Algebraic properties describe basic rules related to addition, subtraction, multiplication, and division. The names of the properties will not be included on the test, but it is important to understand the properties and how they are used.
Commutative property of addition
Changing the order of the addends does not change the result.
4 + 8 = 8 + 4
Commutative property of multiplication
Changing the order of the factors does not change the result.
5 × 9 = 9 × 5
Associative property of addition
Changing the grouping of the addends does not change the result.
(2 + 6) + 4 = 2 + (6 + 4)
Associative property of multiplication
Changing the grouping of the factors does not change the result.
(3 × 5) × 4 = 3 × (5 × 4)
Distributive property of multiplication over addition
A factor outside parentheses enclosing a sum can be distributed to each term inside the parentheses.
7(10 + 3) = 7(10) + 7(3)
Subtraction and division have neither commutative nor associative properties.