7th Grade Math Properties: Definitions and Examples
Math properties are the rules that all math problems follow. Understanding these rules, or properties, will help students be more successful in math class. Here is a review of the math properties used in 7th grade.
What Math Properties Are Taught in 7th Grade?
Identity
An identity refers to numbers that don't change when combined with another number. There are two identities:
 The additive identity is zero because a number doesn't change when you add zero to it. Example: 5 + 0 = 5, or n + 0 = n
 The multiplicative identity is one because a number doesn't change when you multiply it by one. Example: 5 x 1 = 5, or n x 1 = n
Zero Product
Closely related to identity, the zero product property states that if you multiply any number by zero, the answer is always zero. Example: 5 x 0 = 0, or n x 0 = 0
Commutative
When you can change the order of numbers in an equation without changing the answer, you are using the commutative property. Addition and multiplication are commutative (e.g., 5 + 4 = 9 and 4 + 5 = 9; 4 x 5 = 20 and 5 x 4 = 20). Subtraction and division are not (e.g., 5  4 does not equal 4  5; 5 ÷ 4 does not equal 4 ÷ 5).
Associative
When you can list a group of numbers in any order and combine them however you wish without changing the answer, you are using the associative property. Only addition and multiplication are associative. Examples: 54 + (45 + 3) = (54 + 45) + 3 = 45 + (3 + 54) and 6(5 x 12) = (6 x 5) x 12 = (12 x 6) x 5
Distributive
Equations with parentheses use the distributive property. When you distribute, you take a number and do the same operation to all the numbers inside the parentheses.
The distributive property of math is usually referred to as the distributive property of one operation  most often multiplication  over another operation  generally addition or subtraction. The rule for distribution of multiplication over addition is that you multiply a number by each of the numbers added together in a set of parentheses. Example: 5(n + 3) = (5 x n) + (5 x 3) or 5n + 15
The distributive property of multiplication over subtraction works the same way. The only difference is you are subtracting instead of adding. Example: 5(n  3) = (5 x n)  (5 x 3) or 5n  15
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