1. Commutative Properties
Commutative Property of Addition: In a sum, you can add the numbers in any order. Ex: 4 + (-7) = a + b = b +a
Commutative Property of Multiplication: In a product, you can multiply the numbers in any order. Ex: 8(-5) = -5(8) ab = ba

2. Associative Properties
Associative Property of Addition:
Changing the grouping of the numbers in a sum does not change the sum.
Ex:
(9+6) + 2 = 9 + (6+ 2)
(a + b) + c = a + (b + c)
Associative Property of Multiplication: Changing the grouping of the numbers in a product does not change the product. Ex: (3 ∙ 10) ∙ 4 = 3 ∙ (10 ∙ 4) (ab)c = a(bc)

3. Identity Properties Identity Property of Addition:
When 0 is added to any number, the result is identical to the original number.
Ex:
9 + 0 = 9
a + 0 = a
Identity Property of Multiplication: When any number is multiplied by 1, the result is identical to the original number. Ex: 4 ∙ 1 = 4 a ∙ 1 = a

4. Distributive Property
The product does not change when the same factor is distributed across two addends. Ex: 3 × (2 + 4) = 3×2 + 3×4 So the "3" can be "distributed" across the "2+4" into 3 times 2 and 3 times 4.