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Associativity

property of binary operations allowing sequences of operations to be regrouped without changing their value

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 , there are two plus signs (+) in a row. This means we can add it in either this order:

Or this order:

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


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

This is true because:

And:


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