This document defines integers and related concepts like positive and negative numbers. It discusses that integers include all whole numbers and their opposites on the number line, including zero. Positive numbers are greater than zero, while negative numbers are less than zero. Opposite numbers are the same distance from zero in opposite directions. The additive inverse of a number is its opposite. Rules for adding, subtracting, multiplying and dividing integers are also defined.

6. DEFINITION
•Integers
• All the whole numbers and all of their
opposites on the negative number
line including zero.

7. •Positive number
– a number greater than zero.
0 1 2 3 4 5 6
DEFINITION

8. •Negative number
– a number less than zero.
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
DEFINITION

9. DEFINITION
•Opposite Numbers
– numbers that are the same
distance from zero in the opposite
direction
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6

10. DEFINITION
•Additive Inverse
– the opposite of a number
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6

11. DEFINITION
•The sum of a number and
its additive inverse is zero.
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-3 + 3 = 0 3 + (-3) = 0

12. Find the opposite of the following.
•

13. Find the opposite of the following real life scenarios.

14. DEFINITION
•Absolute Value
The distance of a number
from zero on a number line.

15. INTEGERS ARE USED TO MEASURE
TEMPERATURE.

16. INTEGERS ARE USED TO MEASURE
TEMPERATURE.

17. INTEGERS ARE USED TO MEASURE SEA
LEVEL.
0
10
20
30
-10
-20
-30
-40
-50
Above sea level
Below sea level

18. INTEGERS ARE USED TO MEASURE SEA
LEVEL.

19. HINT
•If you don’t see a negative or
positive sign in front of a
number, it means that it is
positive.
9
+ 9
=

20. PLOTTING INTEGERS ON A NUMBER LINE
•
1. Is it positive or negative?
2. Where is it on the number line?
3. Mark the estimated point.

21. PLOTTING INTEGERS ON A NUMBER LINE

22. PLOTTING INTEGERS ON A NUMBER LINE

23. COMPARING INTEGERS
• Numbers on the right has a bigger value than
numbers on the left.
RIGHT > LEFT

24. COMPARING INTEGERS (> , <)
2 ____ 4
-1 ____ 5
-2 ____ -3
0 ____ 7
0 ____ -6

25. INTEGER ADDITION RULES
•1. Same signs
• Add the numbers.
• The sum gets the sign of the numbers.
9 + 5 = 14
-9 + -5 = -14

26. ADD THE INTEGERS.
•-3 + -5 =
•4 + 7 =
•(+3) + (+4) =
•-6 + -7 =
•5 + 9 =
•-9 + -9 =
-8
-18
14
-13
7
11

27. INTEGER ADDITION RULES
• 2. Different signs
• Don’t mind the signs.
• Subtract the numbers.
• The difference gets the sign of the bigger
number.
-9 + +5
9 - 5 = 4 -9 + +5 = -4

28. ADD THE INTEGERS.
•3 + -5 =
•-4 + 7 =
•(+3) + (-4) =
•-6 + 7 =
•5 + -9 =
•-9 + 9 =
-2
5 – 3 = 2
0
-4
1
-1
3
9 – 9 = 0
9 – 5 = 4
7 – 6 = 1
4 – 3 = 1
7 – 4 = 3

29. ADDING INTEGERS WITH A NUMBER
LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
POSITIVE = count up to the RIGHT
NEGATIVE = count down to the LEFT
+
-

30. ADDING INTEGERS WITH A NUMBER
LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
+
-
+3 + -5 = -2

31. ADDING INTEGERS WITH A NUMBER
LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
+
-
+6 + -4 = +2

32. ADDING INTEGERS WITH A NUMBER
LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
+
-
+3 + -7 = -4

33. ADDING INTEGERS WITH A NUMBER
LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-
+
-3 + +7 = +4

34. Add the following.

35. Find the missing integer that will make the
statement true.

36. INTEGER SUBTRACTION
RULES
1. Subtracting a negative number
• Change the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!

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

38. INTEGER SUBTRACTION
RULES
2. Subtracting a positive number
• Subtract smaller from bigger number.
• If bigger number comes first, the answer is
positive.
• If smaller number comes first, the answer is
negative.
9 – 7 = 2
7 – 9 = -2

39. INTEGER SUBTRACTION
RULES
2. Subtracting a positive number
• Just add the numbers.
• The answer is negative.
-9 – 7 = -16 -7 – 9 = -16

40. SUBTRACTING INTEGERS WITH A
NUMBER LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-
+
6 – 3 = +3

41. SUBTRACTING INTEGERS WITH A
NUMBER LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-
+
3 – 6 = -3

42. SUBTRACTING INTEGERS WITH A
NUMBER LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
-
-1 – 5 = -6
-

43. SUBTRACTING INTEGERS WITH A
NUMBER LINE
0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
+
-1 – -5 = -1 + 5 = 4
-

44. SUBTRACT THE FOLLOWING.

45. ADD OR SUBTRACT

46. INTEGER MULTIPLICATION/
DIVISION RULES
1. Same signs

47. INTEGER MULTIPLICATION/
DIVISION RULES
1. Different signs

48. Multiply or divide the following.

49. • 21
• -3
• ____ x [-(-2)] = -24
• -12 x 2 = -24
• 4 x –(-2) x –(-4) = 32