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# Chapter1.7

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### Chapter1.7

1. 1. Commutative andCommutative and Associative PropertiesAssociative Properties
2. 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. 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. 4. Commutative Property of addition - (Order) Commutative Property of addition - (Order) Commutative Property of multiplication - (order) Commutative Property of multiplication - (order) For any numbers a and b , a + b = b + a.For any numbers a and b , a + b = b + a. For any numbers a and b , a • b = b • a.For any numbers a and b , a • b = b • a. 45 + 5 = 5 + 4545 + 5 = 5 + 45 6 • 8 = 8 • 66 • 8 = 8 • 6 50 = 5050 = 50 48 = 4848 = 48 Commutative PropertiesCommutative Properties
5. 5. Associative Property of addition - (grouping symbols) Associative Property of addition - (grouping symbols) Associative Property of multiplication - (grouping symbols) Associative Property of multiplication - (grouping symbols) For any numbers a, b, and c, (a + b) + c = a + (b + c). For any numbers a, b, and c, (a + b) + c = a + (b + c). For any numbers a, b, and c, (ab) c = a (bc). For any numbers a, b, and c, (ab) c = a (bc). (2 + 4) + 5 = 2 + (4 + 5)(2 + 4) + 5 = 2 + (4 + 5) (2 • 3) • 5 = 2 • (3 • 5)(2 • 3) • 5 = 2 • (3 • 5) (6) + 5 = 2 + (9)(6) + 5 = 2 + (9) 11 = 1111 = 11 (6) • 5 = 2 • (15)(6) • 5 = 2 • (15) 30 = 3030 = 30 Associative PropertiesAssociative Properties
6. 6. Evaluate: 18 + 13 + 16 + 27 + 22 + 24Evaluate: 18 + 13 + 16 + 27 + 22 + 24 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) 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) (18 + 22) + (16 + 24) + (13 + 27)(18 + 22) + (16 + 24) + (13 + 27) (40) + (40) + (40) = 120(40) + (40) + (40) = 120 Commutative and Associative PropertiesCommutative and Associative Properties • Commutative and Associative properties are very helpful to solve problems using mental math strategies.
7. 7. Evaluate: 4 • 7 • 25Evaluate: 4 • 7 • 25 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) 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) 4 • 25 • 74 • 25 • 7 (4 • 25) • 7(4 • 25) • 7 (100) • 7 = 700(100) • 7 = 700 Commutative and Associative PropertiesCommutative and Associative Properties • Commutative and Associative properties are very helpful to solve problems using mental math strategies.

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