The document discusses integers and operations on integers. Integers include all whole numbers and their opposites. It provides examples and rules for adding, subtracting, multiplying, and dividing integers. The key rules are: for addition and subtraction, integers with the same sign are added/subtracted and opposites are subtracted/added; for multiplication and division, integers with the same sign are multiplied/divided and opposites are multiplied/divided with a negative result. Multiple examples are worked through to demonstrate each rule.

1. Integers

2. INTEGERS
Integers are all the positive
whole numbers, zero, and
their opposites (negatives).
EXAMPLES:
• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, …
• 0
• -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, …

3. Adding
Integers

4. ADDING INTEGERS
1st Condition
Same sign
+ + +
- + -
Add, then copy the sign
=
=
+
-

5. ADDING INTEGERS
Example 1:
5 + 3 = 8

6. ADDING INTEGERS
Example 2:
6 + 2 = 8

7. ADDING INTEGERS
Example 3:
-5 + -3 = -8

8. ADDING INTEGERS
Example 4:
-7 + -5 = -12

9. ADDING INTEGERS
Example 5:
-6 + -4 = -10

10. You Try!
1. 5 + 2 = 7 ✔
2. -4 + -2 = -6 ✔
3. 1 + 3 = 4 ✔
4. -6 + -3 = -9 ✔

11. VERY
GOO
D

12. ADDING INTEGERS
2nd Condition
Different sign
- + +
+ + -
Subtract, then copy the higher sign
=
=
Higher
sign
Higher
sign

13. ADDING INTEGERS
Example 1:
-7 + 2 = -5

14. ADDING INTEGERS
Example 2:
-4 + 6 = 2

15. ADDING INTEGERS
Example 3:
4 + -3 = 1

16. ADDING INTEGERS
Example 4:
7 + -10
= -3

17. ADDING INTEGERS
Example 5:
-4 + 10
= 6

18. ADDING INTEGERS
Example 6:
5 + -7 = -2

19. You Try!
1. -5 + 2 = -3 ✔
2. 4 + -2 = 2 ✔
3. -1 + 3 = 2 ✔
4. 3 + -6 = -3 ✔

20. EXCELLENT
!

21. Quiz:
1. 6 + 3 = 9 ✔
2. -5 + -3 = -8 ✔
3. -2 + 4 = 2 ✔
4. 4 + -7 = -3 ✔

22. Quiz:
5. -5 + 3 = -2 ✔
6. -6 + 3 = -3 ✔
7. -7 + 7 = 0 ✔
8. -6 + 8 = 2 ✔

23. Quiz:
9. -4 + -1 = -5 ✔
10. -1 + -6 = -7 ✔
11. -5 + 7 = 2 ✔
12. 1 + -1 = 0 ✔

25. Subtracting
Integers

26. revieW
1. 6 + 3 = 9 ✔
2. -5 + -3 = -8 ✔
3. -2 + 4 = 2 ✔
4. 4 + -7 = -3 ✔

28. Subtracting INTEGERS
1stCondition
Same positive
+ - +
+ + -
Subtract, then copy the higher sign
=
=
Higher
sign
Higher
sign

29. Subtracting INTEGERS
Example 1:
8 - 3 =
8 + -3 = 5

30. Subtracting INTEGERS
Example 2:
4 - 9 =
4 + -9 = -5

31. Subtracting INTEGERS
Example 3:
2 - 3 =
2 + -3 = -1

32. You Try!
1. 5 - 2 = 3 ✔
2. 4 - 2 = 2 ✔
3. 1 - 3 = -2 ✔
4. 3 - 6 = -3 ✔

34. Subtracting INTEGERS
2ndCondition
A negative and a positive
- - +
- + -
Add, then keep a negative sign
=
=
-
-

35. Subtracting INTEGERS
Example 1:
-4 - 6 =
-4 + -6 = -10

36. Subtracting INTEGERS
Example 2:
-5 - 2 =
-5 + -2 = -7

37. Subtracting INTEGERS
Example 3:
-7 - 4 =
-7 + -4 = -11

38. You Try!
1. -5 - 2 = -7 ✔
2. -4 - 2 = -6 ✔
3. -1 - 3 = -4 ✔
4. -3 - 6 = -9 ✔

40. Subtracting INTEGERS
3rdCondition
A positive and a negative
+ - -
+ + +
Add, then keep a positive sign
=
=
+
+

41. Subtracting INTEGERS
Example 1:
9 - -4 =
9 + 4 = 13

42. Subtracting INTEGERS
Example 2:
3 - -5 =
3 + 5 = 8

43. Subtracting INTEGERS
Example 3:
7 - -2 =
7 + 2 = 9

44. You Try!
1. 5 - -2 = 7 ✔
2. 4 - -2 = 6 ✔
3. 1 - -3 = 4 ✔
4. 3 - -6 = 9 ✔

46. Subtracting INTEGERS
4thCondition
Same negative
- - -
- + +
Subtract, then copy the higher sign
=
=
Higher
sign
Higher
sign

