Multiplication 2: The Multiplication Tables

Introduction to the multiplication tables from 2-9.

At this point I think you know a little bit about what multiplication is.

Or "multi"-plication.

What we're going to do in this video is to give you just a ton of more practice,

and start you on your memorization of the multiplication tables.

And if you watch enough Khan Academy videos,

and hopefully you will in the future,

you'll realize that I'm normally not a big fan of memorization.

But the one thing about multiplication

is if you memorize your multiplication tables that we'll start to do in this video,

it'll pay huge benefits the rest of your life.

So I promise you, do it now, you'll never forget it,

and the rest of your life everything will be--

well, I don't want to make false promises to you,

but they'll be better than if you didn't memorize your multiplication tables.

So what are the multiplication tables?

Well that's all of the different numbers

times each other.

So let's actually do a little bit of review.

So if I say, what is two times one?

That is equal to two plus itself one time.

So this is equal to just two.

That's two plus itself one time.

I don't have to say plus anything

because there's only one two there.

I could also write this as one plus itself two times.

So that's also one plus one.

Well that also equals two.

Fair enough.

So two times one is two.

And if you watched the last video, what's two times zero?

Well that's zero.

So you don't have to memorize your zero multiplication tables

because everything times zero is zero, or zero times anything is zero.

So let's see.

What's two times two?

Two times two.

Well, this is equal to--

we're going to add two to itself two times.

So that's two plus two.

And there's only a way to do that.

I could say take this two and add it to itself two times,

but it's the same thing.

And what's two plus two?

That's equal to four.

What's two times three?

Two times three is equal to two plus two plus two.

It can also be equal to three plus three.

We learned in a previous video

this statement can be written either of these ways.

And in either case, what's it equal to?

Well three plus three

is the same thing as two plus two plus two,

and that's equal to six.

All right.

Now what is two times four?

Two times four.

Well that's equal to two plus two plus two plus two.

And notice, it's exactly what two times three was.

Two times three was that.

I have that here, but now I'm just adding another two to it.

So if we're too lazy to sit here and add two plus two is four.

Four plus two is six.

Instead of doing that, we could say,

hey look, we already know that this thing over here, this was six.

We figured it out in the previous line right there.

We figured out this is six, so we could just say, oh, two times four

is going to be two more than that, which is equal to eight.

And you should hopefully see that pattern.

As we go from two times one, to two times two,

to two times three, what's happening?

How much are we going up by?

From two to four we're going plus two.

From four to six we're going plus two.

And then from six to eight we're going plus two.

So you could figure out what two times five is,

even without doing the addition.

Two times five is equal to two plus two plus two plus two plus two.

It could also be written as five plus five.

Two times four could've been written as four plus four as well.

And what's that equal to?

We could add all of these up or we could add these two up.

Or we could just say it's going to be two more than two times four.

So it's going to be ten.

I'll finish the two times tables.

And I think you see all of the patterns that emerge from it.

So two times six.

That's going to be two plus itself six times.

Let's see. One, two, three, four, five, six,

which should also be equal to six plus itself two times.

This could be interpreted either way.

And that's going to be equal to twelve.

Once again, two more than two times five

because we're adding two to itself one more time.

So it's going to be two more.

Let's keep going.

So two times seven.

Two times seven is equal to--

well, I could write two plus two plus two plus two--

this is getting tiring-- plus two plus two.

Is that seven?

One, two, three, four, five, six, seven.

And that's the same thing as seven plus seven,

which you may or may not know is equal to fourteen.

You could just say hey, that's going to be two more than twelve.

So twelve plus one plus two is-- twelve plus one is thirteen.

Twelve plus two is fourteen.

All right, let's just keep going.

Two times eight.

I could do all of this business here where I add the twos

or I could say, look, it's just going to be two more than two times seven.

So I could say it's going to be fourteen plus two.

I'm just adding two to that one.

So I could say it's sixteen.

Or I could also say that's eight plus eight.

That's also sixteen.

I could have done all the twos out,

but if you like you could do that for your own benefit and learning.

We're almost-- well, we could go forever

because there is no largest number.

I can keep going.

Two times nine times ten times one hundred times one thousand times one million.

