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.

1. đ

• ### Polymath

Did Sal literally make this video a few minutes ago?

3rd comment

• ### altmrrelaxed

Is this the first step in understanding how to multiply two-digit numbers inÂ  your head? I'm a little slow, but I could do this in my head just knowing the multiplication tables and how to re-group the digits, then multiply, then add the results.

• ### Lucas John

Hey I hate all the homework I get solve that

• ### superdupe

Sal I wish you could give me a high five right now

• ### Nathan D

Nice! It's always fun to look at things a little different.

• ### Ziko Humlesen

Hi Sal, can you please make a video about directional derivatives.
It would make me very glad đ

• ### jefivefive

Colorful!!! đ
Thanks for Khan Academy!!!
I always use it!!!

• ### Billie Anne Usita

to did she get the 7

C.O.O.L
CONSTAPATED
OVERPOOPED
OLD
= COOL

• ### Laila Harrington

thank you khan academy

• ### Martha Juarez

Makes me more understanding

• ### 1 bro 1 gamer

you are smart.

Very Good!!!

• ### lily kushner

thanks! this really helped me!

• ### BohZoh

4th grade? my grade 8 friends struggle on this type of stuff

• ### Godwin chidiebere Okebaram

37×28 can't work out can someone help please?

• ### ThatCool_Kid - Fortnite

What program did you use to write the letters out? By the way this helped me a lot

63×7+70×63

• ### Oofrr Donk

Iâm trying to do it like 7x+7y

THANKS KHAN

• ### Jordan Delgado

you are good at math

• ### Gravy Tray

That helped me a lot thanks

• ### Priyanka Nag

Thnx a lot its useful to me

• ### america

nooooooooooooo

• ### Michelle Lee

Can someone help me 7 x 256 am sorry am dum

thanks

• ### KRISHNA KALAMKAR

Too long process but good

• ### VAN LASCOLA

LOVE THIS STUFF!

• ### Phil Neff

im still confused…
and im in 5th…
I wasnt taught this in class today

• ### Josh

I donât understand new math this makes no sense.

• ### Marissa Swift

Am I he only kid watching this cuz I didnât understand my homework

Me tooooo

• ### Gacha Gamer

Anybody who dislikes khan academy doesn't like learning.

• ### Kelly Ursini

You should draw the sides of the rectangle grid to more closely match the numbers. For instance, since 80 plus 7 is along the top of the grid, it makes more sense to have the line representing 80 to be longer than the line representing 7. This is an "area model" using length times width. đ Then do the same thing with the numbers going along the left side. That is the way that helps students relate the multiplication to geometry as "area."

• ### Rodolfo Ramirez

Way to confusing
đ
1/10

• ### BlueBerryAppple 12

Khan Acedemy literally has saved my life so many times.

• ### Lopamudra Kar

Sir, please make videos on Vedic maths (especially DIVISION)!!

• ### Madeline Rios

Thank you so much this helped me with my homework so much

• ### Midnight Sparkle

HOW IS THIS 4TH GRADE? Iâm in grade 6 and I donât get it and weâve never learned it before.

• ### SavageSmoothies

What program is he using

• ### Abel Alemu

I swear he always saves me from a test.

Thx!

• ### Ted Latif Gikas

what program did they use to draw all of that because i like it

• ### manjari devi

Thanks very much bro

• ### YEET !!!

Thank you khan academy for this video!!
âĄÂșâĄÂșâĄ

• ### Josefina Salinas

I don't understand my homework too!