An integer is a whole number that can be positive, negative, or zero, with four main operations: addition, subtraction, multiplication, and division. Rules for these operations include that the sum of two positive integers is always positive, and the product or quotient of integers with the same signs is positive; if the signs are different, the result is negative. To subtract integers, one must add the opposite, and the rules for multiplication and division are identical.

1. INTEGERS
INTEGERS

2. What is an
Integer?

3. • An integer is a positive or
negative whole number,
including 0.
…-3, -2, -1, 0, 1, 2, 3…

4. There are
“4”
Integer
Operations

9. 4 Integer Operations
• Addition +
• Subtraction -
• Multiplication x
• Division ÷

10. Rule #1 for
Adding Integers (+)
• The sum of two positive integers is
always positive.
5 + 1 = 6

11. Rule #2 for
Adding Integers (+)
• The sum of two negative integers is
always negative.
-5 + (-1) = -6

12. Rule #3 for
Adding Integers (+)
• The sum of a positive and a negative
integer could be positive, negative, or
zero.

13. Rule #3 for
Adding Integers Continued
• When you add a positive and negative
integer, you are really subtracting. Then,
you give the answer the sign of the
greater absolute value.
5 + (-1) = -4
-5 + 1 = 4
-5 + (-5) = 0

14. Let’s Practice “Addition”
1) 5 + 6 =
2) -3 + (-2) =
3) -6 + 5 =
4) 8 + (-7) =
5) -9 + 9 =

15.  Let’s Check
1) 5 + 6 = 11
2) -3 + (-2) = -5
3) -6 + 5 = -1
4) 8 + (-7) = 1
5) -9 + 9 = 0

16. Rules for
Subtracting Integers (-)
• To subtract an integer, add its
opposite.
• You will need to correctly change all
subtraction problems into addition
problems!

17. How do you
change a
subtraction
problem into an
addition problem?

18. There are three steps:
1. Keep the first integer the same.
(Same)
2. Change the subtraction sign into an
addition sign. (Change)
3. Take the opposite of the number that
immediately follows the newly placed
addition sign. (Change)

22. Examples:
5 – (-2) = 5 + 2 = 7
-5 – 2 = -5 + (-2) = -7
Think …
Same, Change, Change

23. Let’s Practice “Subtraction”
1) 5 – 2 =
2) -3 – 4 =
3) -1 – (-2) =
4) -5 – (-3) =
5) 7 – (-6) =

24.  Let’s Check
1) 5 – 2 = 5 + (-2) = 3
2) -3 – 4 = -3 + (-4) = -7
3) -1 – (-2) = -1 + 2 = 1
4) -5 – (-3) = -5 + 3 = -2
5) 7 – (-6) = 7+ 6 = 13

25. Rules for
Multiplying Integers (x)
• The product of two integers with the
same signs is POSITIVE.
• The product of two integers with
different signs is NEGATIVE.

26. Rules Summary for
Multiplication
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative= Negative
• Negative x Positive = Negative

27. Let’s Practice “Multiplication”
1) 6 x (-3) =
2) 3 x 3 =
3) -4 x 5 =
4) -6 x (-2) =
5) -7 x (-8) =

28.  Let’s Check
1) 6 x (-3) = -18
2) 3 x 3 = 9
3) -4 x 5 = -20
4) -6 x (-2) = 12
5) -7 x (-8) = 56

29. Did you know that
the rules for
multiplication and
division are the
same?

30. Guess what….
They are!

31. The rules for division are exactly
the same as those for multiplication.
If we were to take the rules for
multiplication and change the
multiplication signs to division signs,
we would have an accurate set of
rules for division.

32. Rules for
Dividing Integers (÷)
• The quotient of two integers with
the same signs is POSITIVE.
• The quotient of two integers with
different signs is NEGATIVE.

33. Rules Summary for
Division
• Positive ÷ Positive = Positive
• Negative ÷ Negative = Positive
• Positive ÷ Negative= Negative
• Negative ÷ Positive = Negative

34. Let’s Practice “Division”
1) 18 ÷ (-2) =
2) -48 ÷ (-6) =
3) -27 ÷ 9 =
4) 64 ÷ 8 =
5) 30 ÷ (-5) =

35.  Let’s Check
1) 18 ÷ (-2) = -9
2) -48 ÷ (-6) = 8
3) -27 ÷ 9 = -3
4) 64 ÷ 8 = 8
5) 30 ÷ (-5) = -6

36. Let’s Review…

37. What is an integer?

38. ANSWER
• An integer is a positive or
negative whole number,
including 0.

39. Can you give an example
of an integer?

40. ANSWER
• …-3, -2, -1, 0, 1, 2, 3…

41. What are the four
operations?

42. ANSWER
• The four operations are:
addition, subtraction,
multiplication, and division.

43. How do you add
integers?

44. ANSWER
• The sum of two positive integers is always
positive.
• The sum of two negative integers is always
negative.
• When you add a positive and negative
integer, you are really subtracting. Then, you
give the answer the sign of the greater
absolute value.

45. How do you
subtract integers?

46. ANSWER
• To subtract an integer, add its
opposite.
• Same, Change, Change

47. How do you multiply
integers?

48. ANSWER
• If the signs are the same, your answer
is always positive.
• If the signs are different, your answer
is always negative.

49. How do you divide
integers?

50. ANSWER
• If the signs are the same, your answer is
always positive.
• If the signs are different, your answer is
always negative.
*Multiplication and Division Rules are the
same!