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Multiplying two 2-digit numbers using partial products

26 times 37 is the same as 20 times 37 plus 6 times 37. The distributive property allows us to find each part of the product, like 3 tens times 2 tens, then add them all to get the whole product. Created by Sal Khan.

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Video transcript

- [Instructor] In a previous video, we figured out a way to multiply a two-digit number times one-digit number. What we did is we broke up the two-digit numbers in terms of its place value, so the three here in the tenths place that's three tens, this is seven ones. So we view 37 sixes as the same thing as 30 sixes, three tens times six plus seven sixes, seven times six. And then we added those together to get a total of 222. What we'll try in this video is now see what happens if we try to do two digits times two digits, so let's try to tackle 37, 37 instead of six let's multiply that times 26 so we're trying to figure out 37 26's is one way to think about it. So pause this video and see if you can tackle that and see if you can maybe use a similar method to what we used before. Well one way to think about it is you could view this as 37 26's or you could view this as 37 sixes plus 37 20's. So first we could do the 37 sixes which is exactly what we did over here, we said hey that's the same thing and we could do it in either order we could say hey let's first think about 30 sixes, so we're going to multiply 30 times six 30 sixes is 180, so that right over there is three tens times six. And then we could think about the seven ones times six. And so that's going to be 42. That's the seven ones times six or the seven sixes. And then we could do the same thing with the 20's we could say hey what are three tens, what are 30 20's going to be. So let's write that over here or you could say what are three tens times two tens. Well that would be six times ten times ten, so let me write this down this is three tens times two tens that's what we're going to do now. Times two tens and that's the same thing as which is equal to 30 times 20 which is the same thing as three times two times ten times ten. Well that's going to be 600, so we could write that here 600 and just be very clear, we've already thought about 37 sixes, that's these two numbers up here we have to add that we still have to add them. But now we're thinking about 37 20's so first we thought about 30 20's which is 600 and now we could think about seven 20's so seven 20's is going to be seven times two is 14 so seven times 20 is 140. So I'll write that right over here. 140 to be clear this is seven ones times two tens. Or seven 20's and now we can add it all together to get what the total would be. So in the total we have, that's why it's useful to have everything stacked by their place value, we could look at the ones place so we say okay we only have a total of two ones here, so I'll put a two there. Now let's see tens we have eight tens plus four tens is 12 tens plus another four tens is 16 tens. 16 tens we can also break up as 106 tens, so we could write the six tens here and then put that 100 up here. So 100 plus another hundred is 200 plus 600's is 800's plus one more hundred is 900's. And so there you have it, this is equal to 962. I really want you to understand what we just did, it might look a little bit complicated but first we thought about what is 37 sixes that's where we got these numbers from and that's what we had done in a previous video. And then we just thought about well what is 37 20's going to be and that's where these numbers came from and actually let me write that down. This whole thing that I'm circling in orange, that is 37 sixes or I'll write it as 37 times six and then this is 37 20's so 37 times 20. So if it's not obvious, pause the video or after this video reflect on why this works, try it with other numbers 'cause if you really understand this then your multiplication life and actually your mathematical lives in your future will only become more and more intuitive.