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**Properties of Real Numbers**

Commutative Property Think… commuting to work. Deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY. a+b = b+a 4 • 6 = 6 • 4

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**Properties of Real Numbers**

Associative Property Think…the people you associate with, your group. Deals with grouping when you Add or Multiply. Order does not change.

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**Properties of Real Numbers**

Associative Property (a + b) + c = a + ( b + c) (nm)p = n(mp)

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**Properties of Real Numbers**

Additive Identity Property s + 0 = s Multiplicative Identity Property 1(b) = b

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**Properties of Real Numbers**

Additive Inverse Property a + (-a) = 0 Multiplicative Inverse Property a∙( ) = 1, a 0

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**Properties of Real Numbers**

Distributive Property a(b + c) = ab + ac (r + s)9 = 9r + 9s

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**Name the Property 5 = 5 + 0 5(2x + 7) = 10x + 35 8 • 7 = 7 • 8**

24(2) = 2(24) (7 + 8) + 2 = 2 + (7 + 8) Additive Identity Distributive Commutative

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**Name the Property Associative 7 + (8 + 2) = (7 + 8) + 2 Multiplicative**

Identity Distributive 7 + (8 + 2) = (7 + 8) + 2 1 • v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b

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**Properties of Real Numbers**

Reflexive Property a + b = a + b The same expression is written on both sides of the equal sign.

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**Properties of Real Numbers**

Symmetric Property If a = b then b = a If = 9 then 9 = 4 + 5

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**Properties of Real Numbers**

Transitive Property If a = b and b = c then a = c If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

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**Properties of Real Numbers**

Substitution Property If a = b, then a can be replaced by b. a(3 + 2) = a(5)

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**Name the property Distributive Substitution Reflexive Symmetric**

5(4 + 6) = 5(4 + 6) = 5(10) 5(4 + 6) = 5(4 + 6) If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6) 5(4 + 6) = 5(6 + 4) If 5(10) = 5(4 + 6) and 5(4 + 6) = then 5(10) = Distributive Substitution Reflexive Symmetric Commutative Transitive

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