2. 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 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 Property of addition - (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 45 + 5 = 5 + 45 6  8 = 8  6 50 = 50 48 = 48

5. Associative Property of addition - (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  3)  5 = 2  (3  5) (6) + 5 = 2 + (9) 11 = 11 (6)  5 = 2  (15) 30 = 30

6. Commutative and associative properties are very helpful to solve problems using mental math strategies Solve: 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) (40) + (40) + (40) = 120

7. 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 (4  25)  7 (100)  7 = 700 Group numbers that can be formed easily. (Associative property)