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 – changing the order in which you add or subtract numbers does not change the sum or product.
Associative Property – 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 and Associative Properties
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

5. Commutative and 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)
Solve:
( ) + ( ) + ( )
(40) + (40) + (40) = 120

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