PERFORMS ADDITION ON

INTEGERS.
M6NS-III-156
ANNALICE R. QUINAY
MASTER TEACHER 1
SAN JOSE ES
SAN PABLO CITY
Which of the two integers in each pair has a greater distance from zero?

+5 & -4
-2 & -9
-10 & -6
+7 & -3
-12 & + 1
•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.
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.
Adding Integers
Use a number line to help visualize the addition of
integers.
25  7

63 9

 2   4    6
Adding Integers
Use a number line to help visualize the addition of
integers.
4   3  1

83  5
 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.
Add -2 + (-4) = -6
Add 5 + 6 = 11
Add -3 + (-5) = -8
Add -3 + -2 = -5
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.
Add -5 + 3 = -2

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

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

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

Remove all
the zero
pairs.
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.
 GROUP
ACTIVITY
ADD THE FF. INTEGERS.
1) -8 + 8 = 0
2) -9 + -11 = -20
3) 13 + (-19) = -6
4) 7+5= 12
5) -12 + 10 = -2
6) -22 + (-16) = -38
7) 18 + (-5) = 13
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
Add the following integers.
8  7  15  12   30    42
9   10    1  54  20   32
 3   19   22 18   18  0

 2  29  27 6   2    15 
4   15 
83  5
 11
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?

 7 rose 4 rose 8
7 48
38

5 F
PERFORMS SUBTRACTION ON
INTEGERS.
M6NS-III-156
DAY 2
PERFORMS SUBTRACTION ON
INTEGERS.
M6NS-III-156
DAY 2
I LOVE NUMBERS!!!
 Quick Review of Adding Integers
• Adding Rule #1 • Adding Rule #2
– If the signs are the same, – If the signs are DIFFERENT,
add as you normally do. pretend the signs aren’t there.
– Subtract the smaller from the
– Keep the same sign. larger one.
– Keep the sign of the number
• 5 + 8 = 13 with the GREATEST Absolute
• -8 + -17 = -25 Value.
• 19 + -11 = 8
• 24 + -86 = -62
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?
 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 do.
 29,028 –(-1,312)
Keep Change Opposite

29,028 - (+1,312) = 30,340

Now follow the adding integers rules.
•Show video clip on
how to add integers.
Subtracting Integers
Use a number line to help visualize the subtraction of
integers.
10  4  10   4   6

 8  2   8   2    10

9 15  9   15   6
GROUP
ACTIVITY
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.
-3 - 5 = -8
5 - (-3) = 8
8
-2 - (-10) =
-3 - 8 = -11
-6 - 8 = -14
3 - (-9) = +12
-7 - (-3) = -4
-9 - 0 = -9
-9 – (-7)=-2
16 - (-10) = +26
-9 - (-17) = -8
-4 – (-9) = +5
5 – (-1)= -6
-8 - (-10) = +2
-9 - (+7) = -17
-4 – (9) = -13
PRACTICE… BY PAIR….
1. -7 – 15 =
2. 23 – 98 =
3. -48 - -13 =

4.5 - -6 =

5.17 – 8 =
PRACTICE… BY PAIR….
1. -7 – 15 = -22
2. 23 – 98 = -75
3. -48 - -13 = -35

4.5 - -6 = 11

5.17 – 8 = 9
How do we
subtract
integers?
(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.
Evaluation:
Subtract the following integers.
13  4   14  5 
74   3   4  
12   17    6  5  2   3 
 9   1 

69 
Evaluation:
Subtract the following integers.
13  4  9  14  5   19
 7  4   11  3   4  
12   17   3 4 
12 17  1
29  6  5  2   3 
 9   1   8  11  2   3 
 13   3 
69  3
 13  3   10
Subtracting Integers
Evaluate the following expressions and problems.
Subtract 6 from  15
 15  6   21

8   2   9   7  
8297 
697 
3 7 
4
 Multiplying
Integers Day 3
Objective: To perform multiplication of integers
•What two numbers will give you a
product of 64 and a quotient of 4?
•16 and 4
•16 x 4 = 64
•16 ÷ 4 = 4
 Subtract the ff.
18- 7=
-26-12=
35- (-8)=
20- (-20)=
-25-(-25)=
Multiplying Integers
 Rule 1:
Positive x Positive = POSITIVE

