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.

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What Math Properties Are Taught in 7th Grade?


An identity refers to numbers that don't change when combined with another number. There are two identities:

  1. 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
  2. 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


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).


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


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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