I was shocked and suprised to find out, last night, that our lass couldn't do Long division and instantly went to fetch a calculator. .

Me question is, how many other people don't know how to work stuff out manually and would you do the same, and run for the calculator. .

Cheers. . . Munky

Using a calculator is fine if you understand the operations that the calculator is carrying out for you but I don't think that it should be a substitute for brain power.

I can do long division no problem, remember all my multiplicaton tables and can generally carry out mental arithmatic very well but then I am a product of a 60's / early 70's education when such things were actually taught in schools.

Originally posted by munky
I was shocked and suprised to find out, last night, that our lass couldn't do Long division and instantly went to fetch a calculator. .

Me question is, how many other people don't know how to work stuff out manually and would you do the same, and run for the calculator. .

Cheers. . . Munky


In the main, my mental arithmatic is pretty reasonable - but long division is an area I am pretty poor at indeed.

Alex

Yeah. . . I'm an 80's kid and being 23, thought that most around my age would be able to do this. . . Our lass is 19 and she didn't know how to do it and never really grasped the concept of it when at school. .

I'm sure if I didn't get it. . I'd have been given more of em to do until I did get it. It appear that she was allowed to use a calculator and this was an acceptable short cut as teachin was probably to much effort for a teacher. . . sheeshh. .

I can't do long division unless it is algebraic, and I have a degree in Mathematics :o :rolleyes:

I have a degree in maths.

I can't do long division.

But, I could give you a damn good estimate, to about 4 significant figures in a few seconds.
Thats all you need in a practical situation. If you need to know more exactly use a calculator (though I cant think of many situations where you would)

Of course when I say I can't do long division I obviously could, I just don't need to so have never found out how to do it.

how does long division differ from normal division?

Originally posted by Yodameister
Of course when I say I can't do long division I obviously could, I just don't need to so have never found out how to do it.

Same here!

Originally posted by Phanerothyme
how does long division differ from normal division?

1/4 =0.25 156789432/456= Long Division

How do you do long division? I don't think I've ever been taught how to do it.

I'm not saying I can't do it, but I'm sure there must be an easier way to do it than the techniques I usually use.

I can do long division but must admit I will use the calculator as it's easier and quicker. Having said that I don't generally have much need to do long division so it's a rare occasion anyway.

I also went to school in the 60's/70's (left 1976) and we all had to learn it then.

im really not that good when it comes to maths, i had a horrible teacher at school that had a problem with my broyher years before and took it out on me!

Originally posted by geno
im really not that good when it comes to maths, i had a horrible teacher at school that had a problem with my broyher years before and took it out on me!

Although i'm not bad at maths in general, i too had severe problems with certain teachers due to my older brother kicking the s*** out of one of them.
Now he is a IT tutor!

I dunno if i can remember how to do long division... not really done it since like year 5 or 6 or something? lol... we did some crazy division stuff for A level... but meh well

I could probably figure it out and remember it in a few mins if I needed to... but like said above I could probably give a rough estimate to the answer without putting pen to paper anyways..

calculators are there to be used anyways... my brains had enough maths for a few years after doing A level maths and a module in maths for computing on my degree last year...

I'm actually surprised how few of the current young teens dont know their times tables... or even people of my age (19)... i mean, 2's, 5's, 10's people know... but not everyone seems to know their 7's, 8's, 11's, 12...

I'm 63 and still remember my times tables i was taught at a very young age in Shirecliff school, the younger you learn them the easier it becomes later on, i also still remember being taught at the same age to count in French, never had to use to but i still retain it all.

I think I can just about manage it....

I remember being taught the use of logarithms, then how to use a slide rule, and finally at A level we were allowed to use calculators on, I believe, the Physics paper.

Even now, the ability to estimate (essential with logs and the slide rule) is a pretty useful knack to have - even if it's just for calculating my share of a restaurant bill!

Joe

had to use silly squares to make sure indenting works, hope this helps those who've forgotten.

�_�_613/13

start�_here

�_�_�_________�_
13�_|613

then�_working�_from�_the�_most�_signifcant�_digits �_(ie�_the�_left),�_how�_many�_times�_does�_13�_go �_into�_61.

