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### Course: 4th grade > Unit 3

Lesson 3: Multi-digit multiplication: place value and area models- Using area model and properties to multiply
- Multiply 2-digits by 1-digit with area models
- Multiply 2-digits by 1-digit with distributive property
- Multiplying with area model: 6 x 7981
- Multiply 3- and 4-digits by 1-digit with area models
- Multiply 3- and 4-digits by 1-digit with distributive property

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# Multiplying with area model: 6 x 7981

Sal uses an area model to multiply 6x7981. Created by Sal Khan.

## Want to join the conversation?

- How does using a grid help? The way I do it is a little more understanding to me(212 votes)
- using a grid can help you solve problem easily! :3 :3 :3 :3(6 votes)

- Is there a way to get more structure and information on these equations, because like other people responded on other reviews, I don't really understand the area model on these multiplication problems. If you can give me more instruction?(29 votes)
- I still don't understand the grid completely and for some reason can't use it well anymore...(14 votes)
- What you need help with first?(3 votes)

- My teacher calles it the box metod.(7 votes)
- I am confused what the grid helps with. Why can't you use addition right away? With this question I would add before using the grid, would that still work?(7 votes)
- Let's multiply 6 times 7,981. And the way we're going to do it right now is just to represent or expand out 7,981 as 7,000 plus 900 plus 80 plus 1. And so multiplying 6 times 7,981 is the same thing as multiplying 6 times 7,000 plus 6 times 900 plus 6 times 80 plus 6 times 1. You'd essentially distribute the 6. And to help us keep track of things, let me draw a little grid right over here. So this is the 6, and we're going to have to think about what 6 times 7,000 is, 6 times 900, 6 times 80, and 6 times 1. So I'll make a little square for our rectangle for each of them. Let me do that. So here we go. And so we just need to think about, what is 6 times 7,000? Well 6 times 7 is 42. So 6 times 7,000 is 42,000. 6 times 900, well once again, 6 times 9 is 54. So 6 times 900 is 5,400. 6 times 80, well 80 is eight 10s. So 6 times 8 is 48, but since it's six times 80 or eight 10s, this is going to be 48 10s, or 480. And then finally, 6 times 1, of course, is equal to 6. So to find what this product is, we just have to take the sum of each of these numbers. What 6 times 7,000 is plus 6 times 900 plus 6 times 80 plus 6 times 1. So let's do that right over here. So it's going to be 42,000 plus 5,400 plus 480 plus 6. And we get, let's see, in the ones place, we just have a 6. In the tens place, we just have an 8. In the hundreds place, 4 plus 4 is 8. In the thousands place, 2 plus 5 is 7. And then finally, the ten thousandths place, we still have a 4. So we get 47,886. So this Is equal to 47,886. And what I encourage you to do is to think about how this is really underlining what we're doing here. It's not that different than what you might have done with the traditional multiplication techniques. And this is a useful way of thinking about it because now you really understand what's going on. And actually, when you start doing things like this in your head, at least for myself, this is actually how I try to tackle the multiplication problem. When someone says 6 times 7,981, if I was just looking at this and I didn't have any paper, I would say, OK, what's 6 times 7,000? I'd say, OK, that's 42,000. I'll try to remember that. What's 6 times 900? Oh that's 5,400. Well if I add that to the 42,000, I get 47,400. Then, what's 6 times 80? 480. Have to add that to the 47,400 to get to 47,880. And then, what's 6 times 1? Well that's 6. Well add that to the 47,880, which I've been keeping in my brain, and that's going to be 47,886. So this helps you understand what's really going on when you multiply multiple digits, and it's a useful technique for doing mental multiplication.(2 votes)

- how does the grid work,it did not help me on the test(7 votes)
- you got this guys!(6 votes)
- I think it helps to see the numbers you are adding to get your answer(6 votes)
- Can someone help me? Sal explains stuff oddly fast ;-;(5 votes)

## Video transcript

Let's multiply 6 times 7,981. And the way we're going
to do it right now is just to represent or expand
out 7,981 as 7,000 plus 900 plus 80 plus 1. And so multiplying 6 times
7,981 is the same thing as multiplying 6 times 7,000
plus 6 times 900 plus 6 times 80 plus 6 times 1. You'd essentially
distribute the 6. And to help us keep
track of things, let me draw a little
grid right over here. So this is the 6,
and we're going to have to think about what
6 times 7,000 is, 6 times 900, 6 times 80, and 6 times 1. So I'll make a little square for
our rectangle for each of them. Let me do that. So here we go. And so we just need to think
about, what is 6 times 7,000? Well 6 times 7 is 42. So 6 times 7,000 is 42,000. 6 times 900, well once
again, 6 times 9 is 54. So 6 times 900 is 5,400. 6 times 80, well
80 is eight 10s. So 6 times 8 is 48, but since
it's six times 80 or eight 10s, this is going to
be 48 10s, or 480. And then finally, 6 times
1, of course, is equal to 6. So to find what this
product is, we just have to take the sum of
each of these numbers. What 6 times 7,000 is plus
6 times 900 plus 6 times 80 plus 6 times 1. So let's do that
right over here. So it's going to be 42,000
plus 5,400 plus 480 plus 6. And we get, let's see, in the
ones place, we just have a 6. In the tens place,
we just have an 8. In the hundreds
place, 4 plus 4 is 8. In the thousands
place, 2 plus 5 is 7. And then finally, the
ten thousandths place, we still have a 4. So we get 47,886. So this Is equal to 47,886. And what I encourage
you to do is to think about
how this is really underlining what
we're doing here. It's not that
different than what you might have done with the
traditional multiplication techniques. And this is a useful way of
thinking about it because now you really understand
what's going on. And actually, when
you start doing things like this in your head,
at least for myself, this is actually how I try
to tackle the multiplication problem. When someone says 6 times 7,981,
if I was just looking at this and I didn't have any
paper, I would say, OK, what's 6 times 7,000? I'd say, OK, that's 42,000. I'll try to remember that. What's 6 times 900? Oh that's 5,400. Well if I add that to
the 42,000, I get 47,400. Then, what's 6 times 80? 480. Have to add that to the
47,400 to get to 47,880. And then, what's 6 times 1? Well that's 6. Well add that to
the 47,880, which I've been keeping in my brain,
and that's going to be 47,886. So this helps you
understand what's really going on when you
multiply multiple digits, and it's a useful technique for
doing mental multiplication.