1. 1 Multiplying and Dividing Integers For this lesson we will be using a real life situation about greenhouses. Greenhouses are used to keep plants both warm in the winter and cool in the summer. We are gong to use integers to help us talk about the temperature! You MUST play this as a slide show and not just scroll through the slides! You MUST play this as a slide show and not just scroll through the slides! You may write the examples but you do not have to. You may write the examples but you do not have to.

2. 2 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ?

3. 3 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of a Model:

4. 4 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of our Model: Make 3 trips into the greenhouse to add... seven ice cubes each time.

5. 5 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of our Model: Make 3 trips into the greenhouse to add... seven ice cubes each time. What is the overall effect?

6. 6 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of our Model: Make 3 trips into the greenhouse to add... seven ice cubes each time. What is the overall effect? The temperature drops by 21°.

7. 7 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of our Model: Make 3 trips into the greenhouse to add... seven ice cubes each time. What is the overall effect? The temperature drops by 21°. So, (+3) x (-7) =

8. 8 Multiplying and Dividing Integers Ex) Consider: (+3) x (-7) = ? Think of our Model: Make 3 trips into the greenhouse to add... seven ice cubes each time. What is the overall effect? The temperature drops by 21°. So, (+3) x (-7) = (-21)

9. 9 Multiplying and Dividing Integers Ex) (-5) x (-4) =

10. 10 Multiplying and Dividing Integers Ex) (-5) x (-4) = We need to make 5 trips into the greenhouse to remove... four ice cubes each time.

11. 11 Multiplying and Dividing Integers Ex) (-5) x (-4) = We need to make 5 trips into the greenhouse to remove... four ice cubes each time. The temperature will rise by 20° C.

12. 12 Multiplying and Dividing Integers Ex) (-5) x (-4) = We need to make 5 trips into the greenhouse to remove... four ice cubes each time. The temperature will rise by 20° C. So, (-5) x (-4) = (+20)

13. 13 Multiplying and Dividing Integers Ex) (-3) x (+8) =

14. 14 Multiplying and Dividing Integers Ex) (-3) x (+8) = We need to make 3 trips into the greenhouse to remove... 8 hot coals each time.

15. 15 Multiplying and Dividing Integers Ex) (-3) x (+8) = We need to make 3 trips into the greenhouse to remove... 8 hot coals each time. Overall Effect:

16. 16 Multiplying and Dividing Integers Ex) (-3) x (+8) = We need to make 3 trips into the greenhouse to remove... 8 hot coals each time. Overall Effect: A decrease in temperature of 24° C.

17. 17 Multiplying and Dividing Integers Ex) (-3) x (+8) = We need to make 3 trips into the greenhouse to remove... 8 hot coals each time. Overall Effect: A decrease in temperature of 24° C. So, (-3) x (+8) = (-24)

18. 18 Multiplying and Dividing Integers Ex) (+5) x (+6) =

19. 19 Multiplying and Dividing Integers Ex) (+5) x (+6) = We are making 5 trips into the greenhouse to add... 6 hot coals each time.

20. 20 Multiplying and Dividing Integers Ex) (+5) x (+6) = We are making 5 trips into the greenhouse to add... 6 hot coals each time. Overall Effect:

21. 21 Multiplying and Dividing Integers Ex) (+5) x (+6) = We are making 5 trips into the greenhouse to add... 6 hot coals each time. Overall Effect: The temperature increases by 30° C.

22. 22 Multiplying and Dividing Integers Ex) (+5) x (+6) = We are making 5 trips into the greenhouse to add... 6 hot coals each time. Overall Effect: The temperature increases by 30° C. So, (+5) x (+6) = (+30)

23. 23 Multiplying and Dividing Integers We have:

24. 24 Multiplying and Dividing Integers We have: (+3) x (-7) = (-21)

25. 25 Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20)

26. 26 Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24)

27. 27 Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30)

28. 28 Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30) Can we write some rules?

29. 29 Multiplying and Dividing Integers RULES:

30. 30 RULES: 1) When multiplying integers with the same signs, the answer will be

31. 31 Multiplying and Dividing Integers RULES: 1) When multiplying integers with the same signs, the answer will be positive.

32. 32 Multiplying and Dividing Integers RULES: 1) When multiplying integers with the same signs, the answer will be positive. 2) When multiplying integers with different signs, the answer will be

33. 33 Multiplying and Dividing Integers RULES: 1) When multiplying integers with the same signs, the answer will be positive. 2) When multiplying integers with different signs, the answer will be negative. Write these rules in your notebook!

34. 34 Multiplying and Dividing Integers RULES: 1) When multiplying integers with the same signs, the answer will be positive. 2) When multiplying integers with different signs, the answer will be negative. Will this be true for division?

35. 35 Multiplying and Dividing Integers If: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30)

36. 36 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30)

37. 37 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24) (+5) x (+6) = (+30)

38. 38 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24)(-24) ÷ (-3) = (+8) (+5) x (+6) = (+30)

39. 39 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24)(-24) ÷ (-3) = (+8) (+5) x (+6) = (+30)(+30) ÷ (+5) = (+6)

40. 40 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24)(-24) ÷ (-3) = (+8) (+5) x (+6) = (+30)(+30) ÷ (+5) = (+6) Are the rules the same?

41. 41 Multiplying and Dividing Integers If:Then: (+3) x (-7) = (-21)(-21) ÷ (+3) = (-7) (-5) x (-4) = (+20)(+20) ÷ (-5) = (-4) (-3) x (+8) = (-24)(-24) ÷ (-3) = (+8) (+5) x (+6) = (+30)(+30) ÷ (+5) = (+6) Are the rules the same?Yes!

42. 42 Multiplying and Dividing Integers RULES: 1) When multiplying or dividing integers with the same signs, the answer will be positive.

43. 43 Multiplying and Dividing Integers RULES: 1) When multiplying or dividing integers with the same signs, the answer will be positive. 2) When multiplying or dividing integers with different signs, the answer will be negative. Write these rules in your notebook!

44. 44 Multiplying and Dividing Integers Homework Time!