To keep track of how far he has gone on two consecutive days, Victor can add the two distances in any order and the total remains the same.

This is called the Commutative Property of Addition.

For example, if the Prologue of the Tour is 5.6 km and Stage 1 is 180.5 km, Victor can add the distances in either order to get the total for the two days.

5.6 + 180.5 = 180.5 + 5.6 =186.1

5.6 + 180.5 + 205.5

(5.6 + 180.5) +205.5 = 5.6 + (180.5 + 205.5)

186.1 + 205.5 = 5.6 + 386

391.6 = 391.6

The Commutative Property (changing the order of the numbers) and the Associative Property (changing the order of the additions) are important because they allow us to easily simplify expressions which contain only addition.

In the example above, the right side of the equation is easier because you can combine the second two decimal numbers into a whole number.

Because addition is commutative and associative, for any expression involving only addition, you can change the order of addends and add parentheses whenever you desire.

Here is a page from Victor's racing journal. Tell which property he used to calculate the distance he rode: