Multiplication of Integers Objective: I can use properties of rational numbers to multiply two integers Strategies to use: Repeated addition -> 3 * 4 (add 4 three times) Commutative Property -> -4 * 3 = 3 * (-4) Distributive Property over Addition -> -4 * (4 + 3) = (-4 * 4) + (-4 * 3) Multiplication Property of 0  any number multiplied by 0 equals 0.

Rules to Multiply Integers Multiply two integers with like signs – the product is positive Multiply two integers with unlike signs – the product is negative Multiply two integers when one factor is 0 – the answer is zero Question: Sam says the (-76) * 84 and 76 * (-84) have the same product. Do you agree? Explain your thinking.

Guided Instruction A stock falls 6 points each day for 3 days. What integer represents the change in stock price for the 3 days? To find the integer for the change over 3 days, multiply (3 * -6) which equals -18 So, the change over 3 days can be represented by -18

Independent Practice The temperature drops 2 degrees each hour for 4 hours. What integer represents the change in temperature over those 4 hours?

Think * Pair *Share With your shoulder partner, describe a real world situation for the equation 5 * -3 = -15

Division of Integers The rules for dividing integers are similar to the rules for multiplying integers. Divide two integers with like signs – the quotient is positive Divide two integers with unlike signs – the quotient is negative Divide by any non-zero integer – the quotient is 0 You cannot divide any number by zero

Question When you divide two integers is the quotient always an integer? Explain (Before you provide an answer, check at least two situations)

Question A submarine dives 10 feet per minute for 12 minutes. Which expression represents this situation? F. 12(10) G. 12(–10) H. 12 ÷ 10 I. 12 ÷ (–10)

Sandra has $32 in her purse. She pays $15 for a CD. Which expression represents this situation? 32 + 15 B. -32 + 15 C. -32 + (-15) D. 32 + (-15)

Patrick turned on his air conditioning and the temperature in his apartment decreased 4 degrees. Write an integer to represent the change in temperature. F. -4° G. -2° H. 2° I. 4°

Chi is 38 feet underground touring a cavern Chi is 38 feet underground touring a cavern. He goes down a ladder 7 feet. What is his new location? -45 feet B. -38 feet C. -31 feet D. -7 feet

An archaeologist descends 30 feet into a tomb, then climbs up 18 feet An archaeologist descends 30 feet into a tomb, then climbs up 18 feet. Which value represents his final position? - 48 ft -12 ft 12 ft D. 48 ft

What is the value of each expression? 10 + (- 8) 2 24 ÷ (-6) -4 - 8(- 4) 32

What is the value of each expression if m = -3, n = 8, and p = -1? np -18/m 12 -8 6

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