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# Distributive property when multiplying

CCSS.Math:

## Video transcript

what we're going to do in this video is dig a little bit deeper into our understanding of multiplication and just as an example we're going to use four times seven and some of you might know what four times seven is but even in this case I think you might get something from this video because we're going to think about how you can break down a multiplication question into simpler parts and that's going to be useful well beyond four times seven it's going to be useful in your future when you're tackling more and more complicated things now there's a couple of ways that we can visualize four times seven my favorite ways to visualize it with angry cats so let's bring on the angry cats yep they're still angry and we can see that this is a representation of four times seven we have four rows right over here four rows and each of those rows have seven cats and so you can see that right over here each of those rows have seven cats some people would call this a four by seven grid or four by seven or a whatever however you'd want to view it but if someone were to ask you what's the total number of cats it would be four rows times seven columns four times seven now another way to represent four times seven is also with a tape diagram you might see something like this where here we're visualizing it as seven fours or you could view it as 4 plus 4 plus 4 plus 4 plus 4 plus 4 plus 4 now that's all well and good and you can add that up if you like but what I promised you is that we would figure out ways to break down things that might simplify things in the future well what if you didn't know what four times seven is but you knew what four times five is and you knew what four times two is well what's interesting is that seven is five plus two so what if we try to first figure out this many cats so four rows and five columns right over there and then we tried to figure out this many cats four rows and two and you can see that it's the exact same number of cats so one way to think about it is four times seven is the exact same thing as four times and I'm going to use parentheses and that just means to do that part first is equal to four times instead of seven I could write that as 5 plus two because that's what seven is so all this is saying is four times seven is the same thing as 4 times 5 plus two where you do the five plus two first because we have those parentheses around it and five plus two is indeed equal to seven and we can see that that is equivalent to the total number of cats that we have here which we could view as what we just circled off in this orange pink color which would be four rows of five so that would be equal to 4 times 5 4 times 5 and then to that we can add this second group of cat heads or angry cat heads and that is 4 rows of 2 so that's 4 times 2 and we could put parentheses if we want just to make it a little bit more readable now why did I do that well some folks might find 4 times 5 a little bit more straightforward I could skip count by 5 I can go 5 10 15 20 also 4 times 2 might be a little bit more straightforward and so it could be easier to say hey this is just going to be 4 times 5 which is 20 plus 4 times 2 which is equal to 8 and so that is just going to be equal to 28 and you could have thought about it the same way down here with what is sometimes called a tape diagram we could say all right if I have 5 fours that's this amount right over here that is the 4 times the 5 and then I could add that to the two fours the 4 times the 2 right over here and that's another way to get to 4 times 7 so the big picture here is even if you're not dealing with 4 times 7 even if you're not dealing with angry cats and in most of our lives we we actually try to avoid angry cats there might be a way to break down the numbers that you're multiplying into ones that you might be more familiar with I'll give you one more example let's say someone were to ask you well what is six times nine pause this video and see if you can break down break this down in some useful way well maybe you know what six times ten is and you also know what six times one is so you could rewrite nine as ten minus one well then this would mean that six times nine is the same thing as six times 10 minus one based on exactly what we just did up here that says that this whole thing is going to be the same thing as 6 times 10 6 times 10 minus 6 times one one way to think about it is I just distributed the six that's the distributive property right over there and then 6 times 10 is equal to 60 and then 6 times one is equal to 6 and it might be easier for me to say hey 16 minus 6 in my head that's equal to 54 so I know what some of you are thinking 6 times 9 seems so clean and now I've involved all of this other symbolism symbols and I've written down more numbers but at the end of day I'm trying to give you skills for breaking down problems and including ways that you might want to do in your head if you're like hey I'm kind of foggy on what 6 times 9 is but 6 times 10 hey I know that's 60 and 6 times 1 of course that 6 well what if I have you this is 6 times 10 minus 1 and then I could tackle it and get 54 and once again you might know 6 times 9 you might know 4 times 7 but in the future it might be useful for bigger and bigger numbers to think about how could I break this down