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Properties Absent copy 9/16

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Commutative Property Commutative property of addition an multiplication (Back and Forth) change the order Associative Property (Change the group) order stays the same Identity Property Additive identity property of 0 Multiplicative identity Property of 1 You can change the order of two Addends/factors when you add or multiply. Only when add/mult. ex:2 + 5 = 5 + 2 3 (6 9) = 3 (9 6) It doesn’t matter which two factors you solve first in the ( ) when you add or multiply ex: 2 + (5 + 7) = (2 + 5) + 7 (3 6) 9 = 3 (6 9) The factors keep their identity. How can the factors keep their (identity) ex: 3 + 0 = 3, 10 + 0 = 10 Ex: 5 1 = 5, 7 1 = 7

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Inverse Property Additive inverse Multiplicative inverse Distributive Property (to share the wealth) How do we get to 0 ? Ex: 3 + (-3) = 0, -5 + 5 = 0 How do we get to 1 ? ex: 3 1 = 1, 1 2 = 1 3 2 When you can not add/sub what is in the grouping because they are not like terms (3x + 5) and you have a number right outside the grouping you have to distribute the number and multiply it to everything inside the grouping. Ex: 3(4x + 3) = 3(4x) + 3(3) = 12x + 9

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Summary: 1. Commutative to commute back and forth 2. Associative to have diff. friends 3. Identity yourself 4.Inverse How do I get to 0 when adding How do I get to 1 when Mult. 5. Distributive Share with everything in group

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Combining Like Terms You can only combine terms that have EXACTLY the same variable parts. Ex:1)2x + 3x 2)10n + 3n 2 + 9n 2 3)10x – 4(x 2 – 2x) = 5x.

Combining Like Terms You can only combine terms that have EXACTLY the same variable parts. Ex:1)2x + 3x 2)10n + 3n 2 + 9n 2 3)10x – 4(x 2 – 2x) = 5x.

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