The associative property of addition states that if we add more than two numbers, the grouping of the addends does not change the sum. Let's look at an example.
1 + (2 + 4) = (1 + 2) + 4
On the left side of the problem, the order of operations tells us that we must simplify inside the parentheses first. When we do this, we will get 6 and if we add 1 we get 7.
On the right side of the problem, we musty also follow the order of operations and do the operation inside the parentheses first. In the parentheses, we have 1 + 2 which equals 3 and if we add 4 to that we get 7.
The sum is the same on both sides of the problem even though we grouped the addends differently.
In general terms, the associative property of addition can be written as followed.
a + (b + c) = (a + b) + c
This is where a, b, and c represent any numbers.
