Division 2

Dividing into larger numbers. Introduction to long division and remainders.

Let's now see if we can divide into larger numbers.

And just as a starting point, in order to divide into larger numbers,

you at least need to know your multiplication tables

from the one-multiplication tables all the way to, at least, the ten-multiplication.

So all the way up to ten times ten, which you know is one hundred.

And then, starting at one times one and going up to two times three,

all the way up to ten times ten.

And, at least when I was in school,

we learned through twelve times twelve.

But ten times ten will probably do the trick.

And that's really just the starting point.

Because to do multiplication problems like this,

for example, or division problems like this.

Let's say I'm taking twenty-five and I want to divide it by five.

So I could draw twenty-five objects,

and then divide them into groups of five or divide them into five groups,

and see how many elements are in each group.

But the quick way to do is just to think about,

well, five times what is twenty-five, right?

Five times question mark is equal to twenty-five.

And if you know your multiplication tables,

especially your five-multiplication tables,

you know that five times five is equal to twenty-five.

So something like this, you'll immediately just be able to say,

because of your knowledge of multiplication,

that five goes into twenty-five five times.

And you'd write the five right there.

Not over the two,

because you still want to be careful of the place notation.

You want to write the five in the ones place.

It goes into it five ones times, or exactly five times.

And the same thing.

If I said seven goes into forty-nine.

That's how many times?

Well you say, that's like saying seven times what--

you could even, instead of a question mark, you could put a blank there--

seven times what is equal to forty-nine?

And if you know your multiplication tables,

you know that seven times seven is equal to forty-nine.

All the examples I've done so far is a number multiplied by itself.

Let me do another example.

Let me do nine goes into fifty-four how many times?

Once again, you need to know your multiplication tables to do this.

Nine times what is equal to fifty-four?

And sometimes, even if you don't have it memorized,

you could say nine times five is forty-five.

And nine times six would be nine more than that, so that would be fifty-four.

So nine goes into fifty-four six times.

So just as a starting point,

you need to have your multiplication tables from one times one

all the way up the ten times ten memorized.

In order to be able to do at least some of these more basic problems relatively quickly.

Now, with that out of the way, let's try to do some problems

that might not fit completely cleanly into your multiplication tables.

So let's say I want to divide--

I am looking to divide three into forty-three.

And, once again, this is larger than three times ten or three times twelve.

Actually, look.

Well, let me do another problem.

Let me do three into twenty-three.

And, if you know your three-times tables,

you realize that there's three times nothing is exactly twenty-three.

I'll do it right now.

Three times one is three.

Three times two is six.

Let me just write them all out.

Three times three is nine, twelve, fifteen, eighteen, twenty-one, twenty-four, right?

There's no twenty-three in the multiples of three.

So how do you do this division problem?

Well what you do is you think of what is the largest multiple of three that does go into twenty-three?

And that's twenty-one.

And three goes into twenty-one how many times?

Well you know that three times seven is equal to twenty-one.

So you say, well three will go into twenty-three seven times.

But it doesn't go into it cleanly,

because seven times three is twenty-one.

So there's a remainder left over.

So if you take twenty-three minus twenty-one, you have a remainder of two.

So you could write that twenty-three divided by three is equal to seven,

remainder-- maybe I'll just, well, write the whole word out --remainder two.

So it doesn't have to go in completely cleanly.

And, in the future, we'll learn about decimals and fractions.

But for now, you just say, well it goes in cleanly seven times,

but that only gets us to twenty-one.

But then there's two left over.

So you can even work with the division problems

where it's not exactly a multiple of the number

that you're dividing into the larger number.

But let's do some practice with even larger numbers.

And I think you'll see a pattern here.

So let's do four going into--

I'm going to pick a pretty large number here --three hundred forty-four.

And, immediately when you see that,

you might say, hey Sal, I know up to four times ten or four times twelve.

Four times twelve is forty-eight.

This is a much larger number.

This is way out of bounds

of what I know in my four-multiplication tables.

And what I'm going to show you right now is a way of doing this,

just knowing your four-multiplication tables.

So what you do is you say

four goes into this three how many times?

And you're actually saying

four goes into this three how many hundred times?

So this is-- because this is three hundred, right?

This is three hundred forty-four.

But four goes into three no hundred times, or four goes into--

I guess the best way to think of it --four goes three zero times.

So you can just move on.

Four goes into thirty-four.

So now we're going to focus on the thirty-four.

So four goes into thirty-four how many times?

And here we can use our four-multiplication tables.

Four-- Let's see, four times eight is equal to thirty-two.

Four times nine is equal to thirty-six.

So four goes into thirty-four-- nine is too many times, right?

Thirty-six is larger than thirty-four.

