Associativity
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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.