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Integer Operations Review Integer Operations Review 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. Integer Operations Review Add: (+5) + (+7) What happens when we combine hot coals with hot coals? (+5) + (+7) = (+12) We get a big pile of hot coals. Integer Operations Review Add: (-4) + (-9) What happens when we combine ice cubes with ice cubes? (-4) + (-9) = (-13) We get a big pile of ice cubes. Integer Operations Review Add: (-8) + (+5) What happens when we combine ice cubes with hot coals? (-8) + (+5) = (-3) The five hot coals melt five ice cubes. They cancel out. Integer Operations Review Subtraction: What are 2 different ways that we could lower the temperature in the Greenhouse by 6ºC ? We could remove 6 hot coals, or We could add 6 ice cubes. Instead of subtracting an integer, we may add its opposite. Integer Operations Review Subtract: (-5) – (+13) = (-5) + (-13) = (-18) Subtract: (+15) – (-17) = (+15) + (+17) = (+32) Multiplying and Dividing Integers Multiplying and Dividing Integers is even easier !!!! You only need to remember 2 simple rules . . . 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. Let’s see how this works: 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) 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) 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) 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) Multiplying and Dividing Integers We have: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30) Multiplying and Dividing Integers We have: (+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 . . . It might be a little confusing . . . It might be a little confusing . . . Just remember that multiplying and dividing are opposite operations. Multiplying and Dividing Integers If: (+3) x (-7) = (-21) (-5) x (-4) = (+20) (-3) x (+8) = (-24) (+5) x (+6) = (+30) 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) 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) 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) 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) 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. 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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dividing integers, Multiplying and dividing integers, multiplying integers, subtracting integers, different signs, adding integers, the sign, negative numbers, integers worksheets, multiplication and division

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posted: | 4/16/2011 |

language: | English |

pages: | 24 |

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