Mathematics 7-Real numbers in Integers.ppt

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1. 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-
•Multiplicationx
•Division ÷

10. ADDITION OF INTEGERS
Subtract
Subtract
Add
Add

11. ADDITION OF INTEGERS
•Kapag parehas na positive = ADD
•Kapag parehas na negative = ADD pero
ang sign ay negative
•Kapag hindi magkapareho ng sign =
SUBTRACT OR MINUS and then copy
the sign ng mas malaking number

12. Let’s Practice “Addition”
1) 6 + 6 =
2)-1 + (-9) =
3)-6 + 6 =
4)6 + (-7) =
5)-9 + 9 =
6) 10 + 6 =
7) -11 + 5 =
8) 4 + (-6) =
9) 12 + (-5) =
10) -9 + (-9) =

13. Let’s Practice “Addition”
1) 6 + 6 = 12
2)-1 + (-9) = -10
3)-6 + 6 = 0
4)6 + (-7) = -1
5)-9 + 9 = 0
6) 10 + 6 = 16
7) -11 + 5 = -6
8) 4 + (-6) = -2
9) 12 + (-5) =7
10) -9 + (-9) =-18

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

15. SUBTRACTION OF INTEGERS
number
number

16. Rules for
Subtracting Integers (-)
•Kapag nauna ang mas maliit number =
NEGATIVE ang answer
•Kapag nauna ang mas malaking na
number = POSITIVE ang answer
•Kapag magkatabi ang negative, gawing
PLUS
•Kapag parehas na NEGATIVE = mag
• ADD lang

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)

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

20. Let’s Practice
“Subtraction”
1) 5 –2 =
2) -3 –4 =
3) -1 –(-2) =
4) -5 –(-3) =
5) 7 –(-6) =
6) 5 –9 =
7) -7 –2 =
8) -8 –(-8) =
9) -9 –(-5) =
10) 6 –(-6) =

21. 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

22. Let’s Check
6) 5 –9 = 5 + (-9) = -4
7) -7 –2 = -7 + (-2) =-9
8) -8 –(-8) = -8 + 8 = 0
9) -9 –(-5) = -9 + 5 = -4
10) 6 –(-6) = 6+ 6 = 12

23. 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.

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

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

27. Answer the following
1) 6 x (-3) =
2) 3 x 3 =
3) -4 x 5 =
4) -6 x (-2) =
5) -7 x (-8) =
6) 18 ÷(-2) =
7) -48 ÷(-6) =
8) -27 ÷9 =
9) 64 ÷8 =
10) 30 ÷(-5) =

28. Answer the following
1) 6 x (-3) =
2) 3 x 3 =
3) -4 x 5 =
4) -6 x (-2) =
5) -7 x (-8) =
6) 18 ÷(-2) =
7) -48 ÷(-6) =
8) -27 ÷9 =
9) 64 ÷8 =
10) 30 ÷(-5) =
-18
9
-20
12
56
-9
8
-3
8
-6

29. 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

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

31. Did you know that
the rulesfor
multiplicationand
divisionare the
same?

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!

52. GROUP QUIZ
1. Assign your leader
2. Assign your secretary
3. Assign who will hold/raise
your board
4. Assign your group scorer

54. 2 + (-2)
0

55. 12 + (-4)
8

56. -14 + (-17)
-31

57. 45 + 37
82

58. 64 + (-38)
26

59. -105 + 67
-38

60. 63 –(-58)
121

61. -58 –0
-58

62. -36 –105
-141

63. 76 –76
0

64. 76 –76
0

65. 19 ( -3)
-57

66. 23 (6)
138

67. -6 (-6)
36

68. -12 x -4
48

69. -10 x 6
60

70. -8 (5)
-40

71. -56 ÷7
-8

72. 24 ÷(-3)
-8

73. 99 ÷9
11

74. -50÷(-5)
10