Education

1. PERFORMS ADDITION ON
INTEGERS.
M6NS-III-156

2. •Objectives:
•In this lesson, you are expected to:
•1. Use fundamental operations using
different approaches;
•2. Solve word problems involving
fundamental operations of integers.

3. Which of the two integers in each pair has a greater
distance from zero?
+5 & -4
-2 & -9
-10 & -6
+7 & -3

4. •Problem: You want to buy house
that costs Php800,000. You only
have Php500,000. If you buy the
house, what will your debt be?
•If you spend more money than you
have, you go into debt.

5. Solution:
500,000
- 800,000
-300,000
If you spend more money than you have, you go
into debt. Debt is a good example of working
with negative integers.

7. Adding Integers
Use a number line to help visualize the
addition of integers.

 5
2 7

 3
6 9
 


 4
2 6


8. Adding Integers
Use a number line to help visualize the
addition of integers.


 3
8 5

 

 3
4 1

9. ADDING INTEGERS
•We can use positive and negative counters to model
the addition of integers.
Positive
Integer
Negative Integer
A positive integer paired with a negative integer
form a zero pair. The value of a zero pair is 0.

10. Add -2 +
(-4)
= -6

11. Add 5 + 6 = 11

12. Add -3 + (-
5)
= -8

13. Add -3 +
-2
= -
5

14. Do you notice a pattern or
rule?
Adding Integers with like
signs.
- When the signs are the
same, add the numbers
together and keep the sign.

15. WE NOW HAVE THE FOLLOWING
GENERALIZATION:
ADDING A POSITIVE INTEGER TO MEANS
MOVING ALONG THE REAL LINE A
DISTANCE OF
UNITS TO THE RIGHT FROM . ADDING A
NEGATIVE INTEGER – TO MEANS
MOVING ALONG THE REAL LINE A
DISTANCE OFUNITS TO THE LEFT FROM.

16. Add -5 +
3
Remove all
the zero
pairs.
= -
2

17. Add 4 + (-
1)
= 3
Remove
all the
zero
pairs.

18. Add 3 + (-
7)
Remove all
the zero
pairs.
= -4

19. Add -6 +
5
Remove all
the zero
pairs.
= -
1

20. DID YOU NOTICE A PATTERN OR
RULE?
Adding integers with unlike signs.
- When the signs are different,
subtract the integers and keep the
sign of the larger digit.

21. GROUP
ACTIVITY

22. ADD THE FF. INTEGERS.
1) -8 + 8 =
2) -9 + -11 =
3) 13 + (-19) =
4) 7 + 5 =
5) -12 + 10 =
6) -22 + (-16)
=
0
-20
-6
12
-2
-38
13

26. Adding Integers with like signs.
- When the signs are the same, add the numbers
together and keep the sign.
-9 + -3 = -12
Adding integers with unlike signs.
- When the signs are different, subtract the integers and
keep the sign of the larger integer.
-9 + 3 = -6

27. Add the following integers.


 3
8 5


 7
8 15
 

 10
9 1

   


 19
3 22



 29
2 27
 


 30
12 42



 20
54 32

 

 18
18 0
   



 15
2
6
 

 15
4
11


28. Adding Integers
If the temperature was -7 degrees (Fahrenheit)
at 6 AM, rose 4 degrees by 7 AM and then rose
another 8 degrees by 8 AM, what was the
temperature at 8 AM?
8
4
7 rose
rose

8
4
7 


F

5
8
3


29. PERFORMS SUBTRACTION ON
INTEGERS.
M6NS-III-156
DAY 2

30. PERFORMS SUBTRACTION
ON INTEGERS.
M6NS-III-156
DAY 2
I LOVE NUMBERS!!!

31. Quick Review of Adding Integers
• Adding Rule #1
–If the signs are the
same, add as you
normally do.
–Keep the same sign.
• 5 + 8 =
• -8 + -17 =
• Adding Rule #2
– If the signs are
DIFFERENT, pretend the
signs aren’t there.
– Subtract the smaller
from the larger one.
– Keep the sign of the
number with the
GREATEST Absolute
Value.
• 19 + -11 =
• 24 + -86 =
13
-25
8
-62

32. THE HIGHEST POINT IN ASIA IS THE
TOP OF MOUNT EVEREST, AT A HEIGHT
OF 29,028 FEET ABOVE SEA LEVEL.
THE LOWEST POINT IS THE DEAD SEA,
WHICH 1312 FEET BELOW SEA LEVEL.
HOW MUCH HIGHER IS MOUNT
EVEREST THAN THE DEAD SEA?

33. 3 Steps to Subtract
Integers
• Keep
–Keep the 1st number
• Change
–Subtraction sign to Addition
• Opposite
–Write down the opposite of the 2nd
number
-Then add the way you normally

34. 29,028 –(-1,312)
Keep Change Opposite
29,028 - (+1,312) =
Now follow the adding integers rules.
30,340

35. •Show video clip on
how to add
integers.

