Partial quotient division
Partial Quotient Method of Division 2 Another example of doing long division using the partial quotient method
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- 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
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