�_�_�_�_�_4
�_�_�_________�_
13�_|613
�_�_�_�_52

The�_4�_goes�_up�_on�_top,�_the�_actual�_value�_of �_13*4�_goes�_below.�_�_Then�_subtract�_52�_from�_ 61�_and�_bring�_down�_the�_3.

�_�_�_�_�_4
�_�_�_________�_
13�_|613
�_�_�_�_52
�_�_�_�_�_93

repeat�_ad�_infinitum


�_�_�_�_�_47.153
�_�_�_________�_
13�_|613
�_�_�_�_52-
�_�_�_�_�_93
�_�_�_�_�_91-
�_�_�_�_�_�_2.0
�_�_�_�_�_�_1�_3-
�_�_�_�_�_�_�_�_70
�_�_�_�_�_�_�_�_65-
�_�_�_�_�_�_�_�_�_50
�_�_�_�_�_�_�_�_�_39-

and�_so�_on�_until�_you�_get�_board�_if�_it's�_an� _irrational�_number,�_maybe�_i�_could�_have�_chose n�_a�_better�_example,�_but�_i'm�_not�_redoing�_it .

now�_the�_question�_is,�_will�_the�_indenting�_sho w...
�_�_�_�_�_�_�_�_�_

that looks terrible. sorry.

See me after school Cyclone!!!

8 out of 10 for effort, but bugger all for neatness.

Smarten yourself up boy!

I gave up at 47.153846(this decimal pattern repeated ad infinitum)

I gave up after the first [], See i can't even do a square! :hihi: :confused:

613/13
To get a good estimete, repeatedly divide each side by a small number until you can do it in your head:

613/13 =
600ish/12ish =
50ish

Good enough when cutting timber, and essential to make sure you don't accept a mis-keyed calculator result as gospel

For those who have forgotten here's how you do long division (I apologise for the slight problem with the layout but this post was laid out correctly in Notepad but when I pasted it in into the software used on this forum some spaces I put in to make the numbers line up in columns disappeared so I've replaced them with * but the 365 after the / on the second line of the sum is slightly to the left of where it should be):

Sum: 365 divided by 7

7/365

(I can't do lines across so imagine there are horizontal lines below the 7 and above the 365)

3 is less than 7 so you put a 0 above the first 3:

**0
7/365

0 times 7 is 0 so you put a 0 underneath the first 3, subtract and put the answer on the bottom line:

**0
7/365
**0
**3

You bring the 6 down to the bottom line:

**0
7/365
**0
**36

7 goes into 36 5 times so you put a 5 on the top line above the 6:

**05
7/365
**0
**36

5 times 7 is 35 so you put 35 under the 36 and subtract and put the answer on the bottom line:

**05
7/365
**0
**36
**35
***1

You bring the 5 down to the bottom line:

**05
7/365
**0
**36
**35
***15

7 goes into 15 twice so you put a 2 above the 5 on the top line:

**052
7/365
**0
**36
**35
***15

2 times 7 is 14 so you put 14 underneath the 15 and subtract and put the answer on the bottom line:

**052
7/365
**0
**36
**35
***15
***14
****1

If the answer on the bottom line had been zero the sum would have been complete but it is not so you can do one of two things. Firstly you can say that 365 divided by seven equals 52 with 1 remainder. Secondly you can put a decimal point after the 365 and keep adding 0s to the 365 and dividing and subtracting until you get a 0 on the bottom line but you would never get a 0 because you are dividing by 7 and there will always be a remainder. If you were dividing a whole number which wasn't a mulitple of 5 by 5 you would get an answer with one decimal point and if you were dividing a whole number which wasn't a multiple of 9 by 9 you would get an answer with a recurring number after the decimal point.

you just copied me but used *'s instead of squares...

I'm more confused now than I was originally. :confused:

Where's Harry Smith when you need him?

Originally posted by Skatiechik
I can't do long division unless it is algebraic, and I have a degree in Mathematics :o :rolleyes:

I'm better at doing long division when it's algrebraic too lol I never understood it properly the first time I learnt it with just integers, although I can do it now if I need to :)

Originally posted by munky
I was shocked and suprised to find out, last night, that our lass couldn't do Long division and instantly went to fetch a calculator. .

