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Associativity

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(Redirected from Associative property)

Associative property is a property of mathematical operations (like addition and multiplication). It means that if you have more than one of the same associative operator (like +) in a row, the order of operations does not matter.


For example, if you have <math> 2+5+10\ </math>, there are two plus signs (+) in a row. This means we can add it in either this order:

<math> (2+5)+10=(7)+10=17\ </math>

Or this order:

<math> 2+(5+10)=2+(15)=17\ </math>

The answer comes out the same both ways because addition is associative. In other words, associativity means:

<math> (2+5)+10=2+(5+10)\ </math>


Not all operations are associative. Subtraction is not associative, which means:

<math> (10-5)-2\ne10-(5-2) </math>

This is true because:

<math> (10-5)-2=(5)-2=3\ </math>
<math> 10-(5-2)=10-(3)=7\ </math>

And:

<math> 7\ne3 </math>


Also, associativity is different from commutativity, which lets you move the numbers around.