Division 3: More long division and remainder examples

More long division and remainder examples

It never hurts to get a lot of practice.

So, in this video I'm just going to do

a bunch more of essentially what we call long division problems.

And so if you have four divided into two thousand two hundred ninety-two.

And I don't know exactly why they call it long division,

and we saw this in the last video a little bit.

I didn't call it long division then,

but I think the reason why is it takes you a long time

or it takes a long piece of your paper.

As you go along, you kind of have this thing,

this long tail that develops on the problem.

So all of those are, at least, reasons in my head

why it's called long division.

But we saw in the last video there's a way to tackle any division problem

while just knowing your multiplication tables

up to maybe ten times ten or twelve times twelve.

But just as a bit of review, this is the same thing

as two thousand two hundred ninety-two divided by four.

And it's actually the same thing--

you probably haven't seen this notation before--

as two thousand two hundred ninety-two divided by four.

These-- This, this, and this--

are all equivalent statements on some level.

And you could say, hey Sal, that looks like a fraction.

In case you have seen fractions already.

And that is exactly what it is.

It is a fraction.

But anyway, I'll just focus on this format

and in future videos we'll think about other ways to represent division.

So let's do this problem.

So four goes into two how many times?

It goes into two no times, so let's move on to--

let me switch colors--

Let's move on to the twenty-two.

Four goes into twenty-two how many times?

Let's see.

Four times five is equal to twenty.

Four times six is equal to twenty-four.

So six is too much.

So four goes into twenty-two five times.

Five times four is twenty.

There's going to be a little bit of a leftover,

And then we subtract.

Twenty-two minus twenty?

Well that's just two.

And then you bring down this nine.

And you saw in the last video exactly what this means, right?

When you wrote this five up here, notice you wrote hundreds place.

So this is really a five hundred.

But in this video I'm just going to focus more on the process,

and you can think more about what it actually means

in terms of where I'm writing the numbers.

But I think the process is going to be crystal clear,

hopefully, by the end of this video.

So we brought down the nine.

Four goes into twenty-nine how many times?

It goes into it at least six times.

What's four times seven?

Four times seven is twenty-eight.

So it goes into it at least seven times.

What's four times eight?

Four times eight is thirty-two, so it can't go into it eight times.

So it's going to go into it seven.

Four goes into twenty-nine seven times.

Seven times four is twenty-eight.

Twenty-nine minus twenty-eight,

to get our remainder for this step in the problem, is one.

And now we're going to bring down this two.

We're going to bring it down and you get a twelve.

Four goes into twelve?

That's easy.

Four times three is twelve.

Four goes into twelve three times.

Three times four is twelve.

Twelve minus twelve is zero.

We have no remainder.

So four goes into two thousand two hundred ninety-two exactly five hundred seventy-three times.

So this two thousand two hundred ninety-two divided by four we can say is equal to five hundred seventy-three.

Or we could say that this thing right here is equal to five hundred and seventy-three.

Let's do a couple of more.

Let's do a few more problems.

So I'll do that red color.

Let's say we had seven going into six thousand four hundred seventy-five.

Maybe it's called long division

because you write it nice and long up here and you have this line.

I don't know.

There's multiple reasons why it could be called long division.

So you say seven goes into six zero times.

So we need to keep moving forward.

So then we go to sixty-four.

Seven goes into sixty-four how many times?

Let's see.

Seven times seven is?

Well, that's way too small.

Let me think about it a little bit.

Well seven times nine is sixty-three.

That's pretty close.

And then seven times ten is going to be too big.

Seven times ten is seventy.

So that's too big.

So seven goes into sixty-four nine times.

Nine times seven is sixty-three.

Sixty-four minus sixty-three, to get our remainder at this stage, is one.

Bring down the seven.

Seven goes into seventeen how many times?

Well, seven times two is fourteen.

And then seven times three is twenty-one.

So three is too big.

So seven goes into seventeen two times.

Two times seven is fourteen.

Seventeen minus fourteen is three.

And now we bring down the five.

