All right, this is
Fifth-grade module two lesson seven we're continuing to use the area diagram in order to understand the standard algorithm
The only difference is the problems is are going to get a lot bigger there now
We're going to kind of like be multiplying these big old huge three digit by three digit
Which is going to cause our area model to look a little bit different this time
So in this problem, we've got
273 times
346 so once again, we're going to think of this like a rectangle
only now because our
Numbers are kind of getting a little bulky here
We're gonna break this up even smaller into what we call partial products, so instead of just writing
273 across the Top like this what we're gonna do is break it up into its place value. So we're gonna call this
273
Similarly down this left hand side and we're gonna break it up into its place value component, so it's Gonna be
346 all right and then essentially we're going to treat each one of these as a small we have nine
Rectangles here, and we're gonna treat those as nine little rectangles that we are Gonna find the area for
so this first rectangle right here is
a six by 200
Rectangle so that area is Gonna be
1200 because 6 times 2 is 12 and then we're Gonna add the two zeros
For this rectangle right here. We're gonna do 6 times 70 which gives us
420 and
Then for this rectangle right here that's going to be 6 times 3 which is
18
All right, similarly. We're gonna do this next rectangle right here
Which is 40 times?
200 well nice way to do that in your head 4 Times 2
4 times 2 is 8 then we have 1 2 3 0 so 1 2 3 0 so that's
8,000
the next rectangle right here is going to be 40 times 70 and
40 Times 70
4 times 7 is 28 and then we add two extra zeros
And I'm gonna kind of zoom in a little bit make it a little bit easier and then
Our next rectangle way over here is Gonna be
40 Times 3 which is
120
Our rectangle right here is Gonna be 300
by
200 oh my goodness such a huge number
But it's actually pretty darn easy to do because 3 times 2 is 6 and then we have 1 2 3
4 zeros 1 2 3 4 zeros and then our next rectangle is going to be 300 times
70 which is going to be 21
and then we add in or Stick-on 3 extra zeros, so that's
21,000 and then lastly we've got 300 times 3 which is 900
So now now that we've filled in all of our
rectangles
Now we're gonna find the partial products or the sums of each of these rows?
So we're gonna add this row together. So we've got
1200 Plus
420 Plus
18
so that is Gonna be
1638
1638 that because we're multiplying by 6 that actually is Gonna go right here
1638
Now here, we're multiplying by 4 and if we add each of these row or 40 really?
But if we add this row we get 8,000 plus 2,000 is 10,000
plus 800 is 10 thousand eight hundred and
So we get ten thousand
920 and that is going to go right here, so we've got the 0 the 2
the 9 the 0 and the 1
There we go and then our and I'm going to scooch these little arrows
and
Then our last row down here. We've got
60,000 plus
21,000 so that's eighty one thousand
Eighty one thousand plus nine hundred that's Eighty one thousand nine hundred
So that's gonna look like 81 oops. I goofed up there 81 thousand nine hundred
so zero zero nine
Eighty One and
Now we're ready to add all of these up so from our partial products. We'd add these numbers up and get our answer down here
Or in our standard algorithm. We're gonna add them up over here and
Eight plus zero plus zero is 8 3 plus two plus zero is five. Oh
My goodness 9 plus 9 is 18
plus 6 is 24 carry the 2
And that's two plus one plus zero plus one is four and eight plus one is nine. So our answer is
ninety four thousand four hundred fifty-eight
All right, we're gonna practice that big partial products again only this time. We're going to use a word problem to do it
We have a farmer at the Farmers market each of the ninety four vendors
makes five hundred two dollars in profit each weekend, how much profit
Will all the vendors make well that means we're gonna be multiplying ninety four times
Five hundred and two all right now. What's really kind of cool about this one is
We have a zero in one of our place values
Which really means I'm going to break up our rectangle a little bit different
I'm Gonna call this ninety, and I'm gonna call this four
That's not terribly surprising, but what might be a little surprising be surprising is up here. I'm just going to break it up into two
Place values because it doesn't make sense to have a tens place value and just put a zero there
So we don't actually need it, so I'm gonna erase it not even have it
we don't need it, and so that's what our box is gonna look like and
then when we multiply
so here
For in this box right here is gonna be four times of 500 and four times 500 is
four times five is 20, and then we just stick on those extra two zeros right here and
Then we have four times two is eight
And then down here in this box down here. We've got 90 times 500
Well 9 times 5 is 45 and then we're going to stick on three zeros 1 2 3 and
then we've got 90 times 2 which is 180 and
Now we're free to add up each of our rows this rows really easy, it's 2008
This row pretty easy
45,000 Plus 180 is
45,000 180 not much work there, and now we're free to add them up
oops
no, we're gonna add them up and
I'm going to add these guys up right here, so is 8 plus 0 is 8 0 plus 8 is 8
1 plus 0 plus 1 is 1 2 plus 5 is 7 and then the 4 so the answer is?
47,000 188 and Remember that's dollars, so Forty-seven thousand one hundred and eighty-eight dollars
But let's just make sure we know what we're doing and let's do this using the standard
Algorithm so the standard Algorithm, and we actually do have to write that
502 Times 94
And now we're going to multiply
So first we're going to begin by multiplying the four times the two then the four times the zero then the four times the five
So 4 times 2 is 8 4 times 0 right there is 0?
4 times 5 is 20 there's our answer 20
2008 just like we have right here, and now we're gonna multiply
by that 9 but really that's not a 9 really that's a 90 so we know our answer is Gonna end in a 0
Because we're multiplying by 90 and so 9 times 2 is 18
So I'm gonna put the 8 carry the 1 9 times 0 is 0 plus 1 is 1 and
9 times 5 is 45 so there's our 45, and we can see that that's exactly what we had here
45,000 180 now, we're free to add all of this up
8 plus 0 is 8 0 plus 8 is 8 0 plus 1 is 1 2 plus 5 is 7 and then the 4 and?
once again, we get exactly
47,000 188
so that's what lesson 7 looks like where we're going to where we continue to use that area diagram to teach students the
Standard algorithm of multiplication