36. Subtracting Integers
Use a number line to help visualize the
subtraction of integers.

 4
10 6


 2
8 10


15
9 6

 

 4
10
 


 2
8
 

 15
9

37. GROUP
ACTIVITY

38. GROUP ACTIVITY:
MATERIALS: FLASH CARDS/POWER POINT, SHOW-ME-BOARD
MECHANICS:
A.DIVIDE THE CLASS INTO 5 GROUPS.
B.CHOOSE A LEADER
C. TEACHER FLASHES NUMBERS ON THE SLIDES
D.LEADER WILL WRITE THE CORRECT ANSWER ON THE SHOW-ME-
BOARD
E.THE FIRST GROUP TO FLASH THE CORRECT ANSWER WILL GET 1
POINT
F.THE TEACHER CHECKS THE ANSWERS.

39. -3 - 5
=
-8
5 - (-3)
=
8
-2 - (-10)
=
8
-3 - 8
=
-

40. -6 - 8
=
-14
+1
2
3 - (-9) =
-7 - (-3)
=
-4
-9 - 0
=
-9

41. -9 – (-
7)=
-2
+2
6
16 - (-10) =
-9 - (-
17) =
-8
-4 – (-9)
=
+
5

42. 5 – (-
1)=
-6
+2
-8 - (-10) =
-9 - (+7)
=
-
17
-4 – (9) = -
13

43. PRACTICE… BY PAIR….
1.-7 – 15 =
2.23 – 98 =
3.-48 - -13 =
4.5 - -6 =
5.17 – 8 =

44. PRACTICE… BY PAIR….
1.-7 – 15 =
2.23 – 98 =
3.-48 - -13 =
4.5 - -6 =
5.17 – 8 =
-22
-75
-35
11
9

45. How do we
subtract
integers?

46. (Subtraction of integers means adding the
minuend and the opposite of the subtrahend.) or
Subtract Integers
1.Keep
Keep the 1st number
2.Change
Subtraction sign to Addition
3.Opposite
Write down the opposite of the 2nd number
-Then add the way you normally do.

47. Evaluation:
Subtract the following
integers.

 4
13


 4
7
 

 17
12
 


 1
9

9
6


 5
14
 


 4
3
 




 3
2
5
6

48. Evaluation:
Subtract the following
integers.

 4
13 9


 4
7 11

 

 17
12
29
 


 1
9 8


9
6 3



 5
14 19

 


 4
3
1
 




 3
2
5
6
 



 3
2
11
 


 3
13


 3
13 10


17
12


 4
3

49. Subtracting Integers
Evaluate the following expressions and
problems.
15
6 
from
Subtract


 6
15 21

   




 7
9
2
8
4



 7
9
2
8


 7
9
6


 7
3

50. Multiplying
Integers Day 3
Objective: To perform multiplication of integers

51. •What two numbers will give you a
product of 64 and a quotient of 4?

52. •16 and 4
•16 x 4 = 64
•16 ÷ 4 = 4

53. Subtract the ff.
18- 7=
-26-12=
35- (-8)=
20- (-20)=
-25-(-25)=

54. Multiplying Integers
 Rule 1:
Positive x Positive = POSITIVE
1)4(5) = 20
2)9(7) = 63

55. Multiplying Integers
 Rule 2:
Negative x Negative = POSITIVE
1)-2(-7) = 14
2)-10 • -9 = 90

56. Multiplying Integers
Rule 3:
Negative x Positive =
NEGATIVE
1)-6(5) = -30
2)2 • -8 = -16

57. Multiplying Integers
Rule 4:
Any Number x 0 = ZERO
1)-4(0) = 0
2)0(7) = 0

58. Why?
Positive x Positive = POSITIVE
Your bank records 5 deposits of Php300 each.
5(300) = +1500
Positive x Negative = NEGATIVE
Your bank records 5 withdrawals of Php30 each.
5(-300) = -1500
Negative x Positive = NEGATIVE
Your bank loses track of 5 deposits of Php300 each.
-5(300) = -1500
Negative x Negative = POSITIVE
Your bank loses track of 5 withdrawals of Php300
each.
-5(-300) = +1500

59. Some simple rules will help you when multiplying
negative numbers. The rules are the same for division.
•If there is one negative number, then the answer is
negative.
•If two numbers are negative, then the answer is
positive.
8 x 5 = 40 -8 x 5 = -40
8 x -5 = -40 -8 x -5 = 40
If the signs are the same = positive answer.
If theMultiplication of integers
++  Answer is +
--  Answer is +
+-  Answer is -
-+  Answer is -

60. GROUP
ACTIVITY
• Materials: flash cards/power point, show-me-board
• Mechanics:
• a.Divide the class into 5 groups.
• b.Choose a leader
• c. Teacher flashes numbers on the slides
• d.Leader will write the correct answer on the show-me-board
• e.The first group to flash the correct answer will get 1 point
• f.The teacher checks the answers.
• g.The group having the most number of correct answers wins.

