associative
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The associative property states that the result of an addition or multiplication sentence will be the same no matter the grouping of the terms. Associative: (a + b) + c = a + (b + c) (a × b) × c = a × (b × c)
The way in which numbers are grouped when added or multiplied does not change the sum or product.In symbols the associative property of addition says that (a+b) +c = a + (b +c) where a,b, and c are any numbers.The associative property for multiplication says that (ab)c=a(bc).Informally, the associative property says that grouping does not matter when applying the operation.
It means that in an addition such as: a + b + c it doesn't matter whether you do the addition on the left, or the addition on the right, first. Similar for multiplication.
There are two properties of addition. The COMMUTATIVE property states that the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c. That is IT. No more! The DISTRIBUTIVE property is a property of multiplication over addition (OR subtraction), not a property of addition. The existence of of an IDENTITY and an ADDITIVE INVERSE are properties of the set over which addition is defined; again not a property of addition. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.
The commutative property is a mathematical property in which the order of the equation can be changed and still get the same answer. Addition is commutative because it doesn't matter what order the numbers you are adding are put in, they still add up to the same result.