# How to Do Commutative Operations

Addition and multiplication are both commutative operations. *Commutative* means that you can switch around the order of the numbers without changing the result. This property of addition and multiplication is called the *commutative property*. Here’s an example of how addition is commutative:

3 + 5 = 8 is the same as 5 + 3 = 8

If you start out with 5 books and add 3 books, the result is the same as if you start with 3 books and add 5. In each case, you end up with 8 books.

And here’s an example of how multiplication is commutative:

2 7 = 14 is the same as 7 2 = 14

If you have 2 children and want to give them each 7 flowers, you need to buy the same number of flowers as someone who has 7 children and wants to give them each 2 flowers. In both cases, someone buys 14 flowers.

In contrast, subtraction and division are *noncommutative* operations. When you switch around the order of the numbers, the result changes.

Here’s an example of how subtraction is noncommutative:

6 – 4 = 2 but 4 – 6 = –2

Subtraction is noncommutative, so if you have $6 and spend $4, the result is *not* the same as if you have $4 and spend $6. In the first case, you still have $2 left over. In the second case, you *owe* $2. That is, switching the numbers around turns the result into a negative number.

And here’s an example of how division is noncommutative:

5 2 = 2 r 1 but 2 5 = 0 r 2

For example, when you have 5 dog biscuits to divide between 2 dogs, each dog gets 2 biscuits and you have 1 biscuit left over. But, when you switch the numbers around and try to divide 2 biscuits among 5 dogs, you don’t have enough biscuits to go around, so each dog gets none and you have 2 left over.