Me question is, how many other people don't know how to work stuff out manually and would you do the same, and run for the calculator. .

Cheers. . . Munky

I cant do long division even though I did learn at school. I just never need to do it so I forgot. Anyway a calculator is more reliable than your brain....but kids should still be taught because it teaches you how to solve problems which is still useful of course.

I like long division and multiplication. And enjoy having a bash at some from time to time. I usually finish up working out a 63 times table or something on the paper to help me work it out. I did get my O Level in maths back in the 1980s and never really forgot it.
I brought it up with my mate in the pub, a couple of years ago, who has a similar education to me, and he found it mad that I could do them while I was astounded that he couldn't

Originally posted by Skatiechik
1/4 =0.25 156789432/456= Long Division


000343836
456/156789432
0
--
15
0
---
156
0
----
1567
1368
-----
1998
1824
-----
1749
1368
-----
3814
3648
-----
1663
1368
-----
2952
2736
-----
216


Which is 343836 and 216/456, or about 1/2. I reckon (engineer's guestimate) at about 343836.475 or there-abouts.

Hold on...

According to my calculator it's 343836.473684211 so not far off, eh?

Originally posted by JoePritchard
Even now, the ability to estimate (essential with logs and the slide rule) is a pretty useful knack to have - even if it's just for calculating my share of a restaurant bill!


But everyone knows that the laws of mathematics are different in restaurants. It's bistromathics*, and does not follow any of the conventional laws found in the rest of the universe.

*thanks to Douglas Adams

I used to work in a raw materials warehouse and so found plenty of use for my O level maths and as I was using numbers in a lot of my work much of the maths was done in my head.
However as time passed i saw that the work trainee lads who came for a short stint in the warehouse seemed unable to do even simple maths and when I say simple I mean the first eight times tables. If asked to work out something they'd look around for the calculator and when that wasn't forthcoming stare blankly at the pen and paper I'd provide. Finger counting became more evident and when you're working with microns fingers aren't a great deal of use. Sometimes to throw a spanner in the works I'd revert to feet and inches which again used to completely baffle them. The exscuse was that at school they were allowed to use calculators and they din't understand what the machines were doing.

Originally posted by nightrider
Anyway a calculator is more reliable than your brain

Nope.

Lots of calculators have computational errors embedded into them, although they have sharpened up their act somewhat.

The crucial difference between doing maths on a calculator and doing it on paper or even in your head, is that a calculator cannot check its own results, whereas your head can.

A calculator is useless to someone who doesn't know enough maths. Dangerous even,

How is a mathematically disinclined individual going to tell the difference between a wildly inaccurate result (caused by mis-keying a digit or decimal point,) and a result that sounds about right?

I was never taught how to do long division in school. My teachers would constantly ask for my "working out" but I couldn't supply it, because I didn't know how to do it.

I moved schools at one of the key stages in my learning, and never recovered. My new school was more focussed on teaching me cursive handwriting than sorting out my missing abilities.

It still amazes me how they managed to miss it out.

And sorry peeps, even after reading this thread long division is still GREEK to me.

Originally posted by Phanerothyme
Nope.

Lots of calculators have computational errors embedded into them, although they have sharpened up their act somewhat.


A simple example is division by zero.

20 divided by 0 according to a calculator is Error

20 divided by 0 is actually 20...

Originally posted by muddycoffee
A simple example is division by zero.

20 divided by 0 according to a calculator is Error

20 divided by 0 is actually 20...

ermm, no.
You cannot divide by 0, so the answer in your head should be 'error'.

20/0 could give you the result of infinity, but that would only be of use in quite special mathematical areas. Most of the time a /0 is a nonsense or some sort of mistake.

20/1 is actually 20.

If i have 20 sandwiches on my table and divide them by 2, I would have 2 piles of 10 sandwiches.
In junior school speak I would have 20 shared by 2.

If I have 20 sarnies and I devide them by 0
There are still 20 there but they are not divided.

