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## Integers M7N1a, M7N1c

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**IntegersM7N1a, M7N1c**Mrs. Sims’ World**What are Integers?**We have learned to count by using the numbers 0, 1, 2, 3, 4, 5….. These are called whole numbers. We use whole numbers everyday in life. We use these numbers to count, to keep our checkbook, to measure temperature, and many other things. But, think about this – what do we do when the temperature falls below 0 degrees? What kind of number do we use? We use a negative number to show numbers below 0. A negative number is represented with a negative sign (also can be called a minus sign) in front of the number. Ex. -3, this number is 3 below 0 We say this as negative 3 or minus 3. All the positive numbers and negative numbers are called integers. {…, -4, -3, -2, -1, 0, 1, 2, 3, 4,…}**What is Absolute Value?**The absolute value of a number is the distance that number is from 0 on the number line. Insert # line The absolute value of 7 is written as |7|. The answer is 7. The absolute value of -7 is written as |-7|. The answer is 7. 7 and -7 are the same distance away from 0 which is 7 spaces.**Adding Integers: The Rules**While using negative chips and number lines may help you learn how to add integers, in reality, you need to remember the rules. Here are the rules for addition. If the signs are the same, add the numbers and keep the sign. ex. 7 + 8 = 15 (both numbers are positive) ex. -7 + -8 = -15 (both numbers are negative) If the signs are different, subtract and take the sign of the larger number. ex. -7 + 8 = 1 (I subtract. 8 is the larger number and is positive. My answer will be positive.) ex. 7 + -8 = -1 (I subtract. 8 is the larger number and is negative. My answer will be negative.)**Subtracting Integers: The Rules**While using negative chips and number lines may help you learn how to subtract integers, in reality, you need to remember the rules. Here are the rules for subtraction. You need to change all subtraction problems into addition and then follow the rules for adding integers. ex. 7 - 8 We need to change this to addition. Remember these 3 letters: KCF This means to: Keep Change Flip. Keep the sign of the 1st number, change the subtraction to addition, and flip the 2nd sign. Now our problem looks like this: 7 + -8 Then just follow the rule for addition of integers. Different signs so subtract and take the sign of the larger number. The answer is -1. Try this one: -7 - 8 Yes, it equals -15. Keep the sign of the 1st number, change the subtration to addition, and flip the last sign to positive. We then have -7 + -8 Now, follow the rules for addition of integers - the signs are the same, so add and keep the sign. The main thing to remember on subtraction is to change it to addition and follow the rules for addition.**Multiplying and Dividing Integers: The Rules**I'm just going to get straight to the rules for multiplying and dividing integers because they are really simple. If the signs are the same in either multiplication or division, then the answer will be a POSITIVE number. Yes, that is correct POSITIVE. Even if you have 2 negative numbers, when you multiply or divide, you will get a positive. That's the rule - just remember it. ex. -3 x -3 = 9 3 x 3 = 9 If the signs are opposite (a negative and a positive), the answer will always be a negative. ex. -3 x 3 = -9