1)4(5) = 20
2)9(7) = 63
Multiplying Integers
 Rule 2:
Negative x Negative = POSITIVE
1)-2(-7) = 14
2)-10 • -9 = 90
Multiplying Integers
 Rule 3:
Negative x Positive = NEGATIVE
1)-6(5) = -30
2)2 • -8 = -16
Multiplying Integers
 Rule 4:
Any Number x 0 = ZERO
1)-4(0) = 0
2)0(7) = 0
 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
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.
If the signs are the same = positive answer.

8 x 5 = 40 -8 x 5 = -40 If theMultiplication
++ 
of integers
Answer is +
--  Answer is +

-8 x -5 = 40
+- Answer is -
8 x -5 = -40 -+  Answer is -
 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.
 (-3)( 5)= -15
(5)( -4)= -20
(-2)(-10)= 20
(-3)( 8)= -24
(-6)( 8)= -48
 (3)(-9)= -27
(-7)( -4)= 28
(-9)(0)= 0
(-9)( -7)= 63
(16)( -10)= -160
 (-7)(-9)= 63
(-10)( 4)= -40
(-9)(-2)= 18
(-9)( -6)= 54
(-1)( -9)= -9
HOW DO WE MULTIPLY INTEGERS?
1. IF THE SIGNS ARE THE
SAME THE ANSWER
IS POSITIVE

2. IF THE SIGNS ARE

DIFFERENT THE ANSWER
IS NEGATIVE
 Pair-share: Multiply the ff.
Try it with your seatmate:
6x8= -6x8= 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| =

Click for answers:

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

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

Multiply.
1. (-10)•3 2. (-4)•(-3)
3. 7•(-2) 4. 5•(-2)
 I positively
have negative
feelings about
this!
DRILL: MULTIPLYING INTEGERS

1. (-10)•3 = -30
2. (-4)•(-3) = 12
3. 7•(-2) = -14
4. 5•(-2) = -10
Multiply the following integers.

= −𝟑𝟎

= −𝟗𝟎

= 𝟑𝟓
Whenever we divide two integers
with “like” signs, the answer is
always positive.

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

(+)
𝟗 ÷ ÷−𝟑
(−)==−𝟑
−
(−)
−𝟏𝟓÷÷(+)
𝟑 ==−𝟓
−
IfWhat
youdid
said
youthey’re
notice exactly
about thethe same,
rules for
multiplyingyou’re right! integers?
and dividing
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 If Division of Integers
++  Answer is +
--  Answer is +
-40 ÷ -8 = 5 +-  Answer is -
-+  Answer is -
-40 ÷ 8 = -5
40 ÷ -8 = -5
divide the following integers.

= −𝟔

= −𝟖
1) −𝟔 ÷ 𝟐 2) −𝟔 ÷ (−𝟐)
= −𝟑 = +𝟑
3) 𝟐𝟎 ÷ (−𝟒)
= −𝟓
4) 𝟏𝟎 ÷ (−𝟐) ÷ (−𝟓)
= +𝟏
5) (−𝟐𝟎) ÷ (−𝟓)
= +4
 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
 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
 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
 Summary

Multiplying/Dividing Integers:
Positive + Positive = Positive
Negative + Negative = Positive
Positive + Negative = Negative
 Divide the ff.
Try it with your seatmate:

54  6 =
-54  6 =
54  -6 =
-54  -6 =
|-12  -4| = Click for answers:

54  6 = 9 -54  6 = -9 54  -6 = -9
-54  -6 = 9 |-12  -4| = 3
DIVIDE THE FF.

1. (-28)÷(-7) =4
2. (45)÷(-9) = -5
3. (-75)÷(-5) = +15
4. (-35)÷(-5) = +7
5. (250)÷(-50) =-50
6. (-80)÷2 = -40
Thank
you!