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Let's start with a warm-up problem to avoid getting

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any mental cramps as we learn new things.

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So this is a problem that hopefully, if you understood

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what we did in the last video, you can kind of understand what

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we're about to do right now.

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And I'm going to escalate it even more.

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In the last video I think we finished what a

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four-digit number times a one-digit number.

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Let's up the stakes to a five-digit number.

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Let's do 64,329 times-- let me think of a nice number.

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Times 4.

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I'm going to show you right now that we're going to do the

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exact same process that we did in the last video.

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We just have to do it a little bit longer than we did before.

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So we just start off saying, OK, what's 4 times 9?

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4 times 9 is equal to 36.

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Right?

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18 times 2.

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Yep, 36.

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So we write the 6 down here, carry the 3 up there.

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Just put the 3 up there, then you got 4 times 2.

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And they're going to have to add the 3.

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So let me just write that there.

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Plus 3 is equal to-- you do the multiplication first.

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You can even think of it as order of operations, but you

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just should know that you do the multiplication first.

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So 4 times 2 is 8.

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Plus 3 is equal to 11.

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Put this 1 down here and put the one 10 and 11 up there.

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Then you got 4 times 3.

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You got that one up there, so you're going to have to add

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that plus 1 is equal to-- that's going to equal 12.

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Plus 1, which is equal to 13.

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So it's 13.

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Then you have 4 times 4.

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You have this little one hanging out here from the

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previous multiplications, so you're going to

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to have to add that.

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And that's equal to 16 plus 1.

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It's equal to 17.

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Stick the 7 down here, put the 1 up there.

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We're almost done.

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And then we have 4 times 6.

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Plus 1.

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What is that?

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4 times 6 is 24.

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Plus 1 is 25.

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Put the 5 down here.

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There's no where to put the 2.

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There's no more multiplications to do, so we just put

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the 2 down there.

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So 64,329 is 257,316.

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And in case you're wondering, these commas don't mean much.

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They just help me read the number.

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So I put it after every 3 digits, so I know that for

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example, that everything after this-- so s is 7,000.

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If I had another comma here, this is millions.

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So it just helps me read the problem a bit.

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So if you got that you're now ready to escalate to a slightly

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more complicated situation.

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Although the first way that we're going to do it it's

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actually not going to look any more complicated.

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It's just going to involve one more step.

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So everything we've done so far are a bunch of digits

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times a one-digit number.

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Now let's do a bunch of digits times a two-digit number.

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So let's say we want to multiply 36 times-- instead of

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putting a one-digit number here I'm going to put a

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two-digit number.

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So times 23.

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So you start off doing this problem exactly the way you

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would have done it if there was just a 3 down here.

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You can kind of ignore the 2 for a little bit.

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So 3 times 6 is equal to 18.

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So you just put the 8 here, put the 10 there, or the 1 there

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because it's 10 plus 8.

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3 times 3 is 9.

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Plus 1, so 3 times 3 plus 1 is equal to-- that's 9

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plus 1 is equal to 10.

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So you put the 10 there.

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There's nothing left.

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You put the 0 there.

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There's nothing left to put the 1, so you put the 10 there.

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So you essentially have solved the problem that 36-- let me

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do this is another color.

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That 36 times 3 is equal to 108.

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That's what we've solved so far, but we have this

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20 sitting out here.

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We have this 20.

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We have to figure out what 20 times 360 is.

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Or sorry, what 20 times 36 is.

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This 2 is really a 20.

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And to make it all work out like that, what we do is

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we throw a 0 down here.

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We throw a 0 right there.

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In a second I'm going to explain why

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exactly we did that.

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So let's just do the same process as we did

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before with the 3.

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Now we do it with a 2, but we start filling up here

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and move to the left.

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So 2 times 6.

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That's easy.

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That's 12.

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So 2 times 6 is 12.

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We put the 1 up here and we have to be very careful because

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we had this 1 from our previous problem, which doesn't

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apply anymore.

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So we could erase it or that 1 we could get rid of.

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If you have an eraser get rid of it, or you can just keep

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track in your head that the 1 you're about to write

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is a different 1.

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So what were we doing?

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We wrote 2 times 6 is 12.

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Put the 2 here.

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Put the 1 up here.

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And I got rid of the previous 1 because that would've

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just messed me up.

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Now I have 2 times 3.

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2 times 3 is equal to 6.

