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Operations with Integers PowerPoint Created By: Ms. Cuervo

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What is an Integer? A whole number that is either greater than 0 (positive) or less than 0 (negative) Can be visualized on a number line:

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What is a Number Line? A line with arrows on both ends that show the integers with slash marks Arrows show the line goes to infinity in both directions ( + and -) Uses a negative sign (-) with negative numbers but no positive sign (+) with positive numbers Zero is the origin and is neither negative nor positive

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What are Opposites? Two integers the same distance from the origin, but on different sides of zero Every positive integer has a negative integer an equal distance from the origin Example: The opposite of 6 is -6 Example: The opposite of -2 is 2

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What is Absolute Value? Distance a number is from zero on a number line (always a positive number) Indicated by two vertical lines | | Every number has an absolute value Opposites have the same absolute values since they are the same distance from zero Example: |-8| = 8 and |8| = 8 Example: |50| = 50 and |-50| = 50

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What Can We Do to Integers? Integers are numbers, so we can add, subtract, multiply, and divide them Each operation has different rules to follow

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Adding Rules – Same Signs If the integers have the SAME signs: ADD the numbers & keep the same sign! Positive + Positive = Positive Answer Negative + Negative = Negative Answer Examples: -3 + (-10) = ? ? = -13 6 + (8) = ? ? = 14

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Adding (Same Signs) - Examples #1. -3 + (-10) Step 1: 13 Add the #s Step 2: -13 Keep same sign (Both #s are negative – Answer is negative!) #2. 6 + (8) Step 1: 14 Add the #s Step 2: 14 Keep same sign (Both #s are positive – Answer is positive!)

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Adding Rules – Different Signs If the integers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the BIGGER number! Bigger # is Positive = Positive Answer Bigger # is Negative = Negative Answer Examples: -13 + (7) = ? ? = -6 23 + (-8) = ? ? = 15

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Adding (Different Signs) - Examples #1. -13 + (7) Step 1: 6 Subtract the #s Step 2: -6 Use sign of bigger # (Bigger # is negative - Answer is negative!) #2. 23 + (-8) Step 1: 15 Subtract the #s Step 2: 15 Use sign of bigger # (Bigger # is positive - Answer is positive!)

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Subtracting Rules Put ( ) around second number & its sign Change SUBTRACTION sign to an ADDITION sign Change sign of 2 nd number to its opposite Follow the rules for ADDITION: -SAME signs: Add & keep the same sign -DIFFERENT signs: Subtract & use sign of bigger # Examples: -5 – -10 = ? ? = 5 9 - 23 = ? ? = -14

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Subtracting - Examples #1. -5 – -10 #2.9 - 23 Step 1: -5 – (-10) Insert ( ) 9 – (23) Step 2: -5 + (-10) Change – to + 9 + (23) Step 3: -5 + (10) Change 2 nd sign 9 + (-23) Step 4: 5 Follow adding rules -14 d

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Multiplying Rules Multiply the numbers like usual If the integers have the SAME signs: ANSWER will be POSITIVE If the integers have DIFFERENT signs: ANSWER will be NEGATIVE Examples: -3 · (-5) = ? ? = 15 -9 · (-10) = ? ? = 90 -7 · 7 = ? ? = -49 6 · -6 = ?? = -36

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Multiplying - Examples #1. -3 · (-5) #2. -9 · (-10) 15 Multiply the numbers 90 15 Same signs = Positive Answer 90 #3. -7 · 7 #4. 6 · -6 49 Multiply the numbers 36 -49 Different signs = Negative Answer -36

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Dividing Rules Divide the numbers like usual If the integers have the SAME signs: ANSWER will be POSITIVE If the integers have DIFFERENT signs: ANSWER will be NEGATIVE Examples: -33 ÷ (-3) = ? ? = 11 -90 ÷ (-10) = ? ? = 9 -20 ÷ 2 = ? ? = -10 6 ÷ -6 = ?? = -1

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Dividing - Examples #1. -33 ÷ (-3) #2. -90 ÷ (-10) 11 Divide the numbers 9 11 Same signs = Positive Answer 9 #3. -20 ÷ 2 #4. 6 ÷ -6 10 Divide the numbers 1 -10 Different signs = Negative Answer -1

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Mixed Practice Solve the following problems: -9 + - 9 -18 7 · -4 -28 -10 - (-19) 9 -35 ÷-7 5 15 + -25 -10 -23 - 9 -32

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