Associative Property

The associative property is a mathematical law that applies to addition and multiplication. The word associative comes from the Latin word associatus which means joined to. The associative property is about the order of adding or multiplying when there is more than one addition or multiplication to do. It’s about how additions and multiplications are done when they are joined together.

Let’s look at an example.

Say we have this addition to do .

The brackets show which addition is done first.

Does it matter if we do the addition like this or like this ?

In other words, does it matter if we associate the 5 with the 3 or if we associate the 3 with the 8? Let’s see.

It is clear that, in this example, it doesn’t matter how we associate the numbers, the result is the same.

This is a law and is true for all additions. If a, b and c represent numbers then, the Associative Law for addition says:

The associative law also applies to multiplication. Let’s look at an example.

Say we have this multiplication to do .

Does it matter if we do the multiplication like this or like this ?

Again, we are asking, does it matter if we associate the 5 with the 3 or if we associate the 3 with the 8? Let’s see.

Again, it is clear that, in this example, it doesn’t matter how we associate the numbers, the result is the same.

This is a law and is true for all multiplications. If a, b and c represent numbers then, the Associative Law for multiplication says:

So, to be simple about it, the Associative Law for addition and multiplication says that it doesn’t matter how the numbers are associated when doing addition and multiplication.

Let’s satisfy ourselves that the Associative Law doesn’t apply for subtraction or for division.

Let’s try .

Clearly, in the example, the Associative law does not apply to subtraction.

Now let’s try .

Clearly, in the example, the Associative law does not apply to division.