For any real numbers \(a\), \(b\), and \(c\)

$$\left( {a + b} \right) + c = a + \left( {b + c} \right)$$

If you **add** three numbers together, the **sum** will be the same no matter how you group the numbers.

Notice that on the left side of the equation, we first add the numbers \(a\) and \(b\) because they are inside the parenthesis, a grouping symbol. Then whatever the sum, we add it to the number \(c\). The result of the left side should be equal to the right side. This time, we first add the numbers \(b\) and \(c\) because they are inside the parenthesis. Then, whatever their sum, we add it to the number \(a\).

Let's go over a quick example to illustrate the Associative Property of Addition.

Suppose, we have

$$\displaylines{

a = 3 \cr

b = 5 \cr

c = 2 \cr} $$

Substituting the values into the "formula"

$$\left( {a + b} \right) + c = a + \left( {b + c} \right)$$

We get

$$\displaylines{

\left( {3 + 5} \right) + 2 = 3 + \left( {5 + 2} \right) \cr

8 + 2 = 3 + 7 \cr

10 = 10 \cr} $$

As you can see, it all ends up having the same result. The left and the right sides both have the sum of \(10\).