1. Interesting Integers!

2. What You Will Learn

3. What You Will Learn
 Some definitions related to integers.

4. What You Will Learn
 Some definitions related to integers.
 Rules for adding and subtracting
integers.

5. What You Will Learn
 Some definitions related to integers.
 Rules for adding and subtracting
integers.
 A method for proving that a rule is true.

6. What You Will Learn
 Some definitions related to integers.
 Rules for adding and subtracting
integers.
 A method for proving that a rule is true.
Are you ready??

7. Definition
0

8. Definition
 Positive number – a number
greater than zero.
0

9. Definition
 Positive number – a number
greater than zero.
0 1

10. Definition
 Positive number – a number
greater than zero.
0 1 2

11. Definition
 Positive number – a number
greater than zero.
0 1 2 3

12. Definition
 Positive number – a number
greater than zero.
0 1 2 3 4

13. Definition
 Positive number – a number
greater than zero.
0 1 2 3 4 5

14. Definition
 Positive number – a number
greater than zero.
0 1 2 3 4 5 6

15. Definition
 Positive number – a number
greater than zero.
0 1 2 3 4 5 6

16. Definition
0 1 2 3 4 5 6

17. Definition
 Negative number – a number
less than zero.
0 1 2 3 4 5 6

18. Definition
 Negative number – a number
less than zero.
-1 0 1 2 3 4 5 6

19. Definition
 Negative number – a number
less than zero.
-2 -1 0 1 2 3 4 5 6

20. Definition
 Negative number – a number
less than zero.
-3 -2 -1 0 1 2 3 4 5 6

21. Definition
 Negative number – a number
less than zero.
-4 -3 -2 -1 0 1 2 3 4 5 6

22. Definition
 Negative number – a number
less than zero.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6

23. Definition
 Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

24. Definition
 Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

25. Definition
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

26. Definition
 Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

27. Definition
 Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

28. Definition
 Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

29. Definition

30. Definition
 Integers – Integers are all the
whole numbers and all of their
opposites on the negative
number line including zero.

31. Definition
 Integers – Integers are all the
whole numbers and all of their
opposites on the negative
number line including zero.
7 opposite -7

32. Definition
The absolute value of
9 or of –9 is 9.

33. Definition
 Absolute Value – The size of a
number with or without the
negative sign.
The absolute value of
9 or of –9 is 9.

34. Negative Numbers Are Used to
Measure Temperature

35. Negative Numbers Are Used to
Measure Under Sea Level
30
20
10
0
-10
-20
-30
-40
-50

36. Negative Numbers Are Used to
Show Debt

37. Negative Numbers Are Used to
Show Debt
Let’s say your parents bought a car but
had to get a loan from the bank for $5,000.
When counting all their money they add
in -$5.000 to show they still owe the bank.

38. Hint

39. Hint
 If you don’t see a negative
or positive sign in front of a
number it is positive.

40. Hint
 If you don’t see a negative
or positive sign in front of a
number it is positive.
9

41. Hint
 If you don’t see a negative
or positive sign in front of a
number it is positive.
+9

42. Integer Addition Rules

43. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.

44. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.
9 + 5 = 14

45. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.
9 + 5 = 14
-9 + -5 = -14

46. Solve the Problems
 -3 + -5 =
4 + 7 =
 (+3) + (+4) =
 -6 + -7 =
5 + 9 =
 -9 + -9 =

47. Solve the Problems
 -3 + -5 = -8
4 + 7 =
 (+3) + (+4) =
 -6 + -7 =
5 + 9 =
 -9 + -9 =

48. Solve the Problems
 -3 + -5 = -8
4 + 7 = 11
 (+3) + (+4) =
 -6 + -7 =
5 + 9 =
 -9 + -9 =

49. Solve the Problems
 -3 + -5 = -8
4 + 7 = 11
 (+3) + (+4) = 7
 -6 + -7 =
5 + 9 =
 -9 + -9 =

50. Solve the Problems
 -3 + -5 = -8
4 + 7 = 11
 (+3) + (+4) = 7
 -6 + -7 = -13
5 + 9 =
 -9 + -9 =

51. Solve the Problems
 -3 + -5 = -8
4 + 7 = 11
 (+3) + (+4) = 7
 -6 + -7 = -13
 5 + 9 = 14
 -9 + -9 =

52. Solve the Problems
 -3 + -5 = -8
4 + 7 = 11
 (+3) + (+4) = 7
 -6 + -7 = -13
 5 + 9 = 14
 -9 + -9 =
-18

53. Solve the problems on
Part A of your worksheet
now. Click to the next slide
when done.

54. Check Your Answers
1. 8 + 13 = 21
2. –22 + -11 = -33
3. 55 + 17 = 72
4. –14 + -35 = -49

55. Integer Addition Rules

56. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.

57. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.
-9 + +5 =

58. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.
-9 + +5 =
9-5=4

59. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.
Larger abs. value -9 + +5 =
9-5=4

60. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.
Larger abs. value -9 + +5 =
9-5=4

61. Integer Addition Rules
 Rule #2 – If the signs are different
pretend the signs aren’t there.
Subtract the smaller from the larger
one and put the sign of the one with
the larger absolute value in front of
your answer.
-9 + +5 =
Larger abs. value
9 - 5 = 4 Answer = - 4

62. Solve These Problems
 3 + -5 =
 -4 + 7 =
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

63. Solve These Problems
 3 + -5 = 5 – 3 = 2
 -4 + 7 =
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

64. Solve These Problems
 3 + -5 = 5 – 3 = 2
 -4 + 7 =
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

65. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 =
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

66. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

67. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

68. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

69. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

70. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

71. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
 5 + -9 =
 -9 + 9 =

72. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1
 5 + -9 =
 -9 + 9 =

73. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1
 5 + -9 =
 -9 + 9 =

74. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
 -9 + 9 =

75. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9–5=4
 -9 + 9 =

76. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9–5=4
 -9 + 9 =

77. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9 – 5 = 4 -4
 -9 + 9 =

78. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9 – 5 = 4 -4
 -9 + 9 =
9–9=0

79. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3=1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9 – 5 = 4 -4
 -9 + 9 =
9–9=0

80. Solve These Problems
 3 + -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 3
 (+3) + (-4) =
4–3 =1 -1
 -6 + 7 =
7–6=1 1
 5 + -9 =
9–5=4 -4
 -9 + 9 =
9–9=0 0

81. Solve the problems on
Part B of your worksheet
now. Click to the next slide
when done.

82. Check Your Answers
1. –12 + 22 = 10
2. –20 + 5 = -15
3. 14 + (-7) = 7
4. –70 + 15 = -55

83. One Way to Add Integers Is
With a Number Line
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

84. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

85. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

86. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

87. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
- +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

88. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
- +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

89. One Way to Add Integers Is
With a Number Line
+3 + -5 =
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

90. One Way to Add Integers Is
With a Number Line
+3 + -5 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

91. One Way to Add Integers Is
With a Number Line
+3 + -5 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

92. One Way to Add Integers Is
With a Number Line
+3 + -5 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

93. One Way to Add Integers Is
With a Number Line
+3 + -5 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

94. One Way to Add Integers Is
With a Number Line
+3 + -5 = -2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

95. One Way to Add Integers Is
With a Number Line
+6 + -4 =
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

96. One Way to Add Integers Is
With a Number Line
+6 + -4 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

97. One Way to Add Integers Is
With a Number Line
+6 + -4 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

98. One Way to Add Integers Is
With a Number Line
+6 + -4 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

99. One Way to Add Integers Is
With a Number Line
+6 + -4 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

100. One Way to Add Integers Is
With a Number Line
+6 + -4 = +2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

101. One Way to Add Integers Is
With a Number Line
+3 + -7 =
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

102. One Way to Add Integers Is
With a Number Line
+3 + -7 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

103. One Way to Add Integers Is
With a Number Line
+3 + -7 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

104. One Way to Add Integers Is
With a Number Line
+3 + -7 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

105. One Way to Add Integers Is
With a Number Line
+3 + -7 =
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

106. One Way to Add Integers Is
With a Number Line
+3 + -7 = -4
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

107. One Way to Add Integers Is
With a Number Line
-3 + +7 =
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

108. One Way to Add Integers Is
With a Number Line
-3 + +7 =
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

109. One Way to Add Integers Is
With a Number Line
-3 + +7 =
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

110. One Way to Add Integers Is
With a Number Line
-3 + +7 =
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

111. One Way to Add Integers Is
With a Number Line
-3 + +7 =
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

112. One Way to Add Integers Is
With a Number Line
-3 + +7 = +4
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

113. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.

114. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)

115. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as

116. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as
2 + (+7)

117. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!

118. Here are some more examples.

119. Here are some more examples.
12 – (-8)

120. Here are some more examples.
12 – (-8)
12 + (+8)

121. Here are some more examples.
12 – (-8)
12 + (+8)
12 + 8 = 20

122. Here are some more examples.
12 – (-8) -3 – (-11)
12 + (+8)
12 + 8 = 20

123. Here are some more examples.
12 – (-8) -3 – (-11)
12 + (+8) -3 + (+11)
12 + 8 = 20

124. Here are some more examples.
12 – (-8) -3 – (-11)
12 + (+8) -3 + (+11)
12 + 8 = 20 -3 + 11 = 8

125. Solve the problems on
Part C of your worksheet
now. Click to the next slide
when done.

126. Check Your Answers
1. 8 – (-12) = 8 + 12 = 20
2. 22 – (-30) = 22 + 30 = 52
3. – 17 – (-3) = -17 + 3 = -14
4. –52 – 5 = -52 + (-5) = -57

127. How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?

128. How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?
We can use the same
method we use to check our
answers when we subtract.

