The Associative Property refers to grouping numbers. We will see that regrouping numbers is easy in addition and multiplication. And computations that regroup numbers use the Associative Property.

In addition, the rule is:
a + (b + c) = (a + b) + c

Let’s look at an example!
2 + (3 + 4) = (2 + 3) + 4

Is this true? Let’s simplify using PEMDAS. If you missed the post, you can learn about it here!

2 + (3 + 4) = (2 + 3) + 4   Simplify the numbers inside the parentheses
      2 + 7 = 5 + 4         Simplify both sides of the equation
          9 = 9             Both sides of the equation are equal

The rule is similar for multiplication:
a(bc) = (ab)c

Try to simplify this example.
2 * (3 * 4) = (2 * 3) * 4

2 * (3 * 4) = (2 * 3) * 4   Simplify the numbers inside the parentheses
     2 * 12 = 6 * 4         Simplify both sides of the equation
         24 = 24            Both sides of the equation are equal

We have shown that the Associative Property works for addition and multiplication. Can you think of other examples where the Associative Property holds?

*Side Learning*
What are all the possible ways to express the sum of 2, 3, and 4? Does their sum change?

2 + 3 + 4 = 9
2 + 4 + 3 = 9
3 + 2 + 4 = 9
3 + 4 + 2 = 9
4 + 2 + 3 = 9
4 + 3 + 2 = 9

There are 6 possibilities and each has a sum of 9.
So, changing the numbers around does not change the result!

Try this with multiplication. How many possible ways are there to express the product of 2, 3, and 4?
Do the different expressions have different products?