
To find the total for the first three days
of the Tour, Victor would add
5.6 km + 180.5 km + 205.5 km. Following
the rules for Order of Operations, we would do these additions
from left to right, however, since they are all additions, we
can do them in any order and still get the same answer. Associative Property of Addition. 
duane hyde 
(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: Stage 3 = 169 km Stage 4 = 252 km Stage 5 = 228.5 km Stage 6 = 204.5 km A: Total for stages 3 & 4: 169 + 252 = 252 + 169 = 421 B: Total for stages 3, 4, & 5: 169 + 252 + 228.5 = 169 + (252 + 228.5) = 649.5 C: Total for stages 4, 5, & 6: 252 + (228.5 + 204.5) = 252 + (204.5 + 228.5) = 685 
Written by: Nikki Siegel  Art by: Duane Hyde and Travis Spaid 