Understanding how each operation works enables us to use that information to solve problems. Understanding addition and subtraction means knowing when each of the following properties may be useful.
The commutative property
Connected to the order-irrelevance principle of counting, the commutative property applies to addition. It means that you can swap the position or order of the quantities to be combined without impacting the sum.
For example, 12 + 34 has the same value as 34 + 12.
For example, 12 + 34 has the same value as 34 + 12.
The associative property
The associative property allows us the 'associate' numbers in different ways, meaning the order you add them doesn't matter. Also stemming from the order-irrelevance, the associative property is easier to see in situations where there are more than 2 addends.
For example, 12 + 34 + 6. I could combine 34 and 6 first to make 40, then add the additional 12 to make 52.
For example, 12 + 34 + 6. I could combine 34 and 6 first to make 40, then add the additional 12 to make 52.