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  • - [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.

- [Instructor] What we're going to do

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A2 初級

多桁の数字の標準的な掛け方の紹介 (Introduction to standard way of multiplying multidigit numbers)

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    林宜悉 に公開 2021 年 01 月 14 日
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