There isn't an infinite pile..

20 sandwiches shared by nobody are still 20 sandwiches.

Originally posted by muddycoffee
If i have 20 sandwiches on my table and divide them by 2, I would have 2 piles of 10 sandwiches.
In junior school speak I would have 20 shared by 2.

If I have 20 sarnies and I devide them by 0
There are still 20 there but they are not divided.

There isn't an infinite pile..

20 sandwiches shared by nobody are still 20 sandwiches.

No, dividing by zero is a meaningless concept in the example you have used, so it can hardly have a representative answer on a calculator screen.

Yes, division can be used to represent the sharing out of things, but thats only one sense of it. The wider sense is how many times does this value have to be added to itself to reach another specified value.

However many times you add zero to itself it will never amount to anything else.

Originally posted by muddycoffee
If i have 20 sandwiches on my table and divide them by 2, I would have 2 piles of 10 sandwiches.
In junior school speak I would have 20 shared by 2.

If I have 20 sarnies and I devide them by 0
There are still 20 there but they are not divided.

There isn't an infinite pile..

20 sandwiches shared by nobody are still 20 sandwiches.

that is a nonesense example. You cannot share something between nothing.

if you divide 20 by 1 you get 20. If you divide it by 0.5 you get 40.

this pattern continues, watch.

20 / 1 = 20
20 / 0.5 = 40
20 / 0.25 = 80
20 / 0.125 = 160

You can see where this is going. As the divisor approaches 0 the result approaches infinity.
I do have 2 A-levels in maths, so i've got a fair understanding of the subject.

Originally posted by muddycoffee
20 sandwiches shared by nobody are still 20 sandwiches.

If you have a pile of sandwiches and don't share any of them out, how many piles of sandwiches do you have?

1

You have 20 sandwiches. You cannot divide them into 0 piles, you always need at least 1.

Cyclone has explained it best. I would have used the same proof. The problem is that you will always have an integer value of piles. You can't have half a pile; it's just 1 smaller pile. Just ask anyone with experience of preparation-H!

Originally posted by spiffymonkey
If you have a pile of sandwiches and don't share any of them out, how many piles of sandwiches do you have?

1

You have 20 sandwiches. You cannot divide them into 0 piles, you always need at least 1.

Cyclone has explained it best. I would have used the same proof. The problem is that you will always have an integer value of piles. You can't have half a pile; it's just 1 smaller pile. Just ask anyone with experience of preparation-H!

By your explanation, though, you can only divide things by positive integers (aka "Natural" numbers)

I suppose by Muddycoffe's definition (which is only dealing with integers) that 20 divided by zero is zero with a remainder of 20 (or more technically, it could be any number with a remainder of 20)

Anyway, back on the long division topic (as I may have mentioned before) I can't remember off the top of my head how to do long division on a sheet of paper, but I could probably figure out a pretty effective way of doing it if I had to.

But I do find that for a simple division I can get to within 2 decimal places very quickly in my head that is fine for all practical purposes.

Originally posted by Yodameister
By your explanation, though, you can only divide things by positive integers (aka "Natural" numbers)

I suppose by Muddycoffe's definition (which is only dealing with integers) that 20 divided by zero is zero with a remainder of 20 (or more technically, it could be any number with a remainder of 20)

Anyway, back on the long division topic (as I may have mentioned before) I can't remember off the top of my head how to do long division on a sheet of paper, but I could probably figure out a pretty effective way of doing it if I had to.

But I do find that for a simple division I can get to within 2 decimal places very quickly in my head that is fine for all practical purposes.

when applied to real world objects you can only divide by natural numbers. But the problem is that it's a trivial example that is misleading.

Originally posted by Cyclone
when applied to real world objects you can only divide by natural numbers. But the problem is that it's a trivial example that is misleading.

Yes, its a special case of the wider generalisation.

Which is basically what the definition of applied mathematics is as against pure mathematics.

But whatever set of numbers you are using a basic division by zero is something that is outside the definition.

Just because you can write the symbols 20 / 0 = X it doesn't mean there is a solution.

