Using the any-order property of multiplication

The any-order property of multiplication can be used to simplify calculations by changing the order in which we perform multiplications.

For example:

2 × 2 × 2 × 5 × 5 × 5	= (2 × 5) × (2 × 5) × (2 × 5)
	= 10 × 10 × 10
2 × 17 × 5 = 10 × 17
25 × 7 × 4 = 25 × 4 × 7 = 100 × 7.

Sometimes this reordering happens after we decompose one of the factors, such as when we double twice in order to multiply by four, as in

17 × 4 = (17 × 2) × 2 = 34 × 2 = 68

This technique of moving a factor from one number to another in order to simplify a calculation has applications beyond repeated doubling, as in

36 × 5 = 18 × (2 × 5) = 180.