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
	= 220