Associative Property Resources

Learn More About the Associative Property

The associative property of addition and multiplication states that when adding or multiplying three numbers or more, the answer is always the same regardless of how they are arranged in the equation. You can move them around or you can group them using a parenthesis, and you’ll still come up with the same answer.

Let’s look at examples:

2 + (3 + 4) = 9      4 + 2 + 3 = 9
(2 + 3) + 4 = 9      3 + 2 + 4 = 9

2 × (3 × 4) = 24      4 × 2 × 3 = 24
(2 × 3) × 4 = 24      3 × 2 × 4 = 24

An important thing to remember is that the associative property only works with addition and multiplication, not with subtraction and division. For younger students, it’s enough that they get the idea of how it works. When they start doing more complex math operations like algebra, the associative property comes in handy because it allows them to perform operations much faster.

To see how the associative property can help us solve problems faster, let’s look at the following example:

(4 × 4) × 5 = 16 × 5 = 80

4 × (4 × 5) = 4 × 20 = 80

The answer to both expressions is 80, but as you can see, in the second example, simply changing the grouping makes it easier to derive the answer, since 4 × 20 is easier to solve than 16 × 5. The associative property lets students rethink how expressions are solved and in what order, giving them a more efficient way of deriving the answer.