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VARIABLES & PROPERTIES Identities, Inverses, Commutative, Associative, Distributive

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Shared Learning Target I will be able to ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall ~ properties & order of operations I will demonstrate my knowledge by ~ showing correct work and answers on my classwork, clicker questions, and homework.

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WHAT IS A MATH PROPERTY? A shortcut They teach about the character of numbers They may be used to rearrange an expression or an equation to make the problem a little easier to work with limits to the properties There are limits to the properties Some of them can only be used in certain cases.

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ADDITIVE IDENTITY What number can you add to anything and still get the same number as the answer? Zero (0) ADDITIVE IDENTITY PROPERTY So the ADDITIVE IDENTITY PROPERTY tells us n + 0 = n

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MULTIPLICATIVE IDENTITY What number can you multiply by anything and still get the same number as the answer? ONE (1) multiplicative IDENTITY PROPERTY So the multiplicative IDENTITY PROPERTY tells us n 1 = n

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ADDITIVE INVERSE What number can you add to a number and get zero for the answer? The numbers opposite! ADDITIVE Inverse PROPERTY So the ADDITIVE Inverse PROPERTY tells us n + -n = 0 The additive inverse undoes what you have.

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MULTIPLICATIVE INVERSE

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WHICH PROPERTY IS THIS AN EXAMPLE? 15 + (-15) = ? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

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WHICH PROPERTY IS THIS AN EXAMPLE? 257 + 0= ? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

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WHICH PROPERTY IS THIS AN EXAMPLE? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

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WHICH PROPERTY IS THIS AN EXAMPLE? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

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COMMUTATIVE PROPERTY Only for ADDITION & MULTIPLICATION n + s = s + nns = sn What does this tell us? Its okay to switch the order of the numbers when adding or multiplying NO COMBINING THE OPERATIONS!

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IS THIS THE COMMUTATIVE PROPERTY? 56 + 48 + 95 + 12 = 12 + 48 + 56 + 95 1. Yes 2. No

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IS THIS THE COMMUTATIVE PROPERTY? A B C = B C A 1. Yes 2. No

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IS THIS THE COMMUTATIVE PROPERTY? 15 + 24 2 = 2 + 15 24 1. Yes 2. No

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ASSOCIATIVE PROPERTY Only for ADDITION & MULTIPLICATION a + (b + c) = (a + b) +ca(bc) = (ab)c What does this tell us? Its okay to change how the numbers are grouped in the parenthesis NO COMBINING THE OPERATIONS !

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IS THIS THE ASSOCIATIVE PROPERTY? 500 + (12 + 480) = (500 + 12 + 480) 1. Yes 2. No 0 of 20 Countdown 20

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IS THIS THE ASSOCIATIVE PROPERTY? 56 + (48 + 95) + 12 = (56 + 48) + (95 + 12) 1. Yes 2. No 0 of 20 Countdown 20

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IS THIS THE ASSOCIATIVE PROPERTY? (AB)C= A(BC) 1. Yes 2. No 0 of 20 Countdown 20

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IS THIS THE ASSOCIATIVE PROPERTY? 15 + 24 2 = (15 + 24) 2 1. Yes 2. No 0 of 20 Countdown 20

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DISTRIBUTIVE PROPERTY May use ADDITION & Subtraction a(b + c) = ab + aca(b - c) = ab - ac What does this tell us? We can take the number outside the parenthesis and multiply it by each term (number or variable) inside the parenthesis.

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DISTRIBUTIVE PROPERTY ExampleADDITION 4(25 + 10) = 4(25) + 4(10) 4(35) = 100 + 40 140 = 140

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DISTRIBUTIVE PROPERTY Example Subtraction 5(52 - 22) = 5(52) 5(22) 5(30) = 260 + 110 150 = 150

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DISTRIBUTIVE PROPERTY ExampleAlgebraic ADDITION & Subtraction 5(b + 2) = 5b + 5(2)8(x - 6) = 8x 8(6) 5(b + 2) = 5b + 108(x - 6) = 8x 48 How are these expressions equal? We dont know what b or x are Thats okayits supposed to be like that!

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SUMMARY Additive Identity Multiplicative Identity Additive Inverse Multiplicative Inverse Commutative Property Associative Property Distributive Property

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Shared Learning Target I will be able to ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall ~ properties & order of operations I will demonstrate my knowledge by ~ showing correct work and answers on my classwork, clicker questions, and homework.

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DO YOU FEEL THAT YOU HAVE MET THE TARGET OF: USE THE PROPERTIES THAT WE DISCUSS TO SIMPLIFY AND SOLVE NUMERICAL AND ALGEBRAIC EXPRESSIONS 1. Yes, I can see where the properties can/should be used. 2. I understand what they say but need to see more examples. 3. I remember their names.