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**Operations with Integers PowerPoint**

Created By: Miss Henry

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**Can be visualized on a number line:**

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**

# (-10) Step 1: Add the #s Step 2: Keep same sign (Both #s are negative – Answer is negative!) # (8) Step 1: Add the #s Step 2: 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: (7) = ? ? = -6 23 + (-8) = ? ? = 15

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**Adding (Different Signs) - Examples**

# (7) Step 1: Subtract the #s Step 2: Use sign of bigger # (Bigger # is negative - Answer is negative!) # (-8) Step 1: Subtract the #s Step 2: 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 2nd 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 = ? ? = -14

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**Subtracting - Examples**

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

# · (-5) #2. -9 · (-10) 15 Multiply the numbers Same signs = Positive Answer # · # · -6 Multiply the numbers Different signs = Negative Answer

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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)**

# ÷ (-3) # ÷ (-10) 11 Divide the numbers Same signs = Positive Answer # ÷ # ÷ -6 Divide the numbers Different signs = Negative Answer

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**Solve the following problems:**

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

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**Review Visit the website below for additional information on integers:**

lessons/S1U1L10GL.html Click on the signs below to review the rules for each operation

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**Review Visit the website below for additional information on integers:**

lessons/S1U1L10GL.html Click on the signs below to review the rules for each operation

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