# What is the difference between a commutitative property and a associative propertyIn math?

###### Wiki User

###### March 05, 2008 4:51AM

The "Commutative Laws" just mean that you can **swap
numbers** over and still get the same answer when you **add**,
or when you **multiply**. a + b **=** b + a

a × b **=** b × a You can swap when you add: **3 + 6 = 6 +
3**

You can swap when you multiply: **2 × 4 = 4 × 2**

The "Associative Laws" mean that it doesn't matter how you group
the numbers (ie which you calculate first) when you **add**, or
when you **multiply**. (a + b) + c **=** a + (b + c)

(a × b) × c **=** a × (b × c) This: **(2 + 4)** + 5 **=
6** + 5 **= 11** Has the same answer as this: 2 + **(4 +
5)** = 2 + **9 = 11**

This: **(3 × 4)** **×** 5 **= 12 ×** 5 **= 60** Has
the same answer as this: 3 **×** **(4 × 5)** = 3 **× 20 =
60** Sometimes it is easier to add or multiply in a different
order: {| ! What is 19 + 36 + 4? | 19 + 36 + 4 = 19 + **(36 +
4)** = 19 + **40** = 59 |} Or even rearrange a little: {| !
What is 2 × 16 × 5? | 2 × 16 × 5 **= (2 × 5)** × 16 **= 10**
× 16 = 160 |}