47. Subtracting INTEGERS
Example 1:
-6 - -2 =
-6 + 2 = -4

48. Subtracting INTEGERS
Example 2:
-6 - -2 =
-6 + 2 = -4

49. Subtracting INTEGERS
Example 3:
-1 - -7 =
-1 + 7 = 6

50. You Try!
1. -5 - -2 = -3 ✔
2. -4 - -2 = -2 ✔
3. -1 - -3 = 2 ✔
4. -3 - -6 = 3 ✔

52. quiz:
1. 5 - 2 = 3 ✔
2. 2 - 4 = -2 ✔
3. -1 - 3 = -4 ✔
4. -3 - 6 = -9 ✔

53. Quiz:
5. 5 - -2 = 7 ✔
6. 4 - -2 = 6 ✔
7. -1 - -3 = 2 ✔
8. -3 - -6 = 3 ✔

54. Quiz:
9. 1 - 3 = -2 ✔
10. -6 - -8 = 2 ✔
11. -3 - 3 = -6 ✔
12. 3 - -5 = 8 ✔

55. Quiz:
13. -7 - -5 = -2 ✔
14. 3 - -1 = 4 ✔
15. 6 - 3 = 3 ✔
16. 2 - 3 = -1 ✔

56. Quiz:
17. -8 - -5 = -3 ✔
18. 5 - -6 = 11 ✔
19. 4 - 7 = -3 ✔
20. 4 - -1 = 5 ✔

58. Multiplying
Integers

59. Review:
1. 6 + 3 = 9 ✔
2. -5 + -3 = -8 ✔
3. -2 + 4 = 2 ✔
4. 7 + -4 = 3 ✔

60. Review:
5. 5 - 2 = 3 ✔
6. 2 - 4 = -2 ✔
7. -1 - 3 = -4 ✔
8. -3 - 6 = -9 ✔

61. Review:
9. 5 - -2 = 7 ✔
10. 4 - -2 = 6 ✔
11. -1 - -3 = 2 ✔
12. -3 - -6 = 3 ✔

63. Multiplying INTEGERS
1stCondition
Same sign
+ x +
- x -
Multiply, then keep a positive sign
=
=
+
+

64. Multiplying INTEGERS
Example 1:
4 x 10
= 40

65. Multiplying INTEGERS
Example 2:
2 x 8 = 16

66. Multiplying INTEGERS
Example 3:
-4 x -9 = 36

67. Multiplying INTEGERS
Example 4:
-6 x -2 = 12

68. Multiplying INTEGERS
Example 5:
-7 x -3 = 21

69. You try:
1. 5 x 2 = 10 ✔
2. 3 x 4 = 12 ✔
3. -1 x -3 = 3 ✔
4. -3 x -6 = 18 ✔

70. You try:
5. 6 x 3 = 18 ✔
6. 5 x 4 = 20 ✔
7. -7 x -3 = 21 ✔
8. -4 x -6 = 24 ✔

71. You try:
9. 6 x 0 = 0 ✔
10. 5 x 2 = 10 ✔
11. -7 x -4 = 28 ✔
12. -6 x -6 = 36 ✔

73. Multiplying INTEGERS
2ndCondition
Different sign
+ x -
- x +
Multiply, then keep a negative sign
=
=
-
-

74. Multiplying INTEGERS
Example 1:
-6 x 4 = -24

75. Multiplying INTEGERS
Example 2:
-7 x 3 = -21

76. Multiplying INTEGERS
Example 3:
5 x -3 = -15

77. Multiplying INTEGERS
Example 4:
2 x -4 = -8

78. Multiplying INTEGERS
Example 5:
9 x -3 = -27

79. You try:
1. 5 x -2 = -10
✔
2. 2 x -4 = -8 ✔
3. -1 x 3 = -3 ✔
4. -3 x 6 = -18
✔

80. You try:
5. 5 x -3 = -15
✔
6. 4 x -4 = -16
✔
7. -2 x 3 = -6 ✔
8. -3 x 7 = -21
✔

81. You try:
9. 6 x -3 = -18
✔
