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**Adding & Subtracting Integers!**

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**Let’s have some fun and sing! (to the tune of Row, Row, Row Your Boat)**

Same signs add and keep Different signs subtract

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**Keep the sign of the higher number**

Then you’ll be exact

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**Different signs subtract Keep the sign of the higher number **

Let’s try that again! Same signs add and keep Different signs subtract Keep the sign of the higher number Then you’ll be exact

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**Now, let’s add a second verse for subtracting integers!**

Change the minus to a plus Change the sign of next Then all you do is add them up As if they were a plus

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**Put it all together! Same signs add and keep Different signs subtract**

Keep the sign of the higher number Then you’ll be exact Change the minus to a plus Change the sign of the next Then all you do is add them up As if they were a plus

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**Are you ready?? What You Will Learn**

California State Standard 5NS2.1 Add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. Some definitions related to integers. Rules for adding and subtracting integers. Different methods that will work for you. Are you ready??

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Definition Positive number – a number greater than zero. 1 2 3 4 5 6

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Definition Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

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Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

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Definition Integers – Integers are all the positive whole numbers and all of their opposites, including zero. 7 opposite -7

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**The absolute value of +9 or of –9 is 9. Definition**

Absolute Value – It is the distance a number is from zero on the number line. The absolute value of +9 or of –9 is 9.

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**Negative Numbers Are Used to Measure Temperature**

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**Negative Numbers Are Used to Measure Below Sea Level**

30 20 10 -10 -20 -30 -40 -50

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Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 +

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**Integer Addition Rules**

Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 = -14

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**Integer Addition Rules**

Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. = Larger abs. value Answer = - 4 9 - 5 = 4

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**Integer Subtraction Rule**

Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9

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Let’s try another -2 – (+7) is the same as -2 + (-7) = -9

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One more… 2 – (+7) is the same as 2 + (-7) = -5

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**One Way to Add and Subtract Integers Is With a Number Line**

I like to call this, “Stand – Turn – Walk” Or STW - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

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**Stand at the first integer.**

Let’s give it a try! Stand at the first integer. If the problem is - -2 + (3) Stand at -2 - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

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Turn toward the function sign -2 + (3) You are standing in front of -2 Now turn toward the positive integers on the number line.

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**Walk forward or backward according to the sign of the second integer**

Since the (3) is positive, you will walk forward from the -2 three spaces. The number you stop on is your answer. The answer is positive 1. -2 + (3) = 1

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**You have learned lots of things**

About adding and subtracting Integers. Let’s review!

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**Integer Addition Rules**

Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 = -14

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**Integer Addition Rules**

Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. = Larger abs. value Answer = - 4 9 - 5 = 4

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**Integer Subtraction Rule**

Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!

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**Let’s try some problems using Stand, Turn, Walk**

-6 + (3) = -3 2 + (-4) = -2

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Another? 4 – (-2) = +6 -4 – (-2) = -2

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Aren’t integers interesting?

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