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**ADDING INTEGERS (SAME SIGNS)**

SAME signs ADD and keep the sign = 4 positives positives = positives

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**ADDING INTEGERS (SAME SIGNS)**

SAME signs add and keep the sign = - 6 4 negatives negatives = 6 negatives

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**ADDING INTEGERS (DIFFERENT SIGNS)**

DIFFERENT signs SUBTRACT and keep the sign of the larger number = 2 4 positives negatives = 2 positives

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**ADDING INTEGERS (DIFFERENT SIGNS)**

DIFFERENT signs SUBTRACT and keep the sign of the larger number = -2 4 negatives positives = 2 negatives

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**SUBTRACTING INTEGERS (KFC & follow Rules for addition)**

Problem KFC follow addition rules K – keep the first number F – flip the subtraction to an addition sign C – change the second number to its opposite ****then****** FOLLOW RULES FOR ADDITION!!!!

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**Steps Is it an addition or subtraction problem?**

Addition (go to step 2) Subtraction (go to step 3) Addition – are the signs the same? Yes – add and keep the sign No – subtract and keep the sign of the larger number Subtraction – KFC –Keep the first number; Flip to an addition problem; Change the last number to its opposite – then go back to step 2

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**MULTIPLYING INTEGERS Multiplying is REPEATED ADDITION**

Commutative Property of Multiplication - the order in which numbers are multiplied does not matter a x b = b x a

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**= 8 = 8 MULTIPLYING INTEGERS 4 groups of 2 = 2 groups of 4**

4 x = x 4 4 groups of = groups of 4 = 8 = 8 8

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**(HINT: use the commutative property)**

4 x -2 4 groups of = - 8 What would -2 x be? (HINT: use the commutative property) - 8

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-2 x 4 Use the commutative property to turn the problem around to 4 x -2 - 8

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**Use grouping to model these!!**

-7 x 2 -14 -12 3 x -4

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**What about a negative times a negative?**

-3 x means the opposite of 3 groups of The OPPOSITE would be

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**So we know that -5 (-6 + 6) equals 0**

Another way to look at negative times a negative using the Distributive Property….. 5 ( ) (-5)(-6) + (-5)( 6) ? = 0 For the problem to equal zero, the negative times a negative must equal a positive! 5 ( ) 5 (0) = 0 So we know that -5 (-6 + 6) equals 0

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**Multiplying Integers Rules**

If the signs are the same (+ x + or - x -); multiply and the answer is positive If the signs are different ( + x – or - x +); multiply and the answer is negative

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**Dividing Integers Division is the inverse operation of multiplication.**

4 x 2 = inverse ÷ 2 = 4 4 x (– 2 )= (-8) inverse (-8) ÷ (-2) = 4

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**Dividing Integers ÷ (-5) x 3 =(-15) inverse (-15) 3 = -5**

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**Rules for Division Same as Multiplication:**

If the signs are the same (+ x + or - x -); multiply and the answer is positive If the signs are different ( + x – or - x +); multiply and the answer is negative

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