So four goes into thirty-four eight times.

There's going to be a little bit left over.

Four goes into thirty-four eight times.

So let's figure out what's left over.

And really we're saying,

four goes into three hundred forty how many ten times?

So we're actually saying four goes into three hundred forty eighty times.

Because notice we wrote this eight in the tens place.

But just for our ability to do this problem quickly,

you just say four goes into thirty-four eight times,

but make sure you write the eight in the tens place right there.

Eight times four.

We already know what that is.

Eight times four is thirty-two.

And then we figure out the remainder.

Thirty-four minus thirty-two.

Well, four minus two is two.

And then these threes cancel out.

So you're just left with a two.

But notice we're in the tens column, right?

This whole column right here, that's the tens column.

So really what we said is four goes into three hundred forty eighty times.

Eighty times four is three hundred twenty, right?

Because I wrote the three in the hundreds column.

And then, there is--

let me clean this up a little bit.

I didn't want to make that line there look like a--

when I was dividing the columns-- to look like a one.

But then there's a remainder of two,

but I wrote the two in the tens place.

So it's actually a remainder of twenty.

But let me bring down this four.

Because I didn't want to just divide into three hundred forty.

I divided into three hundred forty-four.

So you bring down the four.

Let me switch colors.

And then-- So another way to think about it.

We just said that four goes into three hundred forty-four eighty times, right?

We wrote the eight in the tens place.

And then eight times four is three hundred twenty.

The remainder is now twenty-four.

So how many times does four go into twenty-four?

Well we know that.

Four times six is equal to twenty-four.

So four goes into twenty-four six times.

And we put that in the ones place.

Six times four is twenty-four.

And then we subtract.

Twenty-four minus twenty-four.

That's-- We subtract at that stage, either case.

And we get zero.

So there's no remainder.

So four goes into three hundred forty-four exactly eighty-six times.

So if your took three hundred forty-four objects and divided them into groups of four,

you would get eighty-six groups.

Or if you divided them into groups of eighty-six,

you would get four groups.

Let's do a couple more problems.

I think you're getting the hang of it.

Let me do seven-- I'll do a simple one.

Seven goes into ninety-one.

So once again, well, this is beyond seven times twelve,

which is eighty-four, which you know from our multiplication tables.

So we use the same system we did in the last problem.

Seven goes into nine how many times?

Seven goes into nine one time.

One times seven is seven.

And you have nine minus seven is two.

And then you bring down the one.

Twenty-one.

And remember, this might seem like magic,

but what we really said was seven goes into ninety ten
times--

ten because we wrote the one in the tens place--

ten times seven is seventy.

Right?-- You could almost put a zero there if you like--

And ninety-one minus seventy is twenty-one.

So seven goes into ninety-one ten times remainder twenty-one.

And then you say seven goes into twenty-one-- Well you know that.

Seven times three is twenty-one.

So seven goes into twenty-one three times.

Three times seven is twenty-one.

You subtract these from each other.

Remainder zero.

So ninety-one divided by seven is equal to thirteen.

Let's do another one.

And I won't take that little break to explain the places and all of that.

I think you understand that.

I want, at least, you to get the process down really really well in this video.

So let's do seven-- I keep using the number seven.

Let me do a different number.

Let me do eight goes into six hundred eight how many times?

So I go eight goes into six how many times?

It goes into it zero times.

So let me keep moving.

Eight goes into sixty how many times?

Let me write down the eight.

Let me draw a line here so we don't get confused.

Let me scroll down a little bit.

I need some space above the number.

So eight goes into sixty how many times?

We know that eight times seven is equal to fifty-six.

And that eight times eight is equal to sixty-four.

So eight goes into-- sixty-four is too big.

So it's not this one.

So eight goes into sixty, seven times.

There's going to be a little bit left over.

So eight goes into sixty, seven times.

Since we're doing the whole sixty,

we put the seven above the ones place in the sixty,

which is the tens place in the whole thing.

Seven times eight, we know, is fifty-six.

Sixty minus fifty-six.

That's four.

We could do that in our heads.

Or if we wanted, we can borrow.

That be a ten.

That would be a five.

Ten minus six is four.

Then you bring down this eight.

Eight goes into forty-eight how many times?

Well what's eight times six?

Well, eight times six is exactly forty-eight.

So eight times-- eight goes into forty-eight six times.

Six times eight is forty-eight.

And you subtract.

We subtracted up here as well.

Forty-eight minus forty-eight is zero.

So, once again, we get a remainder of zero.

So hopefully, that gives you the hang of how to do these larger division problems.

And all we really need to know to be able to do these,

to tackle these, is our multiplication tables

up to maybe ten times ten or twelve times twelve.