61. -15
(-3)(
5)=
(5)( -
4)=
(-2)(-
10)=
(-3)(
8)=
(-6)(
-20
20
-24
-48

62. -27
(3)(-9)=
(-7)( -
4)=
(-9)(0)=
(-9)( -
7)=
(16)( -
28
0
63
-160

63. 63
(-7)(-
9)=
(-10)(
4)=
(-9)(-
2)=
(-9)( -
6)=
(-1)( -
-40
18
54
-9

64. HOW DO WE MULTIPLY INTEGER
1. IF THE SIGNS ARE THE
SAME THE ANSWER
IS POSITIVE
2. IF THE SIGNS ARE
DIFFERENT THE ANSWER
IS NEGATIVE

65. Try it with your seatmate:
6 x 8 = - 6 x 8 = 6 x -8 = -6 x -
8 =
7 x 4 = -7 x 4 = 7 x -4 = -7 x -4 =
|-8 x 3| = |5 x (-2) – 1| =
2 x |3 – 9| =
6 x 8 = 48 - 6 x 8 = -48 6 x -8 = -48 -6 x -8 = 48
7 x 4 = 28 -7 x 4 = -28 7 x -4 = -28 -7 x -4 = 28
|-8 x 3| = 24 |5 x (-2) – 1| = 11 2 x |3 – 9| = 12
Pair-share: Multiply the ff.
Click for answers:

66. Multiplying Integers
Evaluate the
following:


 8
3
 

 20
0
 

 2
5
 
5
10
  

 2
6
8
   


 1
2
9

67. ANSWERS:
Evaluate the
following:


 8
3
 

 20
0
 

 2
5
 
5
10
24

10
0
50

  

 2
6
8
   


 1
2
9
18

 

 2
48
96
 
1
18

68. Multiply.
1. (-10)•3 2. (-4)•(-3)
3. 7•(-2) 4. 5•(-2)
YOU TRY IT!

69. I positively
have negative
feelings about
this!

70. DRILL: MULTIPLYING INTEGERS
= -30
= 12
= -14
= -10
1. (-10)•3
2. (-4)•(-3)
3. 7•(-2)
4. 5•(-2)

71. Multiply the following integers.
= −𝟑𝟎
= −𝟗𝟎
= 𝟑𝟓

72. Whenever we divide two
integers with “like” signs, the
answer is always positive.
+ ÷ + = +
𝟏𝟔 ÷ 𝟒 = 𝟒
(−) ÷ (−) = +
−𝟏𝟐 ÷ (−𝟒) = 𝟑

73. Whenever we divide two
integers with “unlike” signs, the
answer is always negative.
What did you notice about the rules
for multiplying and dividing
(+) ÷ (−) = −
𝟗 ÷ −𝟑 = −𝟑
(−) ÷ (+) = −
If you said they’re exactly the
same, you’re right!
−𝟏𝟓 ÷ 𝟑 = −𝟓

74. Some simple rules will help you when
multiplying negative numbers. The rules are
the same for division.
•If there is one negative number, then the
answer is negative.
•If two numbers are negative, then the answer is
positive.
40 ÷ 8 = 5
-40 ÷ -8 = 5
-40 ÷ 8 = -5
If Division of Integers
++  Answer is +
--  Answer is +
+-  Answer is -
-+  Answer is -

75. = −𝟖
divide the following integers.
= −𝟔

76. 1) −𝟔 ÷ 𝟐
4) 𝟏𝟎 ÷ (−𝟐) ÷ (−𝟓)
5) (−𝟐𝟎) ÷ (−𝟓)
2) −𝟔 ÷ (−𝟐)
3) 𝟐𝟎 ÷ (−𝟒)
= −𝟑 = +𝟑
= −𝟓
= +𝟏
= +4

77. How do we divide integers?
When we divide two integers, the sign rules are
different than when we add or subtract signed
numbers.
When divide two positive integers, the solution is
positive. 12 ÷ 3 = 4
16 ÷ 8 = 2
8 ÷ 8 = 1

78. How do we divide integers?
When we divide two negative
integers, the solution is also
positive.
(-12) ÷ (-3) = 4
(-16) ÷ (-8) = 2
(-8) ÷ (-8) = 1

79. How do we divide integers?
When we divide one positive & one negative
integer, the solution is always negative,
regardless of which is larger or which is
written first.
12 ÷ (-3) = - 4
(-16) ÷ 8 = -2
(-8) ÷ 8 = -1

80. Summary
Multiplying/Dividing Integers:
Positive + Positive = Positive
Negative + Negative = Positive
Positive + Negative = Negative

81. Try it with your seatmate:
54  6 =
-54  6 =
54  -6 =
-54  -6 =
|-12  -4| =
54  6 = 9 -54  6 = -9 54  -6 = -9
-54  -6 = 9 |-12  -4| = 3
Divide the ff.
Click for answers:

82. DIVIDE THE FF.
= 4
= -5
= +15
=-50
= +7
= -40
1. (-28)÷(-7)
2. (45)÷(-9)
3. (-75)÷(-5)
4. (-35)÷(-5)
5. (250)÷(-50)
6. (-80)÷2

83. Thank
you!
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