1. Unit 4: Operations with Integers
Mrs. Lemire

2. vocabulary
Credit – an amount of money that a lender or business allows a person to use to purchase goods and services with a promise to repay the money, usually with interest
Debit – a payment made that removes money from a bank account
Deposit – money placed into a checking or savings account at a bank
Equidistance – having the same distance
Gain – an increase in money or value
Integer – a member of the set of whole numbers and their opposites (+’s, -‘s, and 0)
Inverse – the quantity that cancels out a given quantity
Like signs – having the same sign
Loss – unrecoverable; decrease in; removal of

3. Vocabulary (Cont.)
Negative integer – an integer that is less than zero
Non-negative – a number that is NOT less than zero
Non-positive – a number that is NOT greater than zero
Positive integer – an integer that is greater than 0
Product – the result when two or more numbers are multiplied
Profit – the amount which is gained in one process
Standard algorithm – a step by step solution
Sum – the result when two or more numbers are added
Unlike signs – signs that are different
Withdrawal – decrease in value; money that is removed from a bank account
Zero pair – a number and its opposite, which add to 0
Ex = 0

4. Ways to Represent integer operations
Colored counting chips
Positive and negative signs
Number lines (horizontal and vertical)
Algebraically
-6 + (-7) = -13

5. Adding integers Scenarios P + P (Add) Sign= positive
N + N (Add) Sign= negative
P + N (Subtract) Sign= determined by the number with the largest absolute value
N + P (Subtract) Sign= determined by the number with the largest absolute value
Cheat Codes:
Same signs (like signs) = Addition
Different signs (unlike signs) = Subtraction

6. Subtracting integers Scenario Cheat Code: N – N
Ex. (-7) - (-13) = (-7) + (13)
P – P
Ex. (9) - (13) = (9) + (-13)
N – P
Ex. (-20)-(10) = (-20)+(-10)
P – N
Ex. (16)-(-7) = (16)+(7)
Cheat Code:
Change subtraction to addition (inverse property) and add the opposite
Signs are determined by the number with the largest absolute value
***All scenarios: (Add the opposite)

7. Multiplying and dividing integers
Complete operation ignoring signs (multiply or divide)
Count the number of negative signs
Odd number of negatives = NEGATIVE
Even number of negatives = POSITIVE
Examples:
4(-5) = 4X5 = 20 (odd number of negatives) = -20
-4(-5) = 4X5 = 20 (even number of negatives) = 20
20/(-5) = 20/5 = 4 (odd number of negatives) = -4
(-20)/(-5) = 20/5 = 4 (even number of negatives) = 4

8. Integer Questions
What distance is traveled on an elevator going up 2 floors?
What distance is traveled on an elevator going down 2 floors?
Explain how the distance an elevator travels is like absolute value.

9. Integer Questions
While working on her daily math warm-up, Megan thought to herself that two of the questions were really the same problem.
Is Megan correct? If yes, which two questions is she thinking about and why are they the same? If no, explain why Megan is not correct
Daily Warm-Up
– 11
(-11)
– 11

10. Integer Questions
Compare and contrast the process used to add integers with the same sign and the process used to add integers with different signs

11. Integer Questions
What would happen if people did not use sequencing and order in their lives? Write about why you think doing things in a certain order is sometimes necessary and what you think might happen if we stopped using sequencing and order in our lives.

12. Integer Questions
Explain why the commutative and associative properties do not apply to subtraction and division.