1 / 7

Commutative and Associative Properties

Commutative and Associative Properties. Commutative and Associative Properties. Properties refer to rules that indicate a standard procedure or method to be followed. A proof is a demonstration of the truth of a statement in mathematics.

pwarren
Download Presentation

Commutative and Associative Properties

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Commutative and Associative Properties

  2. Commutative and Associative Properties • Properties refer to rules that indicate a standard procedure or method to be followed. • A proof is a demonstration of the truth of a statement in mathematics. • 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.

  3. 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 {}.

  4. 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

  5. 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

  6. 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) + (40) = 120

  7. 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

More Related