Associative Property

So, what in the world is the associative property? Yes, that's quite a complicated word. But.... Would you like to be able to compute numbers in your head faster and easier? That's just what the associative property will help us to do!

This property, who was named in 1835 by the Irish mathematician Sir William Rowan Hamilton, says that when adding or multiplying, we can change the grouping of numbers and it will not change their answer. The associative property only pertains to addition and multiplication - just like the commutative property.

Let's take a look at the associative property for addition.

If you are being asked to identify properties, the commutative and associative properties can easily be confused. The best way to differentiate between the two properties is that the associative property typically has parenthesis associated with it since it refers to the grouping of numbers.

Now let's take a look at the same property with multiplication.

And... just like with the commutative property, there is one thing we must remember.....

When you are regrouping numbers with the associative property, remember that when you can make "10" or "100" it makes the math much easier. Take a look....

And...it also works with multiplication. Look how easy it is to compute mental math.

Now I bet you will be a mental math whiz! Between the commutative property and the associative property you will be able to mentally compute a lot of your math work!

The last property that you will learn about is the distributive property!

Before moving onto the distributive property, we are going to take a look at our introductory Algebra lesson on Variables used in Algebra.

Algebra Tools - Unit 1