But I'm going to stop at twelve

because that tends to be what people need to memorize.

But if you really want to be a "mathelete"

you want to go up to twenty.

But let's go to two times nine.

That's going to be two more than two times eight.

It's going to be eighteen.

Or that's nine plus nine.

Also eighteen.

What's two times ten?

And ten times tables are interesting.

And we're going to see a pattern there in a second

when we try to complete an entire times tables.

So two times ten?

Two more than two times nine.

It's twenty.

Or we could also say that's ten plus ten.

Ten plus itself two times.

Now what's interesting about this?

This looks just like a two with a zero added.

And you're going to see that with anything times ten,

you just put a zero on the right.

And you can think about why that is.

You can view this as two tens is twenty.

That's what twenty is.

We're almost done.

Let's do two times eleven.

Two times eleven is going to be two more than this right here.

It's going to be twenty-two.

Another interesting pattern.

I have the number repeated twice-- a two and a two.

Interesting.

Something to watch out for

as we look at other multiplication tables.

And then finally--

and it's not finally, we could keep going--

Two times-- that's too dark of a color.

Two times twelve.

Two times twelve is going to be two more than two times eleven.

That's twenty-four.

We could have also written that as twelve plus twelve.

Or we could've said two plus two plus two plus two

plus two... twelve times.

It all gets you to twenty-four.

So that's the two times tables

and I think you see the pattern.

Every time you multiply it by one higher number

you just add two to that number.

So now that we see that pattern,

let's see if we can complete a multiplication table.

So what I want to do, I'm going to write all the numbers.

Let's see.

I hope I have space for this.

One, two, three, four, five, six, seven, eight, nine.

Actually, I'll just do it till nine.

I'll just keep going.

Nine.

Actually I won't have space to do that

because I want you to see the entire table.

So I'm just going up till nine here,

but I encourage you after this video to complete it on your own.

Maybe if we have time I'll complete it here as well.

So these are the first numbers that I'm going to multiply.

And I'm going to multiply it times one, two, three, four,

five, six, seven, eight, and nine.

What I'm going to do is, I'm going to--

So first of all--

Actually I should have written this one under--

well, what's one times one?

So this is the way I'm going to view it.

Whatever is one times one I'm going to write here.

Well that's one.

What's one times two?

That's two.

What's one times three?

That's three.

One times anything is that number,

so I can just write four, five, six, seven, eight, nine.

One times nine is nine.

Fair enough.

Now let's do the two times tables.

I'll do that in a blue.

Actually, let me do one in that color

and now in maybe a darker blue I'll do the two times tables.

What's two times one?

That's two.

It's the same thing as one times two.

Notice, these two numbers are the same thing.

What's two times two?

That's four.

Two times three is six.

We just did this.

Every time you increment or you multiply by a higher number,

you just add by two.

Two times four is eight.

Same thing as four times two.

Two times five is ten.

Two times six is twelve.

I'm just adding two every time.

Up here I added one from every step, here I'm adding two.

Two times seven, fourteen.

Two times eight, sixteen.

Two times nine, eighteen.

All right, let's do our three times tables.

I'll do it in yellow.

Yellow.

Three times one is three.

Notice, three times one is three.

One times three is three.

These are the same values.

Three times two is the same thing as two times three.

Three times two should be the same thing as two times three.

So it's six.

And that makes sense.

Three plus three is six or two plus two plus two is six.

So every time here we're going to increase by three.

You see the pattern.

Three times three is nine.

Three plus three plus three.

So we went from three to six to nine.

So three times four is going to be twelve.

I'm just adding three every time.

Twelve plus three is fifteen.

Fifteen plus three is eighteen.

Eighteen plus three is twenty-one.

Twenty-one plus three is twenty-four.

Twenty-four plus three is twenty-seven.

So three times nine is twenty-seven.

Three times eight is twenty-four.

So if you were to say eight plus eight plus eight, it would be twenty-four.

Let's see if I can--

So now I'm going to speed it up a little bit,

now that we see the pattern.

And you should do this on your own

and you really should memorize everything we're doing.

You should actually go all the way up to twelve in both directions.

So let's see.

Four times one is four.

