Multiplication 4: 2-digit times 1-digit number

Multiplying a 2-digit times a 1-digit number

If you've practiced

and hopefully, memorized your multiplication tables,

you'll now find out that you're prepared to do most any multiplication problem.

You just have to understand,

I guess for lack of a better word,

the system of how to do it.

But we're not just going to teach you the system,

we're going to show you why it works.

So let's start with a multiplication problem

that you probably think that you don't know how to do.

Let's do sixteen times nine.

Sixteen times nine.

And you immediately might say,

Sal, I haven't memorized my sixteen times tables,

there's no way I'm going to be able to do that problem.

And my answer to you is, you can absolutely do it

because we can break it down into problems

that you do know the answer to.

The way you do this one

is first multiply nine times the ones place here.

So you multiply nine times six.

And I think you know what nine times six is.

I'll write it down here.

So nine times six is fifty-four.

You know that from your multiplication tables.

And so what you do is you write fifty-four,

but you only write the four down here in the ones place,

and you carry the five.

That's exactly what you're doing.

We also use word carry when you add

and you kind of have an extra five to deal with,

but let's just call that carrying.

For lack of better words.

Now, we then multiply nine times one.

Nine times one.

Well, that's straightforward.

Nine times one is equal to nine.

Anything times one is equal to itself.

But we have this five sitting up here, so nine times one,

we have to add that five.

So we have to add that plus five.

And so what do we get?

So nine times one plus five

is nine plus five, which is fourteen.

Let me write it right there.

Fourteen.

And there you have it.

Sixteen times nine is one hundred forty-four.

And if you remembered your times tables up to twelve

you also realize that's twelve times twelve.

But just knowing only these two pieces of information,

we were able to solve a harder problem.

Now you might say, Okay Sal, that's a neat little trick you just did,

but how does it work?

And you should always ask that.

You shouldn't just take it--

you shouldn't just memorize the system and assume that it works.

And to explain that I'm just going to rewrite these numbers.

I can rewrite sixteen as ten-- let me do it right here.

Ten plus six.

This is sixteen.

And I can rewrite nine,

well, I'm just going to write nine as nine. Right there.

And now let me do the multiplication problem.

I'll put a little multiplication sign out there.

So first I want to multiply the nine times the six.

And you might say, hey Sal, why did you divide it this way?

Well, I wanted to separate the ones place from the tens place.

This one here that's in the second column,

it isn't a one, it's a ten.

It's a ten plus a six,

so that's why I wanted to write it that way.

But anyway, let's do this problem.

So we do it the exact same way we did it before.

We say nine times six--

let me write that down.

Nine times six is equal to fifty-four.

But instead of writing fifty-four,

I'm going to write that's equal to fifty plus four.

Nine times six is equal to fifty plus four.

Well, this is my ones column right here.

Let me make a little dotted line.

This is my ones column.

So I can only put a four down here,

but I need something to do with the fifty.

I have to put it some place

and just the convention or at least the way that I've learned it,

you put the fifty up here.

I could've put the fifty down here too,

as long as we remember that this fifty now goes into this column.

So you can stick the fifty over here.

That's what we did in the first video.

I just wrote a five.

In that first video, I just put a five here

because that was in the tens place.

A five here really means fifty.

A one here really means ten.

But now I'm writing it out,

so you can see that they really mean fifty and ten.

And then you say, what's nine times ten?

Nine times ten.

Well, you've memorized this.

And anything times ten is just that anything with a zero.

So it's ninety.

So it's nine times ten is ninety,

and then we want to add fifty to it.

So we want to add fifty to it.

What's ninety plus fifty?

It is one hundred forty.

So nine times ten is ninety,

plus fifty is one hundred forty.

And we could rewrite one hundred forty

as one hundred plus forty just to be consistent.

So what we'll do is we'll put the forty down here,

and then we carry the one hundred,

but the one hundred really doesn't go anywhere.

I mean we could write it up here.

We could put it--

Well, we could write the one hundred over here.

We could put it over here.

There's a bunch of different places we could put the one hundred,

but the important thing is that it sticks out into this next column

that I haven't drawn yet.

So then you'll put one hundred here.

So our answer is one hundred plus forty plus four,

which is one hundred forty-four.

Hopefully you found that reasonably explanatory.

Let's try a couple of other problems,

because I think it's all about seeing examples.

So let's try fifty-five times eight.

Fifty-five times eight.

Same exercise.

First, you start with the eight.

Eight times five.

Let me write it down.

Eight times five we know is forty.

So eight times five, you write the zero down here.

