Unit 4: Operations with Integers Mrs. Lemire

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

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. -5+5 = 0

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

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

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)

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

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.

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 1. 5 – 11 2. -5 + 11 3. 5 + (-11) 4. -5 – 11

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

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.

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