# Unit 4: Operations with Integers 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 1. 2.

3. 4. 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 1. NN Cheat Code: Change subtraction to addition (inverse property) and add the opposite

Signs are determined by the number with the largest absolute value Ex. (-7) - (-13) = (-7) + (13) 2. PP Ex. (9) - (13) = (9) + (13) 3. NP

Ex. (-20)-(10) = (-20)+ (-10) 4. PN ***All scenarios: (Add 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: 1. 4(-5) = 4X5 = 20 (odd number of negatives) = -20 2. -4(-5) = 4X5 = 20 (even number of negatives) = 20 3. 20/(-5) = 20/5 = 4 (odd number of negatives) = -4

4. (-20)/(-5) = 20/5 = 4 (even number of negatives) 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. Daily Warm-Up 1. 5 11 2. -5 + 11 3. 5 + (-11) 4.

-5 11 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 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.