Warm Up 8/25 Find the next two numbers in the pattern: 12, 6, 24, 12, 48, …. Explain your reasoning.

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Presentation transcript:

Warm Up 8/25 Find the next two numbers in the pattern: 12, 6, 24, 12, 48, …. Explain your reasoning.

Multiplying and Dividing Integers Objectives I can multiply & divide integers I can interpret products of rational numbers by describing real world situations I can Interpret quotients of rational numbers by describing real world situations I can use the properties of multiplying positive rational numbers to determine the rules for multiplying integers I can use the rules for multiplying integers to develop the rules for dividing integers I can explain why − 𝑝 𝑞 = −𝑝 𝑞 = 𝑝 −𝑞

Multiplying Integers: Positive # · Positive # Portray 4 + 4 + 4 on a number line. Write a product to describe this expression. Write an equation that relates these two expressions. Write an equation that is a product of two integers. What can we conclude about a Positive # times a Positive #?

Portray (-4) + (-4) + (-4) on a number line. Multiplying Integers: Positive # · Negative # or Negative # · Positive # Portray (-4) + (-4) + (-4) on a number line. Write a product to describe this expression. Write an equation that relates these two expressions. Write an equation that is a product of two numbers. What can we conclude about a Negative # times a Positive #?

Multiplying Integers: Negative # · Negative # The negative sign, really means the opposite of. Thus when you multiple a negative times a negative, it is the same thing as multiplying the opposite times the opposite….which is positive.

So Let’s Talk…. What does 3(5) represent? What does -3(5) represent? A real life situation? What does -3(5) represent? What does 3(-5) represent? What does -3(-5) represent?

Multiplying Integers: The Rules

Multiplying Integers: Try it out – Output Side 4(-6) -1(-9) (-5)² -5 · 7 -7 · (-8) 12 · (-2) -10(6) 4(11) What about this… -4 · 6(5) Or this… (-3)(-7)(-2)(-3)

Dividing Integers: Positive # · Negative # or Negative # · Positive # What do you notice about the sign of the numbers in the problem? So what do you think will be true about the rules of dividing integers?

Dividing Integers: The Rules The same as multiplication…

Dividing Integers: Try It Out 14 ÷ 2 -32/(-4) −49 7 -40/(-8) 0 ÷ (-6) −21 −3

Reflection Questions – Talk with your group How do you determine if the quotient of two integer’s is positive or negative? How are products of signed numbers used in real world situations? How are quotients of signed numbers used in real world situations?

Exit Ticket You have the integer cards shown at the right when your teacher tells you to choose a card to multiply four times. If your goal is to get your score as close to zero as possible, which card would you choose? Explain how your choice changes your score. Mrs. McIntire, a seventh grade math teacher, is grading papers. Three students gave the following responses to the same math problem: Student one: 1 −2 Student two: -( 1 2 ) Student three: −1 2 On Mrs. McIntire’s answer key for the assignment, the correct answer is: −0.5. Which student answer(s) is/ are correct? Explain.