long division....what?

richard plumb

Distinguished Member
So my son asked me to help him with long division. No problem I thought...until he showed me the method he was being told to use - which I'd never heard of. Here is a summary: http://www.mathsisfun.com/long_division.html

I really don't get this. It doesn't seem any different to just doing it directly, carrying the remainder to the next number in line and just working it out. This seems to add a bunch of extra steps for no apparent benefit.

Apparantly the method I was used to is called 'the bus stop method'.

aaargh!
 

campy mccamper

Well-known Member
I can remember doing polynomials , calculus and all sorts in school. If you asked me to do them now I would not have a clue.
 

njdbaxter

Well-known Member
started to go through it, very boring and drawn out so got fed up, how is a kid gonna remember all those steps?
 

maxwell

Member
what a total crock that is, no doubt thought up by some chinless academic trying to justify their existence
 

Orson

Moderator
That's the same way I was taught... and that's about 30 years ago.
My kids do it/were taught differently, so I guess things are coming around again, like fashion!
 
Thats 1 long way to get your answer.

425 ÷ 25 in 4 steps. 25 x 20 = 500, 500 - 425 = 75, 75 = 25 x 3, 20 - 3 = 17. Job done.

You wonder why some parents have issues with helping kids these days.
 

maxwell

Member
just shown this to my two lads aged 15 +13 and they have never seen it done like that
 

imightbewrong

Distinguished Member
What a palava for a sum you can do in your head in two seconds :) Probably more compelling if one number isn't a straight multiple of the other.
 

FruitBat

Well-known Member
Looks OK to me. I think that's more or less the way I was taught.

All I would say is:

1. The "0" step is unnecessary. We were never told to include that bit. However, if it helps understanding then fair enough.

2. Possibly the example would look better if the numbers weren't so obvious.


It might look long-winded, but sometimes that's the best way to start off before the method becomes familiar.
 
The example in the link - well, that's how I was taught to do it more about 60 years ago in our C of E Junior School. However, I've never seen the 'Rules' for it written down anywhere ever before. Interesting stuff!

In those days the teachers were very, very good and the one who taught me how to do arithmetic was called Miss Mabel Woollfitt. She was a cousin of Donald Wolfit (note how he changed his name), the famous actor and film star. In fact, she helped me get through '11+'. Actually, I was the only one in our whole small village school that year to pass and get a scholarship to go to the Grammar School. She was one of the old school of so called, 'Dedicated Teachers', which the country had plenty of at that time. They were extremely well-trained and the School Inspectors were also very strict. I'm talking of the '1950's here.

Discipline and dress and cleanliness were all extremely important. Mess about in class and you would get corporal punishment with a ruler on your bare hand, a slipper on your trousered bottom or even the cane on it instead - even if you were a girl!

This was the 'post war era'. We had tons of 'parrot fashion' learning and used to stand in a circle in front of the blackboard and easel and take it in turns to recite our 'tables'. As kids, we used to compete with each other to see who could rattle them off the quickest - not that anyone won anything for the doing of it, and whoever seemed to be the quickest was actually a matter of personal estimation or guesswork. We were all of us in the class quite utterly brilliant at it and my 'Tables' are absolutely engrained in my memory and will be so until I die.

Miss Woollffitt also gave us 20 Mental Arithmetic Questions every morning to start off the day after 'Assembly and Prayers'.

These were the days of:
Pounds, Shillings (20), Pence (12), Half-pennies, Farthings (4)
Miles, Furlongs (8), Chains (10), Yards (22), Feet (3), Inches (12)
Tons, Hundredweights (20), Stones (8), Pounds (lbs) (14), Ounces (16)

...and so I'm sure you can well imagine that questions on this stuff were quite hard according to 'modern day 2011 standards'.

Indeed, to answer mental arithmetic questions on any of the above topics, the amount of stuff you had to commit to and recall from memory was incredible - and the age of the kids in the class was from 9 - 11 years old.

eg, How much would 15 articles cost at 3 3/4p (threepence three farthings) each?

The answer is extremely easy to work out if you 1. Know your tables and 2. Know the quick ways to use to work it out in your head.

So for the example used of 425 divided by 25, I would have been able to write '17' down virtually instantly at 11 years old - and having worked it out using mental arithmetic. And I was not unique in that ability, such was the standard of the teaching in those days.

And if you don't believe me, ask your grand parents. That's why some of us 'oldies' fundamentally know and believe that today's teaching and teachers are 'total crap', when compared with the 'old days'!

And we also read that today's kids are encouraged to use calculators in class too!