130. Suppose you subtract a – b
and it equals c:

131. Suppose you subtract a – b
and it equals c:
a–b=c

132. Suppose you subtract a – b
and it equals c:
a–b=c
5–2=3

133. Suppose you subtract a – b
and it equals c:
a–b=c
5–2=3
To check if your answer is
correct, add b and c:

134. Suppose you subtract a – b
and it equals c:
a–b=c
5–2=3
To check if your answer is
correct, add b and c:
a=b+c

135. Suppose you subtract a – b
and it equals c:
a–b=c
5–2=3
To check if your answer is
correct, add b and c:
a=b+c
5=2+3

137. Here are some examples:

138. Here are some examples:
a–b=c a=b+c

139. Here are some examples:
a–b=c a=b+c
9–5=4 9=5+4

140. Here are some examples:
a–b=c a=b+c
9–5=4 9=5+4
a–b=c a=b+c

141. Here are some examples:
a–b=c a=b+c
9–5=4 9=5+4
a–b=c a=b+c
20 – 3 = 17 20 = 3 + 17

142. If the method for checking
subtraction works, it should
also work for subtracting
negative numbers.

144. If a – b = c, and….

145. If a – b = c, and….
2 – (-5) is the same as

146. If a – b = c, and….
2 – (-5) is the same as
2 + (+5), which equals 7,

147. If a – b = c, and….
2 – (-5) is the same as
2 + (+5), which equals 7,
Then let’s check with the
negative numbers to see if it’s
true…

149. a–b=c a=b+c

150. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7

151. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!

152. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c

153. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c
-11 – (-3) = -8 -11 = -3 + -8

154. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c
-11 – (-3) = -8 -11 = -3 + -8
YES!

155. Solve the problems on
Part D of your worksheet
now. Click to the next slide
when done.

156. Check Your Answers
Continued on next slide

157. Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
Continued on next slide

158. Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
2. Solve: 17 – ( 12) = 29
Continued on next slide

159. Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
2. Solve: 17 – ( 12) = 29
Continued on next slide

160. Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
2. Solve: 17 – ( 12) = 29
Continued on next slide

161. Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
2. Solve: 17 – ( 12) = 29
Check: 17 = -12 + 29
Continued on next slide

162. Check Your Answers

163. Check Your Answers
1. Solve: 20 – ( 5) = 25

164. Check Your Answers
1. Solve: 20 – ( 5) = 25

165. Check Your Answers
1. Solve: 20 – ( 5) = 25

166. Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25

167. Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25
1. Solve: -7 – ( 2) = -5

168. Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25
1. Solve: -7 – ( 2) = -5

169. Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25
1. Solve: -7 – ( 2) = -5

170. Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25
1. Solve: -7 – ( 2) = -5
Check: -7 = -2 + -5

171. You have learned lots of things
About adding and subtracting
Integers. Let’s review!

172. Integer Addition Rules

173. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.

174. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.
9 + 5 = 14

175. Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add
the numbers and then put the sign of
the addends in front of your answer.
9 + 5 = 14
-9 + -5 = -14

176. Integer Addition Rules

177. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.

178. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.
-9 + +5 =

179. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.
-9 + +5 =
9-5=4

180. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.
Larger abs. value -9 + +5 =
9-5=4

181. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.
Larger abs. value -9 + +5 =
9-5=4

182. Integer Addition Rules
 Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
from the larger one and put the sign of the
one with the larger absolute value in front
of your answer.
-9 + +5 =
Larger abs. value
9 - 5 = 4 Answer = - 4

183. One Way to Add Integers Is
With a Number Line
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

184. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

185. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

186. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

187. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
- +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

188. One Way to Add Integers Is
With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left.
- +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

189. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.

190. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)

191. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as

192. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as
2 + (+7)

193. Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!

194. How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?

195. How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?
We can use the same
method we use to check our
answers when we subtract.

197. a–b=c a=b+c

198. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7

199. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!

200. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c

201. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c
-11 – (-3) = -8 -11 = -3 + -8

202. a–b=c a=b+c
2 – (-5) = 7 2 = -5 + 7
It works!
a–b=c a=b+c
-11 – (-3) = -8 -11 = -3 + -8
YES!

203. Discuss with a partner ways
that you know that that is
problem is solved correctly.
6 – (-9) = 15

204. Aren’t integers
interesting?