It's zero plus forty.

And then you say eight times five again.

That's forty.

But then you add the four to here, so you get forty-four.

So it's four hundred forty.

And you can try to do it the same way I did that last one

where I broke it out into fifty plus five and then an eight.

But I think with more examples,

you'll see this will all become a bit of second nature to you.

So let me do another one in this--

let me do it in this salmon. This light red, salmon color.

So let's say I had seventy-eight times-- let's do it times seven.

Eight times seven.

Eight times seven is fifty-six.

Let me write it-- this is a different problem now.

So eight times seven is equal to fifty-six.

We write the six down here, put the five up there.

Seven times seven is forty-nine.

Seven times seven is equal to forty-nine.

But we have to add this five up here, so you add this five.

What's forty-nine plus five?

Well, that's fifty-four.

So seven times seven is forty-nine.

Plus five is fifty-four.

Five hundred forty-six.

Ten minutes ago,

you probably never thought that you could figure out the seventy-eight multiplication tables,

but you see it's a pretty straightforward process.

Let's do a bunch more.

I'm just going to do these until we all just collapse.

Collapse from multiplication fatigue.

Let's do an eighty-nine times-- let's do it times three.

What's three times nine?

Three times nine is equal to twenty-seven.

Put the seven in the ones place.

Put the two up here in the tens place,

because it's twenty plus seven.

Two tens is twenty.

Plus seven is twenty-seven.

And then three times eight is twenty-four.

Three times eight is equal to twenty-four.

But I have this two sitting up here

so I'm going to have to add a two.

So I get twenty-six.

Three times eight is twenty-four.

Plus two is twenty-six.

Two hundred sixty-seven.

Now I'm going to do another one,

but I'm going to up the stakes a little bit.

Just when you thought you were getting comfortable with this,

I'm going to make you uncomfortable!

Let's do two hundred thirty-nine times six.

I thought this was a video about two-digit multiplication times one-digit.

Well, it is, but I just want to show you

that you can really do any number of digits times this one digit,

and it's really the same process.

You could probably guess how we're going to do it.

So what's six times nine?

Let me write it here.

Six times nine.

We saw this show before.

This is fifty-four.

So we put the four down here, we put the five in the tens place

because the fifty in fifty-four is really five tens.

Fair enough.

Now we're going to do six times three.

So six times three,

that's equal to eighteen.

We still have that five hanging out there,

so we have to add that five up there and we get--

what's eighteen plus five?

So six times three is eighteen, plus five is twenty-three.

Just to be clear,

we didn't multiply six times three and add five.

We actually,

if you looked at where we are in our place on the problem,

this is actually a thirty.

I just happened to do a three here.

But this is six times thirty plus fifty.

Because thirty-nine is three tens or thirty.

So this number, actually, even though we said six times three is eighteen.

Plus five is twenty-three.

This number is really two hundred thirty.

So we put the three in the tens place.

Actually, let me do it in a different color

than what I did up here.

This is equal to twenty-three.

We can put the three in the tens place

and then put this two up here.

Now we're almost done, one multiplication left.

This is the six times the two.

That's an easy one.

That's twelve.

But I have this other two hanging out up here,

so I have to add this other two.

So plus two.

And what is that equal to?

That is equal to

twelve plus two is equal to fourteen.

So I write the four.

So six times two is twelve.

Plus two is fourteen.

I write the four down here.

If there was any more digits I would write the one up there,

but there aren't any more digits.

So I write the one over here.

So two hundred thirty-nine times six is one thousand four hundred thirty-four.

Let's do another one.

I need to get some space cleaned out.

And hey, while we're escalating the situation,

let's go to four-digits.

Let's do seven thousand three hundred sixty-two times--

let's do a hard one.

Times nine.

So what's nine times two?

And I won't do this side math over here.

I think you're getting the pattern.

What's nine times two?

Nine times two is eighteen.

Eighteen.

Then we do nine times six.

Nine times six is fifty-four.

And fifty-four plus one is fifty-five.

Fifty-five.

What's nine times three?

Nine times three is twenty-seven-- if we have that memorized.

And then twenty-seven plus five is thirty-two.

Let me switch colors.

Thirty-two.

And then you have nine times seven.

That's sixty-three, but we have this three hanging out there.

So that's nine times seven is sixty-three,

plus three is sixty-six.

You write the six here,

and then you have no where to put the sixty in the sixty-six,

so you write that down here as well.

And so seven thousand three hundred sixty-two times nine

is sixty-six thousand two hundred fifty-eight.

Hopefully you found that useful.