(Stands by mi' bed ready to get shot down)
 
Last edited:

pandemic

Well-known Member
That's the same way I was taught... and that's about 30 years ago.
My kids do it/were taught differently, so I guess things are coming around again, like fashion!
Yep me too, about 20 years ago. We didn't bother with sticking a zero on the front that was pretty obvious.
Also this is how it was thought in the old books from back in the 50s and 60s that my dad showed me.
As far as I'm aware this is 'proper' long division.
 

qwerty321

Member
I'm 22 and I remember doing this method a little bit when I was in the tail end of primary school. Never really understood it or got the hang of it though.
 

tvbox

Distinguished Member
It's called long division because it's long. I use the same 'bus shelter' method, but keep it compact and ignore the zeros and the subtracting... well I right it in small next to the next number if that makes sense. This just writes out the subtracting part
 

Iccz

Member
It's annoying how you have to go through the steps on things like this at school. I remember algebra "2x + 8 = 22 ... what is x?" Would be able to get the answer instantly, but apparently you have to work it out... without just working it out in your head. So you have to balance it etc and show your workings... it's silly because it doesn't matter how you work it out, as long as you work it out!
Hated the whole "rules" thing about a lot of maths.
 

richard plumb

Distinguished Member
its just that its long-winded and a bit confusing looking. Looking at it some more, it just looks like it moves the 'remainder' calculation to a separate step.

So you ignore the remainder, but then you re-multiply, then subtract, which gives you the remainder, then you bring the next digit down.

We just did '42 divided by 25 = 1, remainder 17. carry the 17 to the next digit gives you 175. 175 divided by 25 = 7. Answer 17'

My son has learnt this method (they call it 'bus stop') so I'm hoping they're just showing this as an alternative method
 

richard plumb

Distinguished Member
So for the example used of 425 divided by 25, I would have been able to write '17' down virtually instantly at 11 years old - and having worked it out using mental arithmetic. And I was not unique in that ability, such was the standard of the teaching in those days.


(Stands by mi' bed ready to get shot down)
425/25 is just an example though to describe the method with simple numbers. You'd use it with more complex sums. You know 68779/37 off the top of your head? :devil:

I get your point though. I do encourage my kids to look around the problem. Don't brute force it, think of numbers as objects you can manipulate. eg when he was trying to work out 70 divided by 14, I quietly pointed out that if you double 70, you get 140... and then he was off.
 
richard

No. But i very readily can recognise that there are:

4 x 25 in 100.

4 x 100 in 400

and finally 1 x 25 in 25

I also, from my learned off pat tables know that 4 x 4 = 16.

So the answer must be 16 + 1 items of 25 or 17 of them.

And I can confirm that simple arithmetic like this, can be done in my head.

I can't do the sum 68779/37 in my head. If it is perfectly divisible without any remainder, then from my knowledge of multiplication tables, I can tell you that the answer would end in a 7.

That's about it really.
 

Iccz

Member
richard

No. But i very readily can recognise that there are:

4 x 25 in 100.

4 x 100 in 400

and finally 1 x 25 in 25

I also, from my learned off pat tables know that 4 x 4 = 16.

So the answer must be 16 + 1 items of 25 or 17 of them.

And I can confirm that simple arithmetic like this, can be done in my head.

I can't do the sum 68779/37 in my head. If it is perfectly divisible without any remainder, then from my knowledge of multiplication tables, I can tell you that the answer would end in a 7.

That's about it really.
That is why they teach methodolgy using simple sums first, to help familiarise people with the methods of getting to the answer if they are unable to do it quickly in their head their own way.

Just like with solving equations algebraically. Most people can work out simple things like "x - 5 = 3", so don't need to apply their methods, but the reason it is taught and forced on people is so they learn to apply the methods to work it out. I don't agree with it myself, but it does help people to learn how to do these things if they can't get it straight off in their head.

P.S. The answer to your sum ends in a 9 (if you round up the decimal)
 

Noggin1980

Well-known Member
425/25 is just an example though to describe the method with simple numbers. You'd use it with more complex sums. You know 68779/37 off the top of your head? :devil:

I get your point though. I do encourage my kids to look around the problem. Don't brute force it, think of numbers as objects you can manipulate. eg when he was trying to work out 70 divided by 14, I quietly pointed out that if you double 70, you get 140... and then he was off.
yeah trying to make the numbers simple is the way I do things in my head too. While I couldn't answer your 68779/37 I got pretty close in 30 seconds. Got myself confused when I tried to get the exact answer though.

37 x 1000 = 37000
37000 x 2 = 74000
100 x 37 = 3700

so 74000 - 3700 = 70300 (thats 1900 x37)
70300 - 3700 = 66600 ( thats 1800 x37)

so the answer is somewhere close to the middle of 1800 and 1900.
 

FruitBat

Well-known Member
Given an individual calculation, there may be many techniques and short-cuts that can be used. What is being taught here is not how to work out 425 divided by 25, but a methodology for division.

It is usually called the division algorithm. Perhaps it needs to be viewed in a more general context to see how useful it is.

Here's an example showing factorisation of polynomials:
Code:
         x^2 + x + 1
      -------------------------
x - 1 | x^3 - 1
        x^3 - x^2
        --------------
              x^2 - 1
              x^2 - x
              --------------
                    x - 1
 

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