Multiplication 6: Multiple Digit Numbers

Working our way up to multiplying multiple-digit numbers with each other

We now have the general tools

to really tackle any multiplication problems.

So in this video I'm just going to do a ton of examples.

So let's start off with-- and I'll start in yellow.

Let's start off with thirty-two times eighteen.

Say eight times two is sixteen.

Well, I'll do it in our head this time

because you don't always have all this space to work with.

So eight times two is sixteen.

Put the one up there.

Eight times three is twenty-four.

Twenty-four plus one is twenty-five.

So eight times thirty-two was two hundred fifty-six.

Now we're going to have to multiply this one,

which is really a ten, times thirty-two.

I'll underline it with the orange.

One times two-- oh, we have to be very careful here.

One times two is two.

So you might say hey, let me stick a two down there.

Remember, this isn't a one.

This is a ten, so we have to stick a zero there

to remember that.

So ten times two is twenty.

Or you say one times two is two,

but you're putting it in the tens place, so you still get twenty.

So ten times two is twenty.

It works out.

Then one times three.

And we have to be very careful.

Let's get rid of what we had from before.

One times three is three.

There's nothing to add here, so you just get a three.

And so you get ten times thirty-two is three hundred twenty.

This one right here, that's a ten.

Ten plus eight is eighteen.

So now we just add up the two numbers.

You add them up.

Six plus zero is six.

Five plus two is seven.

Two plus three is five.

Let's keep going.

Let's do ninety-nine times eighty-eight.

That's going to give us a big number!

Eight times nine is seventy-two.

Stick the seven up there.

And then you have eight times nine again.

Eight times nine is seventy-two, but now you have the seven up here.

So seventy-two plus seven is seventy-nine.

Fair enough.

Now we're done with this.

Let's just delete it

just so that we don't get confused in our next step.

In our next step, we're going to multiply this eight now times ninety-nine.

But this eight is an eighty.

So let's stick a zero down there.

Eight times nine is seventy-two.

Stick a seven up there.

Then eight times nine is seventy-two.

Plus seven is seventy-nine.

Two plus zero is two.

Let me switch colors.

Nine plus two is eleven.

Carry the one.

One plus seven is eight.

Eight plus nine is seventeen.

Carry the one.

One plus seven is eight.

Eight thousand seven hundred twelve.

Let's keep going.

Can't do enough of these.

All right, fifty-three times seventy-eight.

I think you're getting the hang of it now.

Let's multiply eight times fifty-three first.

So eight times three is twenty-four.

Stick the two up there.

Eight times five is forty.

Forty plus two is forty-two.

Now we're going to have to deal with that seven.

That seven right there, which is really a seventy.

So we got to remember to put the zero there.

Seven times three, and let's get rid of this.

Don't want to get confused.

Seven times three is twenty-one.

Put the one there and put the two up here.

Seven times five is thirty-five.

Plus two is thirty-seven.

Now we're ready to add.

Four plus zero is four.

Two plus one is three.

Four plus seven is eleven.

Carry the one.

One plus three is four.

Four thousand one hundred thirty-four.

Let's up the stakes a little bit.

So let's say I had seven hundred ninety-six times fifty-eight.

Let's mix it up well.

All right, so first we're just going to multiply eight times seven hundred ninety-six.

And notice, I've thrown in an extra digit up here.

So eight times six is forty-eight.

Put the four up there.

Eight times nine is seventy-two.

Plus four is seventy-six.

And then eight times seven is fifty-six.

Fifty-six plus seven is sixty-three.

I'm sure I'll make a careless mistake

at some point in this video.

And the goal for you is to identify if and when I do.

All right, now we're ready,

so we can get rid of these guys up here.

Now we can multiply this five, which is in the tens place.

It's really a fifty.

Times this up here.

Because it's a fifty we stick a zero down there.

Five times six is thirty.

Put the zero there, put the three up there.

Five times nine is forty-five.

Plus the three is forty-eight.

Five times seven is thirty-five.

Plus four is thirty-nine.

Now we're ready to add.

Eight plus zero is eight.

Six plus zero is six.

Three plus eight is eleven.

One plus six is seven.

Seven plus nine is sixteen.

And then one plus three is four.

So seven hundred ninety-six times fifty-eight is forty-six thousand one hundred sixty-eight.

And that sounds about right,

because seven hundred ninety-six-- it's almost eight hundred.

You know, which is almost one thousand.

So if we multiplied one thousand times fifty-eight we'd get fifty-eight thousand.

But we're multiplying something a little bit smaller

than one thousand times fifty-eight,

so we're getting something a little bit smaller than fifty-eight thousand.

So the number is in the correct ballpark.

Now let's do one more here

where I'm really going to step up the stakes.

Let's do five hundred twenty-three times--

I'm going to do a three-digit number now.

Times seven hundred ninety-eight.

That's a big three-digit number!

But it's the same exact process.

And once you kind of see the pattern

you'll say, hey, this'll apply to any number of digits times any number of digits.

It'll just start taking you a long time

and your chances of making a careless mistake are going to go up,

but it's the same idea.

So we start with eight times five hundred twenty-three.

Eight times three is twenty-four.

Stick the two up there.

Now eight times two is sixteen.

Sixteen plus two is eighteen.

Put the one up there.

Eight times five is forty.

Plus one is forty-one.

So eight times five hundred twenty-three is four thousand one hundred eighty-four.

We're not done.

We have to multiply times the ninety and by the seven hundred.

So let's do the ninety right there.

So it's a ninety, so we'll stick a zero there.

It's not a nine.

And let's get rid of these guys right there.

Nine times three is twenty-seven.

Nine times two is eighteen.

Eighteen plus two is twenty.

And then we have nine times five is forty-five.

Forty-five plus two is forty-seven.

I don't want to write it that thick.

Forty-seven.

Let me make sure I did that one right,

and let's just review it a little bit.

Nine times three was twenty-seven.

We wrote the seven down here and put the two up there.

Nine times two is eighteen.

We added two to that, so we wrote twenty.

Wrote the zero down there and the two up there.

The nine times five was forty-five.

Plus two is forty-seven.

You really have to make sure

that you don't make careless mistakes with these.

Then finally, we have to multiply the seven,

which is really a seven hundred times five hundred twenty-three.

When it was just an eight we just started multiplying here.

When it was a ninety, when we were dealing with the tens place,

we put a zero there.

Now that we're dealing with something that's in the hundreds

we're going to put two zeros there.

And so you have seven-- and let's get rid of this stuff.

Seven times three is twenty-one.

Put the one there.

Stick the two up there.

Seven times two is fourteen.

Fourteen plus our two is sixteen.

Put the one up there.

Seven times five is thirty-five.

Plus one is thirty-six.

And now we're ready to add.

And hopefully we didn't make any careless mistakes.

So four plus zero plus zero.

That's easy.

That's four.

Eight plus seven plus zero.

That's fifteen.

Carry the one.

One plus one plus one is three.

Four plus seven plus six.

That's what's?

Four plus six is ten.

It's seventeen.

And then we have one plus four is five.

Five plus six is eleven.

Carry the one.

One plus three is four.

So five hundred twenty-three times seven hundred ninety-eight

is four hundred seventeen thousand three hundred fifty-four.

Now we can even check to make sure.

And so this is the moment of truth.

Let's see if we have-- let's see,

five hundred twenty-three times seven hundred ninety-eight.

There you go.

Moment of truth.

I don't have to re-record this video.

It's four hundred seventeen thousand three hundred fifty-four.

But we did it without the calculator,

which is the important point.