The any-order property of addition
The combined effect of commutativity and associativity can be described in the following way.
A list of whole numbers can be added two at a time in any order to give the same result.
We often use the any-order property in mental arithmetic, even when implementing the algorithm. For example, when calculating 71 + 68 + 49 + 32 most of us would naturally pair the tens complements to make the calculation easier:
|71 + 68 + 49 + 32||= (71 + 49) + (68 + 32)|
|= 120 + 100|