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.