I'm just going to go up by increments of four.

So four plus four is eight.

Eight plus four is twelve.

Twelve plus four is sixteen.

Sixteen plus four is twenty.

Twenty plus four is twenty-four.

Four times six is twenty-four.

Four times seven, twenty-eight.

I'm just going up by four.

Thirty-two and thirty-six.

All right, five times one.

Five times one is going to be five.

Actually, we know that anything that-- well, I want us to keep changing colors,

so I'll just do it in rows like this.

Five times one is five.

Five times two is ten.

Five times three is fifteen.

I'm just going to increase by five.

Five times tables are very fun as well

because every number you're going to add-- if we multiply five times--

well, we'll learn about even and odd in the future.

But every other number in its times tables is going to end with a five,

and then every other one's going to end with a zero.

Because if you add five to fifteen you get twenty.

You get twenty-five, thirty, thirty-five, forty, forty-five.

Fair enough.

Six times tables, let me do it in green.

Six times one is six.

That's easy.

You add six to that, you get twelve.

You add six to that, you get eighteen.

You add six to that, you get twenty-four.

You add six to that, you get thirty.

Then you go six more, thirty-six, forty-two, forty-eight.

Forty-eight plus six is fifty-four.

So six times nine is fifty-four.

All right, we're almost there.

Seven times one, that's seven.

Seven times one is seven.

Seven times two is fourteen.

Seven times three, twenty-one.

Seven times four, twenty-eight.

Seven times five, what's twenty-eight plus seven?

Let's see, if you add two you get to thirty.

Then you add five, it's thirty-five.

Seven times six, forty-two.

Seven times seven, forty-nine.

Seven times eight--

seven times is going to be seven plus this, so it's fifty-six.

I always used to get confused between seven times eight being fifty-six

and six times nine being fifty-four.

So now that I pointed out to you that I always got confused between those two,

it's your job not to be confused by those two.

Seven times eight you could say has the six in it.

Six times nine doesn't have the six in it.

That's the way I think of it.

Anyway, seven times nine.

We're going to add another seven here.

It's going to be sixty-three.

I'll do it in the same color.

All right, we're at our eight times tables.

Eight times one is eight.

Eight times two is sixteen.

Twenty-four.

Eight times three is twenty-four.

And if we go to three times eight we should also see the twenty-four.

Yep, it's there.

These values are the same.

So we're actually doing things twice.

We're doing it when you do eight times three

and we're doing it when we did three times eight.

Let's see, eight times four, you're going to add eight to it-- thirty-two.

Forty.

Add another eight, forty-eight.

Notice, eight times six, forty-eight.

Six times eight, forty-eight.

All right, eight times seven.

Well, we already pointed that one out, that was fifty-six.

Eight times eight, sixty-four.

Eight times nine, add eight to this, is seventy-two.

Now we're at the nine times tables.

I'm running out of colors.

Maybe I'll reuse a color or two.

I'll use the blue again.

Nine times one is nine.

Nine times two, eighteen nine times three-- we actually know all of these.

We could look it up in the rest of the table

because nine times three is the same thing as three times nine.

It's twenty-seven.

Add nine to that.

Twenty-seven plus nine is thirty-six.

Thirty-six plus nine is forty-five.

Notice, every time you add nine, you go almost up by ten,

but one less than that.

So up by ten would be forty-six, and then one less than that is forty-five.

But anyway, notice, the ones--

well, I'll talk more about it in the future.

But we go from a nine, eight, seven, six, five on this digit,

on the second digit.

And on this digit here you go one, two, three, four.

So it's an interesting pattern.

Another interesting pattern is the digits will add up to nine.

Three plus six is nine, two plus seven is nine.

We'll talk more about that in the future

and maybe prove that to you.

Nine times six, fifty-four.

That was this one as well.

Nine times seven, sixty-three.

Nine times eight, seventy-two.

Nine times nine is eighty-one.

I don't know if you can see that.

Eighty-one.

There you go.

Now, I could keep going.

Actually, I should keep going.

Well, I realize this video is already pretty long.

I want you to memorize this right now

because this is going to get you pretty far.

In the next video I'm going to do the times tables past nine.

See you soon!