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Multiplying and Dividing Integers

Multiplying and Dividing Integers. Multiplying and Dividing Integers. One model that we can use for integers is a greenhouse. In the Greenhouse, positive integers represent a temperature above 0ºC or an increase in temperature.

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Multiplying and Dividing Integers

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  1. Multiplying and Dividing Integers

  2. Multiplying and Dividing Integers One model that we can use for integers is a greenhouse. In the Greenhouse, positive integers represent a temperature above 0ºC or an increase in temperature. Negative integers represent a temperature below 0ºC or a decrease in temperature. A hot coal will increase the temperature by exactly 1ºC. An ice cube will decrease the temperature by exactly 1ºC. There are unlimited amounts of each item in the Greenhouse.

  3. Multiplying and Dividing Integers Multiplying and Dividing Integers is even easier !!!! There are very simple rules . . .

  4. Here’s something to think about: Consider: (+3) x (-7) = ? We can think of it this way: Santa Claus makes 3 trips into the Greenhouse and leaves 7 ice cubes each time. What happens to the temperature? It drops by 21°C. So, . . . (+3) x (-7) = (-21)

  5. Consider: (-5) x (-4) = ? We can think of it this way: A thief makes 5 trips into the Greenhouse and steals 4 ice cubes each time. What happens to the temperature? It rises by 20°C. So, . . . (-5) x (-4) = (+20)

  6. Consider: (-3) x (+8) = ? We can think of it this way: A thief makes 3 trips into the Greenhouse and steals 8 hot coals each time. What happens to the temperature? It drops by 24°C. So, . . . (-3) x (+8) = (-24)

  7. Consider: (+5) x (+6) = ? We can think of it this way: Santa Claus makes 5 trips into the Greenhouse and leaves 6 hot coals each time. What happens to the temperature? It rises by 30°C. So, . . . (+5) x (+6) = (+30)

  8. Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30) Do you see a pattern in these results?

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

  10. Multiplying and Dividing Integers Do these rules hold true for dividing? (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30) We could try to think of examples for division, but . . .

  11. It might be a little confusing . . .

  12. It might be a little confusing . . . Just remember that multiplying and dividing are opposite operations.

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

  14. 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)

  15. 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)

  16. 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)

  17. 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)

  18. 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) So we can see that the 2 simple rules also work for division.

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

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