Ericka B. answered • 04/29/15
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There are 5 properties of math as listed below.
1) Commutative property- this property is only for addition and multiplication and states that numbers can be either added or multiplied in any order without the result being different.
Addition example: 3 + 4 = 4 + 3 (both ways of adding come to the same answer of 7)
Multiplication example: 3 x 4 = 4 x 3 (both ways of multiplying come to the same answer of 12)
2) Associative property- this property is again only for addition and multiplication and states if there are multiple numbers being added or multiplied, they can be grouped in any manner and the result will be the same.
Addition example: 3 + (4 + 5) = (3 + 4) + 5 (both ways come to the same answer of 12)
Multiplication example: 3 x (4 x 5) = (3 x 4) x 5 (both ways come to the same answer of 60)
3) Distributive property- this property states that if we are multiplying a term by another term in parentheses, the multiplicative needs to be distributed among all terms inside the parentheses.
Example: 3(4x + 5) -> 12x + 15 (we multiplied both the 4x and the 5 by 3)
4) Density property- this property is very simple, it essentially states that we will always be able to find another real number that lies between two other real numbers, typically by adding another decimal place
Example: Two real numbers between 4.16 and 4.17, would be 4.161 and 4.162; a real number between 4.161 and 4.162 would be 4.1611, etc.
5) Identity property- this property states that any number added to 0 will be itself (0 is then the "additive identity"), whereas any number multiplied by 1 will be itself (1 is then the "multiplicative identity").
Additive examples: 3 + 0 = 3; 16 + 0 - 16
Multiplicative examples: 3 x 1 = 3; 16 x 1 = 16
Hope this helps!
