Audrey has more than a decade of experience teaching elementary. She has a bachelor's in journalism and a master's in education.
What is the Commutative Property?
Imagine that you and a friend are playing a game of memory with multiplication facts. Some cards have the answers and some don't. You turn over a card with the problem 3 x 6 = 18. Then you turn over another card that has 6 x 3 = ___.
Even though you haven't learned your 6 times tables, your friend says you know the answer, thanks to the commutative property. The commutative property is the ability to solve a multiplication problem and get the same answer no matter what order you multiply the numbers in.
Basically, if 3 x 6 = 18, then 6 x 3 = 18, too.
Learning the 0 to 5 Multiplication Facts
Knowing the commutative property is a helpful shortcut for learning the multiplication facts. When you learn one set of multiplication facts, you automatically know the answer when the same fact appears again, but with the numbers flipped around.
Let's look at this more closely. You and your brother are making Easter baskets with eggs stuffed with candy. Your brother fills 2 eggs with 3 pieces of candy. As a multiplication number sentence that's 2 x 3 = 6 candies. You fill 3 eggs with 2 pieces of candy. Your multiplication problem is 3 x 2 = 6 candies.
See how you got the same answer both times? This is because the numbers you were multiplying with (2 and 3) stayed the same - they just moved around. And even though you grouped the candies differently, 3 candies into 2 eggs, and then 2 candies into 3 eggs, you were always working with 6 candies.
As I said earlier, the commutative property is a shortcut for learning multiplication facts. This is because when you learn the multiplication facts for 2, you learn everything from 2 x 0 = 0 to 2 x 10 = 20. Then, when it's time to learn another set of multiplication facts, you already know the answer to any number x 2, because of the commutative property.
So, later on, when you're learning the multiplication facts for 3, you already know 3 x 2 = 6. That's one less fact for you to learn.
Learning the 6 to 10 Multiplication Facts
Now that you've learned multiplication facts up to 5, the only multiplication facts left are those for 6, 7, 8, 9, and 10. Remember that shortcut we looked at earlier? Thanks to the commutative property, any number from 6 to 10 multiplied by 0, 1, 2, 3, 4, or 5, you've already learned!
For example, you already know 6 x 1 = 6 because 1 x 6 = 6, and 6 x 2 = 12 because 2 x 6 = 12.
But what about 6 x 7 = 42? You haven't learned these higher numbers yet, but you can quickly, just like before.
Say you have 7 groups of cookies with 6 chocolate chips on each and you want to know how many chocolate chips you have altogether. Your multiplication number sentence is 7 x 6 = ____. Using the commutative property, you realize that if 6 x 7 = 42, then 7 x 6 is also 42.
When you're learning to multiply, using the commutative property can make the process much easier. The commutative property means that two numbers multiplied together will always give the same answer no matter the order of the numbers. Understanding the relationship that numbers have with each other will take get you much farther than memorizing a bunch of multiplication facts.
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