Dividing decimal

Dividing decimal numbers

Welcome to the presentation on dividing decimals.

Let's get started with a problem.

If I were to say, how many times does point two eight go into twenty-three point eight two eight?

So you're going to see that these dividing decimal problems

are actually just like the level four division problems.

You just have to figure out where to put the decimal.

So what you do is you always want to take this decimal

and move it over as many spaces as necessary to turn this number into a whole number.

So in this case, we have to move it one space, two spaces over

to put the decimal here.

Well, if I did that with this number

I have to do it with this number as well.

So I moved it over two spaces to the right,

so I have to move this decimal two spaces to the right-- one, two.

Decimal goes here,

and I put the decimal right above, right there.

Now I can treat this twenty-eight as a whole number.

And if I want to, let me see if I could--

well, I won't erase the old decimal

because if you were doing it with a pen you would kind of have the same problem I have.

So now we do it just like a level four division problem.

So we say, how many times does twenty-eight go into two?

Well, no times.

The two is smaller than twenty-eight.

How many times does twenty-eight go into twenty-three?

Once again, still, it goes into it zero times,

because twenty-three is smaller than twenty-eight.

How many times does twenty-eight go into two hundred thirty-eight?

So let's think about that.

Twenty-eight is almost thirty.

Two hundred thirty-eight is almost two hundred forty.

So thirty goes into two hundred forty eight times,

because three goes into twenty-four eight times.

So I'm going to guess that twenty-eight goes into two hundred thirty-eight eight times.

And it literally is a guess.

You have to try out some numbers sometimes.

Eight times eight is sixty-four.

Eight times two is sixteen.

Plus two is twenty-two.

Subtract.

I get fourteen.

I guessed right, because the remainder when I divide twenty-eight into two hundred thirty-eight

and I say it goes into it eight times is fourteen,

which is less than twenty-eight.

So eight was the largest number of times

that the twenty-eight could go into two hundred and thirty-eight without being larger.

So now I bring down this two.

Once again, you recognize this is just purely a level two division problem--

a level four division problem.

So now I say, how many times does twenty-eight go into one hundred forty-two?

Well, once again, I'm going to approximate.

Twenty-eight, it's almost thirty.

Let's see, thirty times four is one hundred twenty.

So yeah, I'll take a guess and I'll say

let's say it goes into it four times.

I could be wrong, but let's see if it works out.

Let me get rid of this old six.

Four times eight is thirty-two.

And four times two is eight.

Plus three is eleven.

Two minus two is zero.

Four minus one is three.

Huh! Interesting!

So it turns out that my remainder here is larger than twenty-eight,

so I actually could have divided twenty-eight into one hundred forty-two one more time.

So let me go back and change that.

See, it's not a mechanical thing.

And if you feel unsure sometimes,

you just have to try numbers and see if they work.

And otherwise, you raise or lower the number accordingly.

So let me erase that four.

I'm going to try not to mess up.

Erase all this stuff down here.

I probably should have tried it out on the side first before doing all this

and I wouldn't have had to go back and erase it.

And then let me get back to what I was doing.

So when I went into it four times the remainder was too large,

so let me try five now.

Five times eight is forty.

Five times two is ten.

Plus four is fourteen.

One hundred forty-two minus one hundred forty is two.

Good!

Two is less than twenty-eight.

This five is correct.

Now I just bring down the eight.

Twenty-eight goes into twenty-eight exactly one time.

One times twenty-eight is twenty-eight,

remainder of zero. Done!

So twenty-eight goes into two thousand three hundred eighty-two point eight, eighty-five point one times.

Or you could say, point two eight goes into twenty-three point eight two eight, eighty-five point one times.

That's the answer we had gotten.

And that makes sense.

It's always good to do a reality check,

because if I took eighty-five point one and I multiplied it by point two eight,

it makes sense that I'd get a number around twenty-three.

Point two eight is almost one third.

So twenty-three is almost one third of eighty-five.

So at least it makes sense in rough numbers.

When you're doing decimals,

if I had gotten eight hundred here instead of eighty-five,

I'd be like, oh, well, point two eight times eight hundred?

I don't know if that equals twenty-three.

So it's always good to just do a reality check,

and get a sense for at least the magnitude of what your answer should be.

Let's do another problem.

Let's do three point three goes into forty-three point two three.

That's a three.

So first thing we want to do is move the decimal.

We just have to move it one space here,

so we move it once space here as well.

Put the decimal right up here.

And now it's just a level four division problem.

Thirty-three goes into four zero times.

Thirty-three goes into forty-three one time.

That's easy.

One times thirty-three is thirty-three.

Do the subtraction.

Forty-three minus thirty-three is ten.

Bring down this two.

Thirty-three goes into one hundred two?

You could eyeball that one and say, about three times,

because three times thirty-three is ninety-nine.

Three times thirty-three is ninety-nine.

One hundred two minus ninety-nine?

Well, that's easy.

That's three.

We just bring down this three.

Thirty-three goes into thirty-three one time.

One times thirty-three is thirty-three.

Minus thirty-three, zero.

So three point three goes into forty-three point two three, thirteen point one times.

Or, if you move the decimal over,

and when you move the decimal over to the right one spot,

all you're doing is you're multiplying both the divisor and the dividend by ten.

Which is fine as long as you multiply both of them by ten.

It's also like saying thirty-three goes into four hundred thirty-two point three, thirteen point one times.

Let's do one more problem.

I think I have time.

YouTube puts a limit on this stuff.

So let's say two point five goes into point three three five zero how many times?

Well once again, let's move the decimal point over one here.

So we move the decimal point over one here.

Put the decimal here.

So how many times does twenty-five go into three?

Well zero.

So you could put a zero here just for fun if you want.

How many times does twenty-five go into thirty-three?

Well, it goes into it one time.

One times twenty-five is twenty-five.

Thirty-three minus twenty-five is eight.

Bring down the five.

Twenty-five goes into eighty-five?

Well, we know twenty-five times three is seventy-five.

So it'll go into it three times.

Three times twenty-five,

we know that's seventy-five.

Eighty-five minus seventy-five is ten.

Bring down the zero.

Up here we had brought down the five before.

And twenty-five goes into one hundred, four times.

So our answer is two point five goes into point three three five zero, point one three four times.

So as you see,

the only different step between what we're doing when we're dividing decimals,

and when we're doing level four division,

is we just have to make sure we get the decimal in the right place.

You shift the decimal here enough so that this becomes a whole number

and you just have to shift the decimal here the same number of times.

And once you do that

it just becomes a level four division problem.

And the whole trick with level four division

is always be willing to try numbers, and if the numbers don't work,

adjust them accordingly.

Don't feel that there should be a way that you can just always power through these problems.

You have to do a little bit of trial and error

and maybe use your eraser or do some work on side every now and then.

But anyway, I think you're ready to do some dividing decimals problems.

I hope you have some fun!