The identity property of addition describes how the sum of any number a and 0 is the number a. The commutative property says that changing the order of the addends a and b does not change their sum. T...The identity property of addition describes how the sum of any number a and 0 is the number a. The commutative property says that changing the order of the addends a and b does not change their sum. To add whole numbers, we first write the numbers so each place value lines up vertically. Then, we add the digits in each place value, working from left to right starting with the ones place. If a sum in a place value is more than 9, carry to the next place value.