What is associative property?

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Associative property refers to the grouping property of numbers and/or binary operations.  This kind of property simply follows the basic rule that the addition or multiplication of a group of numbers will yield the same result regardless of how these numbers are grouped or “associated” with each other.  In the case of basic three numbers for example, their arrangement and grouping will not matter when they are all added together because of their associative or so-called “grouping” property. This property will then yield the same sum for all the added numbers.  The same is true for the multiplication process.  When a set of numbers are multiplied together with some of the numbers grouped or separated, the resulting product will stay the same because of associative property.

The term “associative” when applied to mathematics literally refers to groupings or grouped numbers.  Whenever numbers are grouped, adding them or multiplying them will always yield to the same result.  In the case of numbers 1, 2, and 3 for example, grouping 1 and 2 together and adding 3 will yield to the sum of 6. This will be represented with the formula (1+2)+3=6.  The numbers inside the parenthesis are the numbers that are “associated” or grouped.  In another scenario, if 2 and 3 are grouped and added to 1 in the formula 1+(2+3), the same sum of 6 will result.  This basic example simply proves the associative property of basic numbers in the form of an addition formula.  The same property may also be applied to associated or grouped numbers using a multiplication formula.

Many aspects of mathematics reflect the associative property of numbers.  Various algebraic expressions for example can be created through associated numbers or groupings.  By the simple use of parentheses, numbers can easily be grouped together to display their associative properties.  In this way, calculations and values may be presented with the correct formula or mathematical expression.

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