The document explains the concepts of positive, negative, and neutral integers, emphasizing their locations on the number line and the absolute values of integers. It details rules for adding and subtracting integers, including cases of same and different signs. Additionally, it covers the multiplication and division of integers, highlighting the rules associated with the signs of the factors.

1. 0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
POSITIVE Integers
NEGATIVE Integers
NEUTRAL Integer
Neither positive nor
negative
● located on the RIGHT side
of zero on the number line
● values are GREATER THAN 0
● located on the LEFT side of
zero on the number line
● values are LESS THAN 0
An INTEGER is a positive number, a negative
number, or zero.
● ( – ) (eg. -2) ● ( + ) or none (eg. +2 or 2)

2. -0
-87
-90
+9
-22
67
11
55
-3
Identify the negative integers.
-41

3. ABSOLUTE VALUE
OF INTEGERS

4. The absolute value of an integer is its distance
from zero on the number line. The symbol
for absolute value is a bar||.
0 1 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
“the absolute value of +5 is 5.”
|+5| = 5
|-4| = 4 “the absolute value of -4 is 4.”

5. Give the absolute value of each integer.
a) |7| = 7
b) |-24| = 24
c) |-75| = 75
d) |100| = 100
e) |20| = 20
f) |-333| = 333

6. -11
-87
|-90|
-2
|-22|
|-67|
-9
55
|1000|
Identify the values greater than -10
|40|
-10

7. BATTLE OF VALUES
A battle where the card that has the lesser value wins.

8. |-5| |-8|
VS

9. |-1|
|18|
VS

10. |-9| 8
VS

11. -60
|10|
VS

12. |-12| |-11|
VS

13. |0| -77
VS

14. |-3| 4
VS

15. RULES FOR ADDING AND
SUBTRACTING INTEGERS

16. Adding Integers with the Same Signs
POSITIVE + POSITIVE = POSITIVE
NEGATIVE + NEGATIVE = NEGATIVE
5 + 3 = 8
-5 + -3 = -8
10 + 6 = --
-10 + -6 = 16
16
-16
When adding
integers, SAME signs
🡪 add, copy sign

17. POSITIVE + NEGATIVE = POSITIVE
5 + (-3) = 2 -6 + 10 = 4
Adding Integers with the Different Signs
-3 + 5 = 2 10 + -6 = 4
2 4
POSITIVE + NEGATIVE = POSITIVE
3 + -5 = -2 6 + -10 = -4
-5 + 3 = 2 -10 + 6 = 4
-2 -4
When adding integers, DIFFERENT signs 🡪 subtract, copy the sign of the integer
with the GREATER absolute value

18. 12
1 5 + 7 =
-2
2 -7 + 5 =
-2
3 5 + -7 =
-12
4 -5 + -7 =
2
5 -5 + 7 =
2
6 9 + -7 =
-15
7 -20 + 5 =
-19
8 -8 + -11 =
-50
9 -100 + 50 =
20
10 14 + 6 =
Add the following.
When adding integers, DIFFERENT signs 🡪 subtract, copy the sign of
the integer with the GREATER absolute value
When adding integers, SAME signs 🡪 add, copy sign

19. Subtracting Integers with the Same Signs
POSITIVE - POSITIVE = POSITIVE
5 - 3 = 2
10 - 6 = 4
5 + -3 = 2
10 + -6 = 4
4
3 - 5 = -2
6 - 10 = -4
3 + -5 = -2
6 + -10 = 4
-4
POSITIVE - POSITIVE = NEGATIVE
4
-4
When subtracting integers, SAME signs 🡪 subtract, copy the sign of the
integer with the GREATER absolute value

20. Subtracting Integers with the Same Signs
NEGATIVE - NEGATIVE = POSITIVE or NEGATIVE
-5 – -3 = -2
-6 – -10 = 4
-5 + 3 = -2
-6 + 10 = 4
Minus negative will become PLUS POSITIVE
– -3 will become + 3
4 4

21. Subtracting Integers with Different Signs
POSITIVE - NEGATIVE = POSITIVE
5 – -3 = 8
10 – -6 = 16
5 + 3 = 8
10 + 6 = 4
16
Minus negative will become PLUS POSITIVE
– -3 will become + 3
16
Since the operation will become ADDITION, SAME signs 🡪
add, copy sign

22. Subtracting Integers with Different Signs
NEGATIVE - POSITIVE = NEGATIVE
-5 – 3 = -8
-10 – 6 = -16
-5 + -3 = -8
-10 + -6 = 4
-16
-16
Minus positive will become PLUS NEGATIVE
– 3 will become + -3
ADD, SAME signs (both negative) 🡪 add, copy sign (negative)

23. 1
1 4 + -3 =
-9
2 -4 - 5 =
8
3 3 - -5 =
-1
4 -5 - -4 =
-1
5 3 - 4 =
17
6 10 - -7 =
-50
7 -20 - 30 =
2
8 -8 - -10 =
-50
9 0 - 50 =
-1
10 11 - 12 =
Perform the indicated operation.

24. Operations on Integers:
Multiplication and
Division

25. Multiplying Integers with the Same Signs
POSITIVE × POSITIVE = POSITIVE
NEGATIVE × NEGATIVE = POSITIVE
5 × 3 = 15
-5 (-3) = 15
(10)(6) = --
-10 -6= 16
60
60
●

26. Multiply.
3
10
15
20
12
a. 1 × 3 =
b. -2(-5) =
c. 3 5 =
d. (-5)(-4) =
e. 3 4 =
●
●

27. Multiplying Integers with Different Signs
POSITIVE × NEGATIVE = NEGATIVE
NEGATIVE × POSITIVE = NEGATIVE
5 -3 = -15
-5 3 = -15
10 -6 = --
-10 6 = 16
-60
-60
●
●
●
●

28. Multiply.
-3
-10
-15
-20
-12
a. 1 × -3 =
b. -2 × 5 =
c. -3 × 5 =
d. 5 × -4 =
e. -3 × 4 =

29. -3
1 1 × -3 =
10
2 -2 × - 5 =
-15
3 3 × -5 =
20
4 -5 × -4 =
12
5 3 × 4 =
-70
6 10 × -7 =
6
7 -2 × - 3 =
80
8 -8 × -10 =
-50
9 -1 × 50 =
25
10 5 × 5 =
Multiply.

30. Dividing Integers with the Same Signs
POSITIVE ÷ POSITIVE = POSITIVE
NEGATIVE ÷ NEGATIVE = POSITIVE
2
2

31. Divide.
3
8
5

32. Dividing Integers with Different Signs
NEGATIVE ÷ POSITIVE = NEGATIVE
POSITIVE ÷ NEGATIVE = NEGATIVE
-2
-2

33. Divide.
-7
-4
-3