1. The document provides instructions on adding and subtracting integers on a number line. It introduces absolute value and discusses rules for adding integers with the same or different signs. 2. Key rules covered are: when signs are the same, add and keep the sign; when signs are different, subtract and use the sign of the larger number. Subtraction can be treated as adding the opposite number. 3. Examples are provided to demonstrate applying these rules to problems involving addition, subtraction and absolute value of integers.

1. Objectives
The student will be able to:
1. State the coordinate of a point on a
number line.
2. Graph integers on a number line.
3. Add and subtract integers.
SOL: none
Designed by Skip Tyler, Varina High School

2. Absolute Value
of a number is the distance from
zero.
Distance can NEVER be negative!
The symbol is |a|, where a is any
number.

3. Examples
7 = 7
10
100
10 =
-100 =
5 - 8 = -3= 3

4. |7| – |-2| = ?
1. -9
2. -5
3. 5
4. 9
Answer Now

5. |-4 – (-3)| = ?
Answer Now
1. -1
2. 1
3. 7
4. Purple

6. REVIEW

7. The Number Line
Integers = {…, -2, -1, 0, 1, 2, …}
Whole Numbers = {0, 1, 2, …}
Natural Numbers = {1, 2, 3, …}
-5 0 5

10. To GRAPH
a set of numbers means to locate and
mark the points on the number line.
Graph {-1, 0, 2}.
• • •
Be sure to put the dots on the line -
not above or below.
0 5
-5

12. Name the set of numbers graphed.
{-2, -1, 0, . . . }
The darkened arrow means that the
graph keeps on going. When you
see this, put 3 dots in your set.
0 5
-5
• • • • • • • • •

13. What is the sum of
8 and 7?

15. 6 + 8 = 14

16. What is the sum of
-8 and -7?

17. -8 + -7
-8 + -7
8 + 7 = -15

18. The sum of two negative integers is a
negative integer
What is the sum of
-8 and -6?

20. Examples: Use the number line if
necessary.
4
2) (-1) + (-3) = -4
3) 5 + (-7) = -2
0 5
-5
1) (-4) + 8 =

21. Additional Examples
-3+10
7
answer

22. -8+7
-1
answer

23. -8+(-4)
-12
answer

24. -12+4
-8
answer

25. 2+14
16
answer

26. -2+14
12
answer

27. -2+(-7)
-9
answer

28. -25+(-7)
-32
answer

29. Addition Rule
1) When the signs are the same,
ADD and keep the sign.
(-2) + (-4) = -6
2) When the signs are different,
SUBTRACT and use the sign of the
larger number.
(-2) + 4 = 2
2 + (-4) = -2

30. Karaoke Time!
Addition Rule: Sung to the tune of
“Row, row, row, your boat”
Same signs add and keep,
different signs subtract,
keep the sign of the higher number,
then it will be exact!
Can your class do different rounds?

31. -1 + 3 = ?
1. -4
2. -2
3. 2
4. 4
Answer Now

32. -6 + (-3) = ?
1. -9
2. -3
3. 3
4. 9
Answer Now

33. -3+10
7
answer

34. 13+10
23
answer

35. -3+10
7
answer

36. -8+7
-1
answer

37. -8+17
9
answer

38. -8+(-17)
-25
answer

39. 12+(-17)
-5
answer

40. -17+(-17)
-34
answer

41. -7+ 17
10
answer

42. -7+ (-7)
- 14
answer

43. (+)7+ (+)7
14
answer

46. Seatwork
Add the ff. integers.
1. 2+7 6. -10+7
2. -3+8 7. -9+(-10)
3. (+)17+ (+)27 8. 100+(-10)
4. 10+(-2) 9. 23+(-23)
5. 6+(-9) 10. 10+(-6)

47. The additive inverses (or opposites)
of two numbers add to equal zero.
-3
Proof: 3 + (-3) = 0
We will use the additive inverses for
subtraction problems.
Example: The additive inverse of 3 is

48. What’s the difference between
7 - 3 and 7 + (-3) ?
7 - 3 = 4 and 7 + (-3) = 4
The only difference is that 7 - 3 is a
subtraction problem and 7 + (-3) is
an addition problem.
“SUBTRACTING IS THE SAME
AS ADDING THE OPPOSITE.”
(Keep-change-change)

49. When subtracting, change the subtraction to
adding the opposite (keep-change-change)
and then follow your addition rule.
Example #1: - 4 - (-7)
- 4 + (+7)
Diff. Signs --> Subtract and use larger sign.
3
Example #2: - 3 - 7
- 3 + (-7)
Same Signs --> Add and keep the sign.
-10

50. 11b + (+2b)
Same Signs --> Add and keep the sign.
13b
Okay, here’s one with a variable!
Example #3: 11b - (-2b)

51. Which is equivalent to
-12 – (-3)?
Answer Now
1. 12 + 3
2. -12 + 3
3. -12 - 3
4. 12 - 3

52. 7 – (-2) = ?
Answer Now
1. -9
2. -5
3. 5
4. 9

53. 1) If the problem is addition, follow
your addition rule.
2) If the problem is subtraction, change
subtraction to adding the opposite
(keep-change-change) and then follow
the addition rule.
Review

54. |7| – |-2| = ?
1. -9
2. -5
3. 5
4. 9
Answer Now

55. |-4 – (-3)| = ?
Answer Now
1. -1
2. 1
3. 7
4. Purple