## Multiplying: 2 digits numbers (using distributive property) | 4th grade | Khan Academy

In this video, I’m going

to multiply 87 times 63. But I’m not going to do it

just by using some process, just showing you some steps. Instead, we’re just going to

use the distributive property to actually try to

calculate this thing. So first, what I’m going

to do– let me rewrite 87. So this is the same thing as 87. But instead of

writing 63 like that, I’m going to write

63 as 60 plus 3. Now, what is this

going to be equal to? Well, 87 times 60

plus 3, that’s going to be the same thing

as– and let me actually copy and paste this. So this is going to be the

same thing as 87 times 60 plus 87 times 3. You could say that we’ve

just distributed the 87. We’re multiplying

87 times 60 plus 3. That’s 87 times 60

plus 87 times 3. I could put parentheses here to

make it a little bit clearer. Well, fair enough. But then how do you

calculate what this is? Well, now we can

rewrite 87 as 80 plus 7. So let’s rewrite that. So this is the same thing. Actually, let me

write it this way. I can swap them around. So this is the same

thing as 60 times 87. But I’ll write that

as 60 times 80 plus 7. We could do it like this. 80 plus 7 plus 3 times

80 plus 7, or 3 times 87. Let me just copy

and paste that, so I don’t have to keep

switching colors. Plus 3 times 80 plus 7. So copy and then

let me paste it. And then you have

it just like that. So all I did, just to

be clear– all of what you see right over here,

87 times 60, well, that’s the same thing as

60 times 87, which is the same thing as

60 times 80 plus 7. All that you see

here, 87 times 3, that’s the same thing

as 3 times 87, which is the same thing as

3 times 80 plus 7. That’s just that over here. But look, we can

distribute again. We can distribute the

60 times 80 plus 7. So this is going to be 60– I’m

going to do that same color. Color changing is hard. This is 60 times 80 plus

60 times 7 plus 3 times 80 plus 3 times 7

right over here. So notice what we

really did is we thought about what each

of these digits represent. 8 represents 80. 7 represents 7. 6 represents 60, because

it’s in the tens place. The 8 was in the

tens place, as well. This 3 is in the ones

place, so it’s just 3. And we just multiplied

them all together. We multiplied the

80 times the 60. We multiplied the

80 times the 3. We multiplied the 7 times

the 60 right over here. We multiplied the 7 times the 3. And then we add them

all up together. And this will actually

give us our product. So for example, this right

over here, 6 times 8 is 48. But this isn’t six 8’s. This is 60 80’s. So this is going to be 4,800. We’ve got two 0’s

right over here, so 48 followed by the two 0’s. This right over here,

60 times 7, is 420. 6 times 7 is 42. But it’s going to be 10 times

as much, because this is a 60. And then 3 times 80–

well, same logic. 3 times 8 is 24. So this is going to be 240. And then, finally,

3 times 7 is 21. And then to get the product,

we can add these two together. And you might be

saying, hey, Sal, I know faster ways

of doing this. But the whole reason

I’m doing this is to show you that that fast

way you knew how to do it, it’s not some magical formula

or some magical process you’re doing. It just comes out of really

the distributive property and, hopefully, a little

bit of common sense. So what is this

going to be equal to? Well, we could add them all up. 4,800 plus 420 plus 240 plus 21. Well, you’re going

to get a 1 here. Let’s see. 20 plus 40 plus 20 is 80. Let’s see. 800 plus 400 is 1,200

plus 200 more is 1,400. And so you get 5,481. It’s equal to 5,481. And you might say, gee,

this was a bit of a pain to have to do the distributive

property over and over again. Is there a simpler way

to maybe visualize this? And there is. You could actually

write this as a grid. So we could say we’re

multiplying 87 times 63. We could write it like this. We could say it’s 80

plus 7 times 60 plus 3. And then you can set

up a grid like this. So let me set up

a little box here. It’s 2 digits by 2 digits. So it’s going to be a 2 by 2

grid, 2 rows and 2 columns. And then you just

have to calculate. Well, what’s 60 times 80? Well, we already

calculated that. That’s 4,800. What is 60 times 7? Well, that’s going to be 420. What is 3 times 80? We already calculated that. That is 240. And I want to do that

same color– 240. And finally, what is 3 times 7? 21. You add them all together. You get 5,481. And I encourage you to now just

do this same multiplication problem, the same

87 times 63, the way that you might have

traditionally learned it. And look at the different steps

and why they are making sense and why, at the end

of the day, you really are doing the same thing that

we just did in this video. You’re just doing it

in a different way. And the whole point of

this whole exercise, this whole video, is so

you’re not just blindly doing some type of steps to

find the product of two numbers. But you can actually

understand why those steps work and how those numbers

relate to each other.