10. 5 x -4 = -20
✔
11. -2 x 4 = -8 ✔
12. -3 x 8 = -24
✔

83. quiz:
1. 6 x 2 = 12
✔
2. -3 x -4 = 12 ✔
3. -2 x 3 = -6 ✔
4. 4 x -6 = -24
✔

84. quiz:
5. 4 x -1 = -4 ✔
6. 10
x -8 = -80
✔
7. -4 x -2 = 8 ✔
8. -5 x 2 = -10
✔

85. quiz:
9. -5 x 7 = -35
✔
10. -7 x -2 = 14
✔
11. -6 x -1 = 6 ✔
12. -2 x -2 = 4 ✔

87. Dividing
Integers

88. Review:
1. 6 + 3 = 9 ✔
2. -5 + -3 = -8 ✔
3. -2 + 4 = 2 ✔
4. 7 + -4 = 3 ✔

89. Review:
5. 5 - 2 = 3 ✔
6. 2 - 4 = -2 ✔
7. -1 - 3 = -4 ✔
8. -3 - 6 = -9 ✔

90. Review:
9. 5 - -2 = 7 ✔
10. 4 - -2 = 6 ✔
11. -1 - -3 = 2 ✔
12. -3 - -6 = 3 ✔

91. Review:
13. 6 x 2 = 12
✔
14. -3 x -4 = 12 ✔
15. -2 x 3 = -6 ✔
16. 4 x -6 = -24
✔

93. dividing INTEGERS
1stCondition
Same sign
+ ÷ +
- ÷ -
Divide, then keep a positive sign
=
=
+
+

94. dividing INTEGERS
Example 1:
30
÷ 5 = 6

95. dividing INTEGERS
Example 2:
20
÷ 4 = 5

96. dividing INTEGERS
Example 3:
-36
÷ -9 = 4

97. dividing INTEGERS
Example 4:
-8 ÷ -2 = 4

98. dividing INTEGERS
Example 5:
-6 ÷ -2 = 3

99. You try:
1. 20
÷ 2 = 10
✔
2. 8 ÷ 4 = 2 ✔
3. -9 ÷ -3 = 3 ✔
4. -18
÷ -3 = 6 ✔

100. You try:
5. 30
÷ 2 = 15
✔
6. 12 ÷ 4 = 3 ✔
7. -15
÷ -3 = 5 ✔
8. -18
÷ -6 = 3 ✔

101. You try:
9. 30
÷ 5 = 6 ✔
10. 16 ÷ 4 = 4 ✔
11. -25
÷ -5 = 5 ✔
12. -24
÷ -6 = 4 ✔

103. dividing INTEGERS
2ndCondition
Different sign
+ ÷ -
- ÷ +
Divide, then keep a negative sign
=
=
-
-

104. dividing INTEGERS
Example 1:
-24
÷ 4 = -6

105. dividing INTEGERS
Example 2:
-12
÷ 3 = -4

106. dividing INTEGERS
Example 3:
15
÷ -3 = -5

107. dividing INTEGERS
Example 4:
20
÷ -5 = -4

108. dividing INTEGERS
Example 5:
27
÷ -3 = -9

109. You try:
1. 20
÷ -2 = -10
✔
2. 8 ÷ -4 = -2 ✔
3. -9 ÷ 3 = -3 ✔
4. -18
÷ 3 = -6 ✔

110. You try:
5. 22
÷ -2 = -11
✔
6. 12 ÷ -4 = -3 ✔
7. -15
÷ 3 = -5 ✔
8. -18
÷ 6 = -3 ✔

111. You try:
9. 40
÷ -2 = -20
✔
10. 16 ÷ -4 = -4 ✔
11. -21
÷ 3 = -7 ✔
12. -24
÷ 6 = -4 ✔

113. quiz:
1. 20
÷ 2 = 10
✔
2. -8 ÷ -4 = 2 ✔
3. -9 ÷ 3 = -3 ✔
4. 18
÷ -3 = -6 ✔

114. quiz:
5. 30
÷ 10
= 3 ✔
6. -12
÷ -3 = 4 ✔
7. 30 ÷ -6 = -5 ✔
8. 27
÷ 3 = 9 ✔

115. quiz:
9. 80
÷ -8 = -10
✔
10. -2 ÷ -1 = 2 ✔
11. -35
÷ -5 = 7 ✔
12. -8 ÷ 2 = -4 ✔