And seven goes into thirty-five--

That's in our seven multiplication tables-- five times.

Five times seven is thirty-five.

And there you go.

So the remainder is zero.

So all the examples I did so far had no remainders.

Let's do one that maybe might have a remainder.

And to ensure it has a remainder,

I'll just make up the problem.

It's much easier to make problems that have remainders

than the ones that don't have remainders.

So let's say I want to divide three into--

I'm going to divide it into

let's say, one seven three five zero nine two.

This will be a nice, beastly problem.

So if we can do this we can handle everything.

So it's one million seven hundred thirty-five thousand ninety-two.

That's what we're dividing three into.

So, three goes into--

And actually, I'm not sure if this will have a remainder.

In the future video I'll show you

how to figure out whether something is divisible by three.

Actually, we can do it right now.

We can just add up all these digits.

One plus seven is eight.

Eight plus three is eleven.

Eleven plus five is sixteen.

Sixteen plus nine is twenty-five.

Twenty-five plus two is twenty-seven.

So actually, this number is divisible by three.

So if you add up all of the digits, you get twenty-seven.

And then you can add up those digits--

Two plus seven is nine.

So that is divisible by three.

That's a trick that only works for three.

So this number actually is divisible by three.

So let me change it a little bit,

so it's not divisible by three.

Let me make this into a one.

Now this number will not be divisible by three.

I definitely want a number where I'll end up with a remainder.

Just so you see what it looks like.

So let's do this one.

Three goes into one zero times.

So we can just move forward.

You could write a zero here,

and multiply that out.

But that just makes it a little bit messy in my head.

So we just move one to the right.

Three goes into seventeen how many times?

Well, three times five is equal to fifteen.

And three times six is equal to eighteen and that's too big.

So three goes into seventeen right here five times.

Five times three is fifteen.

And we subtract.

Seventeen minus fifteen is two.

And now we bring down this three.

Three goes into twenty-three how many times?

Well, three times seven is equal to twenty-one.

And three times eight is too big.

That's equal to twenty-four.

So three goes into twenty-three seven times.

Seven times three is twenty-one.

Then we subtract.

Twenty-three minus twenty-one is two.

Now we bring down the next number.

We bring down the five.

I think you can appreciate why it's called long division now.

We bring down this five.

Three goes into twenty-five how many times?

Well three times eight gets you pretty close

and three times nine is too big.

So it goes into it eight times.

Eight times three is twenty-four.

I'm going to run out of space.

You subtract, you get one.

Twenty-five minus twenty-four is one.

Now we can bring down this zero.

You bring down this zero, just like that.

And you get three goes into ten how many times?

That's easy.

It goes into it three times.

Three times three is nine.

That's about as close to ten as we can get.

Three times three is nine.

Ten minus nine--

I'm going to have to scroll up and down here a little bit--

Ten minus nine is one,

and then we can bring down the next number.

I'm running out of colors.

I can bring down that nine.

Three goes into nineteen how many times?

Well, six is about as close as we can get.

That gets us to eighteen.

So three times six.

Three goes into nineteen six times.

Six times three-- let me scroll down.

Six times three is eighteen.

Nineteen minus eighteen-- we subtract it up here too.

Nineteen minus eighteen is one and then we're almost done.

I can revert back to the pink.

We bring down this one right there.

Three goes into eleven how many times?

Well, that's three times because three times four is too big.

Three times four is twelve, so that's too big.

So it goes into it three times.

So three goes into eleven three times.

Three times three is nine.

And then we subtract and we get a two.

And there's nothing left to bring down.

Right? When we look up here there's nothing left to bring down.

So we're done!

So we're left with the remainder of two,

after doing this entire problem.

So the answer, three goes into one million seven hundred thirty-five thousand ninety-one--

it goes into it five hundred seventy-eight thousand three hundred sixty-three remainder two.

And that remainder two was what we got all the way down there.

So hopefully you now appreciate

that you can tackle pretty much any division problem.

And you also, through this exercise,

can appreciate why it's called long division.