You may have to “carry” numbers
to the next column of numbers
being added if the first column is
over 9.
23 1
+ 45 9
69 0
Now we will
add the 2
and 4 that
in the far
left column.
2+4=6
1

43. 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...

44. 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.
What is the total

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

46. 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

47. 50
1 29
78
+ 23
80
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
2+5+2+7+2=18
2
1

48. 5 0
12 9
7 8
+ 2 3
28 0
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
1+1=2
2
1

49. 5 0
1 2 9
7 8
+ 2 3
2 8 0
You got $280
in gifts!
Congratulations!!!
2
1

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

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

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

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

54. 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

55. Example
Since you could
not remove 8
from 5, you
borrowed a ten

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

57. Another example
Always start
with the ones.
5424
-756

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

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

60. 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

61. Let’s Try Some!
4,987
-2,158
3,230
-320
177 212
9282, 1,910

62. Conclusion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
differenceis.

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

64. •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. 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. 66
MULTIPLICATION PRACTICE EXERCISES (con’t)
4. a. 94
x73
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. 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. 68
Shown by using a straight bar “ “ or “ “ sign.•Shown by using a straight bar “ “ or “ “ sign.
485040
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. 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
485040 7434 9828
9117 123720 101010
235888 5638472
989604 13871
5. a. b.
50 123
502500 78997047

70. 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
21147 327000
321952 888888
875848 1512883
99412883 3528073

71. COMBINED
OPERATIONS
+ –
x
÷

72. 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

73. Toaddandtosubtract:
wedotheoperations
fromlefttoright

74. Tomultiplyandtodivide:
dotheoperationfromleftto
right

75. Toperformcomputationinvolving
combinedoperations,
a)first,multiplyordividefrom
lefttoright
b)then,addorsubtractfromleft
toright

76. 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

77. 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.