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## Arithmetic

### Course: Arithmetic > Unit 14

Lesson 2: Multi-digit multiplication- Relate multiplication with area models to the standard algorithm
- Intro to standard way of multiplying multi-digit numbers
- Understanding the standard algorithm for multiplication
- Multiplying multi-digit numbers: 6,742x23
- Multi-digit multiplication

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# Intro to standard way of multiplying multi-digit numbers

The standard algorithm for multiplying a multi-digit number by a single digit number involves multiplying each place value by the single digit, and regrouping as necessary. This method is equivalent to breaking the multi-digit number into parts, multiplying each part by the single digit, and adding the results together. Created by Sal Khan.

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- I'm only in 4th grade and I shared this method to my friends.(5 votes)
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- Why this algorithm? My teacher tought me one other and this worked for me many times before.(1 vote)
- Unless your teacher requires you to use a certain algorithm, it is best to choose the algorithm you are most comfortable with. You may want to use two algorithms (or an algorithm and a shortcut trick) to check your answer.(7 votes)

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## Video transcript

- [Instructor] What we're going to do in this video is think about how we might multiply 592 times seven. And in general we're gonna think about how we would approach
multiplying something that has multiple digits times something that has one digit. And the way we're going
to do it is the way that, if you were to ask your parents, it's probably the way that they do it. And so the typical approach is you would write the larger
multi digit number on top and then you would write the
smaller single digit number below that, and since
it's in the ones place, the seven, you would put it
in the ones place column. So you'd put it right below the ones place in the larger number,
so right below that two. And then you'd write the
multiplication symbol. And the way you'd think about it is, all right, I'm just gonna
take each of these places and multiply it by the seven. So, for example, if I'm
taking those two ones and I'm multiplying it times seven, well that's gonna be 14 ones. Well there's no digit for 14. I can only put four of
those ones over here. And then the other 10 ones I can express as one 10, and so I'd put it up there. Sometimes when people learn it, they say, hey, two times seven is 14. I write the four and I carry the one. But all you're doing is you're saying, hey, 14 is one 10 plus four ones. But then you move over to the tens place. You say, hey, what's
nine tens times seven? Well, nine times seven is 63, so nine tens times seven is 63 tens, plus another 10 is 64 tens. You can only put four
of those tens over here. So the other 60 tens you
can express as six hundreds, so you can stick that right over there. Now a lot of people would
explain that as saying, hey, nine times seven
is 63, plus one is 64. Write the four and carry the six. But hopefully you understand
what we mean by carrying. You're really trying to write 64 tens. Only four of those tens
can be expressed over here. Or that's maybe the cleanest way to do it. And then the other 60 tens you
can express as six hundreds. And then, last but not least, five hundreds times seven
is going to be 35 hundreds, and then you add six
hundreds, you get 41 hundreds. So 41 hundreds, so it's 4,144. Now I wanna reconcile this, or connect it, to with other ways that
you might have seen this. So let's say that, let's do this again. So if we were to write 592 times seven. So one way that we've
approached it in the past is we say, all right, what's two times seven? Well that's going to be 14. Notice that's the same 14. We're just representing it
a little bit differently. Then we might say, well
what is nine times seven? Gonna do the same color. And this really nine tens times seven. That's 63 tens, so you might
write it right over there, which is the same thing as 630. And then you could think about what is five hundreds times seven? Well that's 35 hundreds, so
you could write it like that. Same thing as 3500, and then
you would add everything up. So you have a total of four ones. You have a total of four tens. You have a total of 11 hundreds. You could right 100 there. And then regroup the other 10 hundreds into the thousands place as 1000. 1000 plus three thousands is 4000. So we got the exact same answer because we essentially did the same thing. Over here, when we were carrying it, we were essentially
regrouping things from here and you could think about
it where we're condensing our writing versus what we did here. Here we just very systematically
said two times seven, nine times seven, five times seven, but we made sure to
keep track of the places to figure out what each of those, you could think of it as
partial products, would be, and then we added. While here we carried along the way, essentially regrouping
the values when we said, hey, two ones times seven ones, that's 14 ones, which is the same thing as four ones plus one 10. And so on, and so forth. So I encourage you, one, it's
good to learn this method. It's the most common
way that folks multiply. Once again, your parents
probably learned it this way, but it's really valuable to understand why these two things are the same thing, so really ponder that. Think about that. And see if you can, if it all makes sense what's going on there. You're not just blindly
memorizing the steps.