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Integer Operations Integers are the set of whole numbers and their opposites. The set of whole numbers starts with zero! 0,1,2,3,4,5,… Integers …-1,-2,0,1,2… Adding Integers = positive 1 = negative 1 + + = + +2 + + = -5 Adding integers If the colored chips are the same, then all you have to do is add them together to get the sum. Three red chips plus two red chips equals five red chips. + -3 = + -2 = -5 Adding integers If the colored chips are the same, then all you have to do is add them together to get the sum. Three black chips plus two black chips equals five black chips. + 3 = + 2 = 5 Opposites Opposites are numbers that are the same distance from zero. Distance from zero is called absolute value. It is always positive. The numbers –5 and 5 are both 5 units away from zero, so they have the same absolute value. Adding opposites gives a sum of zero!!! 5 units -5 5 units 0 5 Absolute value is also shown with a vertical line on either side of a number. 5 = 5 -5 = 5 Opposites have the same absolute value. Adding on a number line. Negatives Positives • 0 When you add on a number line you move to the right if you are adding positives. When you add negatives you go to the left. 3 + -2 = -2 +3 • You end up here at positive 1 -6 + 9 = 9 -6 • 0 You end up here at positive 3 Adding integers with unlike signs If one number is positive and the other is negative, you subtract the absolute values and determine whether your answer is positive or negative based on which number has the largest absolute value. -5 + 11 = ? Positive 6 -5 + 11 -5 = 5 11 11 = = 11 11 has the larger absolute value and is positive 5 _________ 6 Therefore your answer is positive! Subtracting Integers If the signs are the same and there are more of the first number, you just subtract and leave the sign the same -5 - -4 = -1 Your answer is –1! What happens when you subtract positives and negatives? -3 - 2 You are trying to take away 2 black chips. You don’t have any. Remember that a red black pair is zero! Since you need two black chips, you have to add two zero pairs! What happens when you subtract positives and negatives? -3 - 2 Your answer is negative 5! When you are trying to take away something that isn’t there; it is like adding more of what you have! -6 – (- 9) = -(-9) -6 • 0 You end up here at positive 3 Subtraction is the opposite of addition! You can re-write subtraction as addition! Change to the opposite! Then everything else changes to its opposite! -5 - 4 -5 + -4 Don’t mess with the original! Leave the first integer alone. -5 + -4 = -9! Whenever you subtract a negative, it is just like adding a positive. 8 – (-9) = 8 + +9 = 17 If you tried to subtract 9 red chips from 8 black chips, you couldn’t do it. You would need to add 9 pairs so you could remove the 9 red chips leaving you with 9 more black chips!