Partial Quotient Method of Division 2

Another example of doing long division using the partial quotient method

I thought I would do another example of partial quotient method

for long division

So there actually has some positives to do

It's actually kind of fun to do

So let's say I want to do something really hairy

like 291 divided into-- let me just throw some digits over here-

actually let's stole another digit right over here-

So this is- how many times does 291 go into- what is this-

9,873,952

And to just kind of get our bearings

we know what 291 times 1 is. That's pretty easy

291 times 1 is clearly just 291

We know what 291 times 10 is. That's clearly 2,910

Let's get some stuff in between here

that will help us to try to approximate

how many times 291 goes into this crazy thing over here

So let's just pick- in the last example I picked 2 and 5-

you could just pick 3 and 6 if you want

You could pick 2 and 7. You could pick whatever you want

You could even just do 1

one of them, one of the above

Let's just say 291 times- let's try 3 out. 291 times 3

So I could do this in my head

or I could just make sure I don't make a mistake

Let me do it right over here

So 291 times 3 is- 1 times 3 is 3. 9 times 3 is 27

2 times 3 is 6. 6 plus 2 is 8

So this is equal to 873

It's actually strange that 873 showed up over there

My brain is doing strange things in the back ground

But anyway

that has actually no relevance to the actual solution of this problem

And let's also try 291 times 6. Let's figure out what that is

So 291 times 6

It's actually going to be this thing times 2

But I'll just calculate it. 291 times 6-

1 times 6 is 6. 9 times 6 is 54. 2 times 6 is 12, plus 5 is 17

So it's 1746

And you might say, Sal

why did you go through the trouble of figuring out this and this?

And I'm just using these as some of the approximation tools

when we try to figure out

how many times 291 goes through this whole crazy mess

So first of all, let's just look at this whole thing

This is 9873952

So let's just say, how many times does 291 go into 9,000,000?

So 291 times 3 would be 873

We want to have a bunch of zeros after the 873

So think of it this way- I'm picking 873

because its leading digit is as closer than 9 as possible

But it's definitely lower than the 9

So you say, okay, 873- and I'm going to have 1,2,3,4 zeros behind it

So 291 times 3 would give me 873

But I have to multiply- times 3 with 1,2,3,4 zeros to get this number

8.73 million

I have to multiply by 30,000

But I got this straight from this idea, that 291 times 3 is 873

So let's subtract this right over here. Let's subtract this

2 minus 0 is 2. 5, 9, 3, 7 minus 3 is 4, 8 minus 7 is 1

9 minus 8 is 1

So now we are left with 1,143,952

So which of these just gets us right under that?

So let's see, if we want to go to-

we can't go straight to 1746

That would be too big over here

We might want to do 873 again

But this time we are going to do 873,000

That is equal to 3- and then you have 1,2,3 zeros. So 1,2,3

3 times 291 is 873. 3000, is 873000

Let me write this a little bit neater

My handwriting is- so this is going to be 3000

3000 times 291

Let me make sure. This is a 2 right over here. 2 minus 0 is 2

And then you subtract again

2 minus 0 is 2. 5 minus 0 is 5. 9 minus 0 is 9. 3 minus 3 is 0

And then you have 4 minus 7

The way I like to do it when I have to start regrouping and borrowing

is making sure I go from the left

So this 1, I could borrow from there. So this becomes 11

And then the 4, I can borrow 1 from here

So that becomes a 10, and this becomes a 14

So 14 minus 7 is 7. 10 minus 8 is 2

Now 270,952. What's right below that?

So it seems we can get pretty close if we do 291 times 6

If we do a 1746, and then add two zeros to it

This is going to be times 6 with two zeros

So this is times 600

Once again, you subtract

We see I'm only using the 6 and 3

because I figured those out ahead of time

so I didn't have to do any extra math

2 minus 0 is 2. 5 minus 0 is 5. 9 minus 6 is 3. 0 minus 4--

Well, there are a couple of ways you can think about doing this

You could borrow from here. That will become a 6

This becomes a 10. 10 minus 4 is 6

Now this one is lower, so it has to borrow as well

Make this into a 16. 16 minus 7-

I have multiple of videos on how to borrow

if I'm doing that part too fast

But the idea here is to show you a different way of long division

So 16 minus 7 is 9

So now, 96,352

And once again

it looks like the 873 is about the closest we can get

So let me put a 873 over here with 2 zeros

So that would literally be 291 times 3 with 2 zeros

Times 300. And so once again, we want to subtract here

2 minus 0- you get a 2. 5. 0. Make this a 16. Make this an 8

16 minus 7 is 9

And then we have to get close to 9,052

Once again, that 873- those digits look pretty good

873- we still want to multiply 3, and then 10

So this is going to be times 30 right over here

We subtract again. 2 minus 0 is 2. 5 minus 3 is 2

And then you have 90 minus 87 is 3

I'm doing the subtraction a little fast

just so we can get the general idea

Then we have to go into 322. How can we get close to that?

Well, actually 291 is pretty darn close to that

So it's 291. You go into it one time

1 times 291 is 291. 2 minus 1 is 1. 32 minus 29 is 3

So you have a remainder of 31

291 cannot go into 31 any more. So that's our remainder

But how many times does it actually go into this big beastly number?

This 9,873,952

Well, there, we just have to add up all of these right over here

30000 plus 3000- we could even do it in our head

30000 plus 3000 is 33,000. 33600. 33900. 33931

33,931

And we're done, assuming I haven't made some silly mistake

291 goes into this thing 33,931 times with a remainder of 31