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# Commutative property of multiplication

CCSS.Math:

## Video transcript

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 3 times 4 the same thing as 4 times 3 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 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 can 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 we let me put all of these up right so we have one two three rows of one two three four cats I want to look at those because 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 keep us in check if we want to think about three times four we could view it as four threes so three six nine twelve or we could view it as three fours four eight and twelve 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 six whether six times four whether it's the same thing as four times six well you could view it as six fours four eight twelve sixteen twenty and then 24 or you could view it as four sixes one six 12 18 and 24 so a 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 your state doing 6 times 4 or 4 times 6 the commutative property of multiplication says hey those two things are going to be equivalent all yes they are angry for being rotated