Notes
Name: __________________________
Date:_______________ Period:______
MULTIPLYING AND DIVIDING INTEGERS –Guided Notes
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Target Objective 1: Multiply, and divide integers
Target Objective 2: Describe situations involving arithmetic operations with integers
Target Objective 3: Describe and solve situations represented by integers and absolute value
I. Review of Multiplication Symbols

There are 4 symbols that are generally used to represent multiplication:
traditional _________ Ex) 2 x 2 = 4
dot _______________ Ex) 3  2 = 6
parentheses ________ Ex) 4(2) = 8 or (4)2 = 8 or (4)(2) = 8
asterisk ____________ Ex) 5 * 2 = 10
II. Rules for Multiplying and Dividing Integers
-When multiplying/dividing two integers with the same sign (two positives or two negatives),
the answer is always positive.
Examples:
3 x 6 = 18
-5 x (-4) = 20
6(2) = 12
- When multiplying/dividing two integers with different signs (positive and negative), the
answer is always negative.
Examples:
-4 * 6 = -24
10 x (-8) = -80
-3(9) = -27
Examples
Ex) 2 x (-12)
Ex) 2  (-3)
Ex) 3(-5)
Ex) -4 x (-4)
Ex) -3  (-2)
Ex) 4 x 5
Ex) 16 ÷ (-4)
Ex) 72 ÷ (-9)
Ex)
Ex) -24 ÷ (-8)
Ex) -81 ÷ (-9)
Ex) (4)(-8)
Ex) 1  8
14
2
Ex)
Ex)
 36
4
18
6
Ex)
3
1
C. Division Involving Zero

When you have ___zero__________ divided by some number, then it is equal to ______zero________.
Ex) 0  10 = 0

Ex) 0  (-9) = 0
Ex)
0
= 0
12
Ex)
0
 0
7
When you divide a number by ___zero___________, then it is equal to ___’not possible’________.
Ex) 10  0 = n.p.
Ex) -5  0 =
Ex)
2
= n.p.
0
Ex)
6

0
*Example: Let’s say you have 10 apples. Mrs. Watkins tells you to divide the group of apples up into 0 groups. Is
this task possible or impossible?
II. Real-Life Applications of Integers
Situation
Depth/
Elevation or
Altitude
Football
Money
Temperature
Time
Weight
Winning/
Losing

Integers are used to describe some of the following real-life situations:
 Depth (below sea level) / Elevation (above sea level)
 Football
 Money (or Stock Market)
 Temperature
 Time
 Weight
 Winning/ Losing

For each situation, look for certain key words that will signal whether you are talking about positive
integers or negative integers:
Positive
Integer
“above”
“ascend”
Example
(Positive Integer)
10 meters above sea level = +10
ascend 10 meters = +10
Negative
Integer
“below”
“descend”
Example
(Negative Integer)
10 meters below sea level = -10
descend 10 meters = -10
“gain”
“profit”
“earn”
“deposit”
“stock went up”
10 yard gain = +10
profit of $10 = +10
earn $10 = +10
deposit $10 = +10
stock went up $10 = +10
10 yard loss = -10
debt of $10 = -10
owe $10 = -10
withdraw $10 = -10
stock went down $10 = -10
“above zero”
“after”
“gain”
“win”
10°F above zero = +10
10 seconds after take off = +10
gain 10 pounds = +10
win by 10 points = +10
“loss”
“debt”
“owe”
“withdraw
“stock went
down”
“below zero”
“before”
“lose”
“lose”
10°F below zero = -10
10 seconds before take off = -10
lose 10 pounds = -10
lose by 10 points = -10
*NOTES:
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You may find some of these key words in different tenses (past or present). If they are in a
different tense, they will still have the same meaning.
These are most of the key words you will see on the Unit 1 test but not necessarily all of them.
You can often use a number line to help you visualize some of these situations.
Let’s define some new words:
-“Altitude” means – how far up / above sea level
-“Ascend” means – to rise up
-“Descend” means – go down
-“Profit” means – make money
-“Debt” or “Debit” means – owe or remove money
-“Deposit” means – put money in
-“Withdraw” or “Withdrawal” means – take out money
Checks for Understanding
1) Depth is a measure of:
2) Elevation or altitude is a measure of:
A) how far down (or how low) you are
B) how far up (or how high) you are
A) how far down (or how low) you are
B) how far up (or how high) you are
3) Below sea level means you are working with:
working with:
4) Above sea level means you are
A) positive integers
A) positive integers
B) negative integers
B) negative integers
5) To ascend means to:
6) To descend means to:
A) go up
B) go down
A) go up
B) go down
7) When you are ascending, you are working with:
working with:
8) When you are descending, you are
A) positive integers
A) positive integers
B) negative integers
B) negative integers
9) A 10 yard gain in football can be described using:
described using:
10) A 10 yard loss in football can be
A) positive integers
B) negative integers
A) positive integers
B) negative integers
11) Profit means that you:
12) Debt or debit means that you:
A) earned or gained more money
B) owe (or lost) money
A) earned or gained more money
B) owe (or lost) money
13) Profit can be described using:
using:
14) Debt or debit can be described
A) positive integers
B) negative integers
A) positive integers
B) negative integers
15) Deposit means that you:
16) Withdraw means that you:
A) you put more money into your bank account.
account
B) you took money out of your bank account.
account
A) you put more money into your bank
17) Deposits can be described using:
18) Withdrawals can be described using:
A) positive integers
B) negative integers
A) positive integers
B) negative integers
19) If your stock goes down in the stock market, then you:
market, then you:
20) If your stock goes up in the stock
A) have earned or made more money.
B) have lost money.
A) have earned or made money
B) have lost money
21) If the temperature is above zero, then you can:
then you can:
22) If the temperature is below zero,
A) describe it using positive integers
B) describe it using negative integers
A) describe it using positive integers
B) describe it using negative integers
23) If it is 7 seconds after takeoff, you can describe the:
can:
24) If it is 7 seconds before takeoff, you
A) describe the situation using positive integers
integers
A) describe the situation using positive
B) describe the situation using negative integers
integers
B) describe the situation using negative
B) you took money out of your bank
Examples
Directions: Use a positive or negative integer to describe the following situations.
Ex) 15 meters below sea level
-15
Ex) lose 10 pounds
Ex) 25 degrees above zero
-10
Ex) profit of $30
30
25
Ex) 22 seconds after take off
22
Ex) deposit $15 into your bank account
15
Ex) 2 seconds before takeoff
-2
Ex) withdrawal of $100 from your bank account
-100