The document discusses integers and their properties. It begins by defining natural numbers, whole numbers, and integers as collections of numbers that include negative numbers. It then discusses integer addition and subtraction on a number line, defining properties like additive inverses. Several practice problems are included to test understanding of integer concepts and properties like closure, commutativity, and associativity of addition and subtraction. The overall purpose is to revise and test understanding of integers and their properties.

1. What are
Integers?
Learning Objective

2. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes

3. Integers
Let’s look at a few numbers!

4. Integers
What do you notice?

5. Integers
What do you notice?
____________
Numbers.

6. Integers
What do you notice?
Natural
Numbers.

7. Integers
What do you notice?
Natural
Numbers.
___________
Numbers.

8. Integers
What do you notice?
Natural
Numbers.
Whole
Numbers.

9. Integers
What do you notice?
Natural
Numbers.
Whole
Numbers.
__________
Numbers.

10. Integers
What do you notice?
Natural
Numbers.
Whole
Numbers.
Integer
Numbers.

11. Integers
________________ are also called counting numbers, e.g.
1,2,3,4,5…
Key terms:

12. Integers
Natural numbers are also called counting numbers, e.g.
1,2,3,4,5…
Key terms:

13. Integers
Natural numbers are also called counting numbers, e.g.
1,2,3,4,5…
_______________ are collection of natural numbers and
zero.
Key terms:

14. Integers
Natural numbers are also called counting numbers, e.g.
1,2,3,4,5…
Whole numbers are collection of natural numbers and
zero.
Key terms:

15. Integers
Natural numbers are also called counting numbers, e.g.
1,2,3,4,5…
Whole numbers are collection of natural numbers and
zero.
_________ are collection of whole numbers and negative
numbers.
Key terms:

16. Integers
Natural numbers are also called counting numbers, e.g.
1,2,3,4,5…
Whole numbers are collection of natural numbers and
zero.
Integers are collection of whole numbers and negative
numbers.
Key terms:

17. Integers
Let’s revise more!
On a number line,
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

18. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the _______.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

19. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

20. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the ______.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

21. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the left.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

22. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the left.
3) subtract a positive integer, we move to the ______.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

23. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the left.
3) subtract a positive integer, we move to the left.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

24. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the left.
3) subtract a positive integer, we move to the left.
4) subtract a negative integer, we move to the _____.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

25. Integers
Let’s revise more!
On a number line, when we:
1) add a positive integer, we move to the right.
2) add a negative integer, we move to the left.
3) subtract a positive integer, we move to the left.
4) subtract a negative integer, we move to the right.
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9

26. Integers
What is additive inverse?

27. Integers
What is additive inverse?
An additive inverse of a number ‘a’, is the number that when
added to a gives the answer 0.

28. Integers
Well
done!

29. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

30. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

31. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
a) Observe this number line and write the temperature of the places marked on it.

32. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
a) Observe this number line and write the temperature of the places marked on it.
Ans. -8°C, -2°C, 5°C, 14°C, 22°C

33. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
b) What is the temperature difference between the hottest and the coldest places
among the above?

34. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
b) What is the temperature difference between the hottest and the coldest places
among the above?
Ans. 30°C

35. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
c) What is the temperature difference between Lahulspiti and Srinagar?

36. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
c) What is the temperature difference between Lahulspiti and Srinagar?
Ans. 6°C

37. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
d) Can we say temperature of Srinagar and Shimla taken together is less than the
temperature at Shimla? Is it also less than the temperature at Srinagar?

38. Integers
Following number line shows the temperature in degree Celsius (°C) at
different places on a particular day.
d) Can we say temperature of Srinagar and Shimla taken together is less than the
temperature at Shimla? Is it also less than the temperature at Srinagar?
Ans. Yes, the temperature of Srinagar and Shimla taken together is less than the
temperature at Shimla. But, it is not less than the temperature at Srinagar.

39. Integers
In a magic square each row, column and diagonal have the same sum. Check
which of the following is a magic square.

40. Integers
In a magic square each row, column and diagonal have the same sum. Check
which of the following is a magic square.

41. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81

42. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81
<

43. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81
<
<

44. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81
<
<
<

45. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81
<
<
<
<

46. Integers
Use the sign of >, < or = in the box to make the statements
true.
a) (-8) + (-4) (-8) – (-4)
b) (-3) + 7 – (19) 15 – 8 + (-9)
c) 23 – 41 + 11 23 – 41 – 11
d) 39 + (-24) – (15) 36 + (-52) – (-36)
e) -231 + 79 + 51 -399 + 159 + 81
<
<
<
<
<

47. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

48. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

49. Integers
Let’s look at some properties of Integers!

50. Integers
Let’s look at some properties of Integers!
1. Closure property
What
does that
mean?

51. Integers
Let’s look at some properties of Integers!
1. Closure property
When you add two integers, the sum is also an integer.
What
does that
mean?

52. Integers
Let’s look at some properties of Integers!
1. Closure property
When you add two integers, the sum is also an integer.
Thus, it is said that integers are closed under addition.

53. Integers
Let’s look at some properties of Integers!
1. Closure property
When you add two integers, the sum is also an integer.
Thus, it is said that integers are closed under addition.
When you subtract two integers, the difference is also an
integer.

54. Integers
Let’s look at some properties of Integers!
1. Closure property
When you add two integers, the sum is also an integer.
Thus, it is said that integers are closed under addition.
When you subtract two integers, the difference is also an
integer. Thus, it is said that integers are closed under
subtraction.

55. Integers
Let’s look at some properties of Integers!
2. Commutative property
What
does that
mean?

56. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) + (8)

57. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) + (8) = 5 & (8) + (-3)

58. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) + (8) = 5 & (8) + (-3) = 5

59. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) + (8) = 5 & (8) + (-3) = 5
Integers can be added in any order, thus addition is
commutative for integers.

60. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) - (8)

61. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) - (8) = -11 & (8) - (-3)

62. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) - (8) = -11 & (8) - (-3) = 11

63. Integers
Let’s look at some properties of Integers!
2. Commutative property
Let’s consider,
(-3) - (8) = -11 & (8) - (-3) = 11
Integers cannot be subtracted in any order, thus subtraction
is not commutative for integers.

64. Integers
Let’s look at some properties of Integers!
3. Associative property
What
does that
mean?

65. Integers
Let’s look at some properties of Integers!
3. Associative property
Let’s consider,
(-5) + [(-3) + (-2)]

66. Integers
Let’s look at some properties of Integers!
3. Associative property
Let’s consider,
(-5) + [(-3) + (-2)] = -10 & [(-5) + (-3)] + (-2)

67. Integers
Let’s look at some properties of Integers!
3. Associative property
Let’s consider,
(-5) + [(-3) + (-2)] = -10 & [(-5) + (-3)] + (-2) = -10

68. Integers
Let’s look at some properties of Integers!
3. Associative property
Let’s consider,
(-5) + [(-3) + (-2)] = -10 & [(-5) + (-3)] + (-2) = -10
Integers can be added in any manner of order, thus addition
is associative for integers.

69. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

70. To revise concepts based on integers
To test integer concepts
To interpret addition and subtraction properties
Learning Outcomes
How confident do you feel?

71. What are
Integers?
Learning Objective

72. Integers
Learning Activity
In a quiz, team A scored – 40, 10, 0 and team B scored
10, 0, – 40 in three successive rounds.
Which team scored more?
Can we say that we can add integers in any order?