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CCSS.Math:

doing this video think about multiplying or strategies for multiplying numbers that are expressed in terms of hundreds or thousands or tens and so we see an example right over here we have 800 times 400 now like always I encourage you to pause this video and see if you can work this out on your own now let's work this through together and I'm going to work it out in a way that at least my head likes to tackle it and once you get enough practice you might even be able to do these types of multiplication problems without even needing to use paper so the key realization here if you say well look this is eight hundreds so that's the same thing as eight times 100 and this over here is four hundreds so this is four times 100 and so it's eight times 100 times four times 100 and if you're multiplying a bunch of numbers like this you can switch the order in which you're doing the multiplication so you can view this as 8 times 4 8 times 4 times 100 times 100 times 100 times 100 times 100 now why is this easier well what is 8 times 4 going to be well 8 times 4 if we know our times tables is 32 it's going to be 32 times what's a hundred times 100 going to be now there's multiple ways that you could think about this and I want you to really think it through but we'll see you'll see that there's a fairly fast way of making sure we got it right but one way to think about it is well let me do it over here 10 times 100 is equal to a thousand and so 100 times a hundred is going to be 10 times that or it's going to be equal to 10,000 so this stuff right over here is equal to 10 10,000 now you might notice something interesting here I have two zeros and then another two zero so I have a total of four zeros and then I have four zeros here because every time if you multiply by 10 you're going to add another zero so if you're multiplying by 100 you're going to add two zeros if you wrap multiply by a thousand you're going to add three zeros and you see that here so you have 32 times 10,000 which is going to be cut B what well let's see 32 32 times a thousand would be 32,000 but this is 32 times 10,000 so it's going to be 320,000 now you might already notice an interesting pattern here 32 times 1 followed by 4 zeros is 32 followed by 4 zeros this is 32 10,000 S which is 30 320,000 now another way you could have thought about it is 8 times 4 gives us our 32 and then we have 2 zeroes there to 0 therefore total of 4 zeros and we have our 4 zeros right over there now I don't want you to just memorize that it works because this is 800 x 480 times 4 gives us the 32 and then the hundred times the hundreds that's where these 4 zeros come from let's do another example so let's do let me delete this and let us do let me get my pen back so let's do 30 times 70 30 or less 230 times 700 pause the video and see if you can figure this out so we can do it like we did before 30 is 3 times 10 700 so times 700 which is 7 times 100 and so if you say 3 times 7 is going to be 21 times times 10 times 100 is going to be a thousand so what's 21 times a thousand well that's going to be 21 21,000 now just like we saw before you'll once you get a hang of it and I always want you to understand where it's coming from three times seven is the 21 and then you're going to multiply that times 10 and then 100 so you have one two three zeroes one two three zeroes let's do one more of these so let's say we wanted to multiply two thousand times eight thousand pause the video and see if you can figure out what this is maybe in your head try to do this one in your head or on paper don't feel bad if you need to use paper that's always prudent well you might get the hang of it now you might be able to do this quite quickly you might be able to say hey two times eight well that's going to be equal to 16 and then I have and then I have three plus three zeroes so that's going to be six zeroes one two three four five six which gives me 16 million and you would absolutely be correct now I want to reinforce what you're doing when you're just counting zeroes like that what you're doing is you're saying hey this is the same thing as two times 1000 times eight times 1,000 eight times 1,000 and then you're just changing the order of multiplication you're saying hey let me multiply the 2 and the 8 you multiply the 2 times the 8 and you get 16 and then you multiply the times a thousand times a thousand so times a thousand times a thousand and a thousand a thousands that's 1 million this is 1 million right over here and notice you see it there too a thousand times a thousand you have three zeroes three zeroes you get six years a thousand thousands is a million 16 times a million is 16 million so hopefully that helps it makes you a little bit more comfortable multiplying these numbers that are multiples of ten hundred thousands even millions