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**Commutative, Associative, Identity & Zero Properties**

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**Commutative and Associative Properties**

Properties refer to rules that indicate a standard procedure or method to be followed.

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**Commutative and Associative Properties**

Commutative Property means changing the order in which you add or subtract numbers does not change the sum or product. Associative Property means changing the grouping of numbers when adding or multiplying does not change their sum or product. Grouping symbols are typically parentheses (),but can include brackets [] or Braces {}.

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**Commutative Properties**

Commutative Property of addition - (Order) For any numbers a and b , a + b = b + a. = 50 = 50 Commutative Property of multiplication - (order) For any numbers a and b , a b = b a. 6 8 = 8 6 48 = 48

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**Associative Properties**

Associative Property of addition - (grouping symbols) For any numbers a, b, and c, (a + b) + c = a + (b + c). (2 + 4) + 5 = 2 + (4 + 5) (6) + 5 = 2 + (9) 11 = 11 Associative Property of multiplication - (grouping symbols) For any numbers a, b, and c, (ab) c = a (bc). (2 3) 5 = 2 (3 5) (6) 5 = 2 (15) 30 = 30

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**Commutative and Associative Properties**

Commutative and Associative properties are very helpful to solve problems using mental math strategies. Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) Evaluate: ( ) + ( ) + ( ) (40) + (40) + (40) = 120

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**Commutative and Associative Properties**

Commutative and Associative properties are very helpful to solve problems using mental math strategies. Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property) Evaluate: 4 7 25 4 25 7 (4 25) 7 (100) 7 = 700

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**For any number a and a x 1 = a**

Identity Property The product of any number and 1 is that number. For any number a and a x 1 = a 72 x 1 = 72

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**Zero Property The Product of any number and 0 is 0**

For any number a and a x 0 = 0 72 x 0 = 0

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**Practice Writing Expressions**

A number multiplied by 5 7 more than a number The product of 5 and a number 125 decreased by a number 96 added to a number

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**Evaluate (solve) Tell which property you used**

27 x 0 x 3 = 1 x 17 x 2 = (49 x 500) x 2 = 36 x 0 x 8 = 5 x 27 x 2 =

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