# Associativity

property of binary operations allowing sequences of operations to be regrouped without changing their value
(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 ${\displaystyle 2+5+10\ }$, there are two plus signs (+) in a row. This means we can add it in either this order:

${\displaystyle (2+5)+10=(7)+10=17\ }$

Or this order:

${\displaystyle 2+(5+10)=2+(15)=17\ }$

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

${\displaystyle (2+5)+10=2+(5+10)\ }$

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

${\displaystyle (10-5)-2\neq 10-(5-2)}$

This is true because:

${\displaystyle (10-5)-2=(5)-2=3\ }$
${\displaystyle 10-(5-2)=10-(3)=7\ }$

And:

${\displaystyle 7\neq 3}$

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