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Associativity

From Simple English Wikipedia, the free encyclopedia

Associative property is a property ofmathematical operations (likeaddition andmultiplication). It means that if you have more than one of the same associative operator (like +) in a row, theorder of operations does not matter.


For example, if you have2+5+10 {\displaystyle 2+5+10\ }, there are two plus signs (+) in a row. This means we can add it in either this order:

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

Or this order:

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

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

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


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

(10−5)−2≠10−(5−2){\displaystyle (10-5)-2\neq 10-(5-2)}

This is true because:

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

And:

7≠3{\displaystyle 7\neq 3}


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

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