Commutative and Associative Properties Commutative Associative and Identity

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Commutative and Associative Properties

Commutative and Associative Properties

Commutative, Associative, and Identity Properties • A property is something that is true for

Commutative, Associative, and Identity Properties • A property is something that is true for all situations • Properties or rules in mathematics are the result from testing the truth or validity of something by experiment or trial to establish a proof. • Therefore, every mathematical problem from the easiest to the more complex can be solved by following step by step procedures that are identified as mathematical properties.

Commutative and Associative Properties • Commutative Property means changing the order in which you

Commutative and Associative Properties • Commutative Property means changing the order in which you add or multiply 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 {}.

Commutative Properties Commutative Property of addition - (Order) For any numbers a and b

Commutative Properties Commutative Property of addition - (Order) For any numbers a and b , a + b = b + a. 45 + 5 = 5 + 45 50 = 50 Commutative Property of multiplication (order) For any numbers a and b , a b = b a. 6 8=8 6 48 = 48

Associative Properties Associative Property of addition - (grouping symbols) For any numbers a, b,

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

Commutative and Associative Properties • Commutative and Associative properties are very helpful to solve

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: 18 + 13 + 16 + 27 + 22 + 24 (18 + 22) + (16 + 24) + (13 + 27) (40) + (40) = 120

Commutative and Associative Properties • Commutative and Associative properties are very helpful to solve

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

Identity Properties If you add 0 to any number, the number stays the same.

Identity Properties If you add 0 to any number, the number stays the same. A + 0 = A or 5 + 0 = 5 If you multiply any number times 1, the number stays the same. Ax 1=A or 5 x 1 = 5

Property of Zero (for Multiplication) Any number multiplied by zero is zero. Ex. A

Property of Zero (for Multiplication) Any number multiplied by zero is zero. Ex. A x 0 = 0 5 x 0=0 0 x 17 = 0