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Operations with Integers

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What is an Integer? By now, you are familiar with basic subtraction problems such as 5 – 2 = 3 and 11 – 4 = 7. In these problems, the difference of two whole numbers is a whole number. – Remember the whole numbers? But some subtraction problems require an expanded set of numbers, such as 5 – 8 = ?

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What is an Integer? Integers are the set of whole numbers and their opposites (also known as negative numbers). **Note: 0 is neither positive nor negative!

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Adding & Subtracting Integers Let’s play integer baseball! There are two teams: Team Positive and Team Negative Each inning you will be given a score where you determine how many points each team scored. Then you will analyze which team won and by how much. Let’s play ball!

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Adding & Subtracting Integers ScoreTeam Positive Points Team Negative Points Which team won? By how much did that team win? So mathematically….? 3 + (-5)35-23 + (-5) = -2 The positive number in the score is 3. The negative number in the score is 5. Team Negative won because they scored 5 points where Team Positive only scored 3 The difference between the two teams scores is 2.

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Adding & Subtracting Integers ScoreTeam Positive Points Team Negative Points Which team won? By how much did that team win? So mathematically….? - 7 + 227-5- 7 + 2 = - 5 The positive number in the score is 2. The negative number in the score is 4. Team Negative won because they scored 4 points where Team Positive only scored 2 The difference between the two teams scores is 2.

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Adding & Subtracting Integers ScoreTeam Positive Points Team Negative Points Which team won? By how much did that team win? So mathematically….? - 7 + - 4011- - 7 + - 4 = -11 There are no positive numbers in the score. The negative numbers in the score are 7 and 4 which means that Team Negative scored 11 points. Team Negative won because they scored 11 points where Team Positive did not score any points The difference between the two teams scores is 11.

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Multiplying & Dividing Integers The rules for multiplying & dividing integers are different. Here’s a little saying to help you remember. Same Signs (+)(+) or (-)(-) The two numbers agree The answer is POSITIVE Different Signs (+)(-) or (-)(+) The two numbers do not agree The answer is NEGATIVE

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Multiplying & Dividing Integers Same Signs (+)(+) or (-)(-) The two numbers agree The answer is POSITIVE Different Signs (+)(-) or (-)(+) The two numbers do not agree The answer is NEGATIVE Let’s try it! 1.(2)(3) = 6 since 2 and 3 are both positive, their product is positive because the signs are the same. 2.(-2)(-3) = 6 since -2 and -3 are both negative, their product is positive because the signs are the same. 3.(2)(-3) = -6 since 2 and -3 have different signs, their product is negative. 4.(-2)(3) = -6 since -2 and 3 have different signs, their product is negative. Note: These same rules apply to dividing integers as well.

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