1. Adding and Subtracting Integers
Mr. Martinez

2. Objectives The student will be able to:
Add and subtract integers using a number line
Add and subtract integers using integer rules
Learn integer rules for adding and subtracting

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

4. 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. - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

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

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

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

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

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

10. SUBTRACT and use the sign of the larger number.
Addition Rule
1) When the signs are the same,
ADD and keep the sign.
(-2) + (-4) = -6
5 + 5 = 10
2) When the signs are different,
SUBTRACT and use the sign of the larger number.
(-2) + 4 = 2
2 + (-4) = -2

11. Solve these problems: =
2. – = =
4. – =

12. Check Your Answers
= 21
2. – = -33
= 72
4. – = -49

13. Solve these problems:
1. – =
2. – =
(-7) =
4. – =

14. Check Your Answers
1. – = 10
2. – = -15
(-7) = 7
4. – = -55

15. The opposites of two numbers add to equal zero.
Example: The opposite of 3 is -3
Proof: 3 + (-3) = 0

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

17. When subtracting, change the subtraction to adding the opposite (keep-change-change) and then follow your addition rule.
Example #1: (-7) changes to (+7)
Different signs, so you subtract and use larger sign.
Answer is 3
Example #2: – 7 changes to (-7)
Same signs, so you add and keep the sign.
Answer is -10

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

19. Solve these problems:
1. 8 – (-12) =
2. 22 – (-30) =
3. – 17 – (-3) =
4. –52 – 5 =

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

21. Review
If the problem is addition, follow your addition rule: 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = = 10 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = (-4) = -2 If the problem is subtraction, change subtraction to adding the opposite (keep-change-change) and then follow the addition rule (-7) changes to (+7) = – 7 changes to (-7) = -10

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

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

24. |7| – |-2| = ? -9 -5 5 9
Answer Now

25. |-4 – (-3)| = ? -1 1 7
Purple
Answer Now