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But then I have this plus 1 up here, so I have to add plus 1.

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So I get 7.

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So that is equal to 7.

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2 times 3 plus 1 is equal to 7.

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So this 720 we just solved, that's literally-- let

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me write that down.

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What is that?

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That is 36 times 20.

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36 times 20 is equal to 720.

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And hopefully that should explain why we had to

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throw this 0 here.

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If we didn't throw that 0 here we would have just a 2--

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we would just have a 72 here, instead of 720.

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And 72 is 36 times 2.

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But this isn't a 2.

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This is a 2 in the 10's place.

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This is a 20.

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So we have to multiply 36 times 20, and that's

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why we got 720 there.

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So 36 times 23.

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Let's write it this way.

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Let me get some space up here.

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So we could write 30-- well, actually, let me just finish

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the problem and then I'll explain to you why it worked.

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So now to finish it up we just add 108 to 720.

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So 8 plus 0 is 8.

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0 plus 2 is 2.

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1 plus 7 is 8.

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So 36 times 23 is 828.

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Now you're saying Sal, why did that work?

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why were we able to figure out separately 36 times 3 is equal

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to 108, and then 36 times 20 is equal to 720, and then

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add them up like that?

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Because we could have rewritten the problem like this.

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We could have rewritten the problem as 36-- the

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original problem was this.

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We could have rewritten this as 36 times 20 plus 3.

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And this, and I don't know if you've learned the distributive

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property yet, but this is just the distributive property.

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This is just the same thing as 36 times 20 plus 36 times 3.

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If that confuses you, then you don't have to worry about it.

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But if it doesn't, then this is good.

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It's actually teaching you something.

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36 times 20 we saw was 720.

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We learned that 36 times 3 was 108.

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And when you added them together we got what?

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828?

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Is that what we got?

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We got 828.

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And you could expand it even more like we did

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in the previous video.

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You could write this out as 30 plus 6 times 20 plus 3.

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Actually, let me just do it that way because I think

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that could help you out a little bit.

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If it confuses you, ignore it.

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If it doesn't, that's good.

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So we could do it 3 times 6.

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3 times 6 is 18.

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18 is just 10 plus 8.

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So it's 8, then we put a 10 up here.

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And ignore all this up here.

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3 times 30.

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3 times 30 is 90.

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90 plus 10 is 100.

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So 100 is zero 10's plus 100.

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I don't know if this confuses you or not.

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If it does, ignore it.

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If it doesn't, well I don't want to complicate the issue.

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And now we can multiply 20.

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We can ignore this thing that we had before.

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20 times 6 is 120.

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So that's 20 plus 100.

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So I'll put that 100 up here.

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20 times 30 is 2 times 3 and you have two 0's there.

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And I think I'm maybe jumping the gun a little bit, assuming

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a little bit too much of what you may or may not know.

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But 20 times 30 is going to be 600.

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and you add another hundred there, that's 700.

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And then you add them all up.

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You get 800.

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100 plus 700.

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Plus 20 plus 8, which is equal to 828.

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My point here is to show you why that system we did worked.

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Why we added a 0 here to begin with.

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But if it confuses you, don't worry about that right now.

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Learn how to do it and then maybe re-watch this video.

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Let's just do a bunch of more examples because I think the

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examples are what really, hopefully, explain

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the situation.

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So let's do 77.

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Let's do a fun one.

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77 times 77.

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7 times 7 is 49.

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Put the 1 up here.

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00:10:00,990 --> 00:10:04,100


225
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7 times 7, well, that's 49.

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Plus 4 is 53.

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There's no where to put the 5, so we put it down here.

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7 times 7 is 49.

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Plus 4 is 53.

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Stick a 0 here.

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Now we're going to do this 7.

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So stick a 0 here.

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Let's get rid of this right there because that'll

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just mess us up.

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7 times 7 is 49.

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Stick a 9 there.

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Put a 4 there.

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7 times 7 is 49.

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Plus 4, which is 53.

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So notice, when we multiplied 7 times 77 we got 539.

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When we multiplied 70 times 77 we got 5,390.

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And it makes sense.

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They just differ by a 0.

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By a factor of 10.

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And now we can just add them up, and what do we get?

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9 plus 0 is 9.

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3 plus 9 is 12.

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Carry the 1.

250
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1 plus 5 is 6.

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6 plus 3 is 9.

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Then we have this 5.

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So it's 5,929.