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### Course: 3rd grade>Unit 1

Lesson 6: Commutative property of multiplication

# Commutative property of multiplication

Sal explores what happens when we multiply numbers in different orders, for example 3x5 and 5x3.

## Want to join the conversation?

• Are there any other operations besides multiplication that are commutative?
• Addition is commutative, but subtraction and division are not.
• would it work the same way for three numbers that are being multiplied?
• Yes, it will work with three or more numbers. As long as it is all multiplication or addition
• What is the difference between Commutative law of multiplication and Commutative property of multiplication?
• Commutative law of multiplication and Commutative property of multiplication are exactly the same thing. In math, a law is the same as a property.

Have a blessed, wonderful day!
• how do we repersent the communitive property of multipication
• The commutative (moving) property of multiplication can most simply be changing places, so 3*2=2*3. We can also use it to our advantage such as 4*4*5, 16*5 is slightly harder to do than 4*5*4 = 20*4=80. 3*6*7, 18*7 is a lot harder than 3*7*6=21*6 which can be done as 20*6+1*6.
we can represent it as a*b=b*a or a*b*c = (a*c)*b.
• can it work for as many numbers as you want?
• Yes, it works for all numbers.
You can always swap the two numbers in the operation and get the same result. This is the meaning of commutativity!
Addition and multiplication are commutative.
Subtraction and division are not commutative.

Hope this helped!
• i burst into laughter when i heard that "meow"
• the meow was funny and I couldn't laugh but lol
• dose switching the order of numbers important
• Not really but it can make solving certain multiplications later on easier.
Keep in mind that addition and multiplication are commutative, and subtraction and division are not commutative!
• What is 9 times 6 =?
• It's 54 so easy.
• lol the angry cats at is funny

## Video transcript

- [Instructor] In this video we're going to talk about one of the most important ideas in mathematics and that's whether order matters when you multiply two numbers. So for example, is three times four the same thing as four times three? Are these two things equal to each other? And regardless of whether these two are equal to each other, is it always the case that if I have some number times some other number, if I swap the order am I going to get an equivalent number? Well, pause this video and see if you can work through that. Try to think about that a little bit before we think through it together. Well, let's think through this particular example. And we're going to do so with the help of some angry cats. So we clearly see some angry cats here. Meow. Yes, they are angry. We could view this as three groups of four. So this is one group right over here of angry cats, four angry cats. This is two groups of four angry cats. And this is three groups of four angry cats if we view the first number here as groups of the second number. But we could also view it as four groups of three. How would we do that? Well, we could have one group of three angry cats. We can have two groups of three angry cats. We can have three groups of three angry cats. And we could of course have four groups of three angry cats. So based on that, if you think of it, the first number as groups of the second number, well, it seems like the order doesn't matter. Another way you could think about it is here you have four rows of three angry cats. You have one, two, three, four rows of one, two, three angry cats. And so to figure out how many total cats you have, you multiply four times three. But you could view this same group of angry cats but just view it with a slightly different perspective. So here we have our angry cats. And then let me rotate our angry cats, probably risking making them a little bit angrier. Let me move them back in. And now, we could view this as three rows, one, two, three, of four cats in each row. So let me put all of these upright. So we have one, two, three rows of one, two, three, four cats. Don't wanna look at those 'cause it might make us a little bit confused. And we're dealing with the exact same number of cats. And so I'm only dealing with three and four here but what you will see is order doesn't matter when you are multiplying two numbers. And we could also see that on a number line. And we could do that with multiple examples. I'll keep a couple of angry cats here looking at us just to keep us in check. If we wanna think about three times four we could view it as four threes. So three, six, nine, 12. Or we could view it as three fours. Four, eight, and 12. And I focused a lot on three and four but we could do it with any two numbers that we're trying to multiply together. So let's say we wanted to do that with, I don't know, let's see whether six times four, whether it's the same thing as four times six. Well, you could view it as six fours. Four, eight, 12, 16, 20, and then 24. Or you could view it as four sixes. One six, 12, 18, and 24. So big takeaway, order doesn't matter when you are multiplying numbers like this. And this is sometimes referred to as the commutative property. It's a fancy word but it's really just saying that whether you're doing six times four or four times six the commutative property of multiplication says, "Hey, those two things "are going to be equivalent." Meow. Yes, they are angry for being rotated.