Anyway, Cyclone think this is the closest we have ever come to agreeing on something so don't ruin it eh?!

Originally posted by Yodameister
Yes, its a special case of the wider generalisation.

Which is basically what the definition of applied mathematics is as against pure mathematics.

But whatever set of numbers you are using a basic division by zero is something that is outside the definition.

Just because you can write the symbols 20 / 0 = X it doesn't mean there is a solution.

Anyway, Cyclone think this is the closest we have ever come to agreeing on something so don't ruin it eh?!

I thought we were agreeing.
I'm sure we've agreed on things before as well. But we can agree to disagree on that last point if you like :suspect: :clap:

Originally posted by Cyclone
I thought we were agreeing.
I'm sure we've agreed on things before as well. But we can agree to disagree on that last point if you like :suspect: :clap:

Hmm when it gets onto mathematical debates I'm a pedant so I nitpick over minor details.

That's what maths is all about!

Originally posted by spiffymonkey
If you have a pile of sandwiches and don't share any of them out, how many piles of sandwiches do you have?

1

You have 20 sandwiches. You cannot divide them into 0 piles, you always need at least 1.

Cyclone has explained it best. I would have used the same proof. The problem is that you will always have an integer value of piles. You can't have half a pile; it's just 1 smaller pile. Just ask anyone with experience of preparation-H!

By the time you lot have finished arguing about sandwiches they will all be stale!
Right then you lot, when have you used algebra, and, can a calculator do algebra? Was it just invented to pee people off or is it useful?
<<<<<<<Stirs a hornets nest up :heyhey:

it's useful for solving problems sometimes, and only very expensive calculators can do it (and then generally not very well).

Originally posted by Cyclone
it's useful for solving problems sometimes, and only very expensive calculators can do it (and then generally not very well).

Useful for solving problems eh?
I am struggling to draw a sheeps head at the minute, would Algebra help me? If so i am willing to learn, honest :heyhey:

Originally posted by viking
Useful for solving problems eh?
I am struggling to draw a sheeps head at the minute, would Algebra help me? If so i am willing to learn, honest :heyhey:

I'd love to get into a pointless argument but I think your signature really does say it all on this occasion!

Mayeb if you understood algebra and maths type stuff you wouldn't end up having to draw sheep.

Thats what inspired me because I am the world's worst artist.

Originally posted by Yodameister
I'd love to get into a pointless argument but I think your signature really does say it all on this occasion!

Mayeb if you understood algebra and maths type stuff you wouldn't end up having to draw sheep.

Thats what inspired me because I am the world's worst artist.

Thanks for the bite, I thought someone might LMAO :hihi: :hihi:

Originally posted by viking
Thanks for the bite, I thought someone might LMAO :hihi: :hihi:

No seriously it was a straight choice between maths and drawing sheep!

Originally posted by Yodameister
No seriously it was a straight choice between maths and drawing sheep!

I know what you mean.
I have a few months off work, and decided, as the worst artist (beer apart) in Sheff, I would take up drawing.
I have done landscapes and trees and Bridges, but have just come across a sheeps head which I will persevere with. :thumbsup:

Originally posted by Yodameister
By your explanation, though, you can only divide things by positive integers (aka "Natural" numbers)

No, by my definition you can only divide PILES OF SANDWICHES by positive integers.

You can divide arbitrary numbers by anything you like.

of course the benefit of having a calculator is that when you do divide by Zero, you get err and not a long argument about sheep and sandwiches.

Actually the errors I was referring to were nothing to do with division by zero which is incalculable. I've googled vainly for a link here, but earlier calculators used a chip where the "firmware" that performed the calculations actually had major flaws particularly rounding recurring fractions and the like.

Worst of the lot is a calculator that would give you

1 + 2 x 3 = 9

instead of 7

Lots of normal calculators make life almost impossible by not allowing parentheses, or worse still not following the expected arithmetic order in a long sum

The solution to this was, IMO the finest pocket calculator series to ever grace the planet - this one (http://www.phys.uwosh.edu/mike/calcs/images/hp34c-d.jpg) - Although the later models with a spiffy card reader were even more flash (but prone to getting crumbs stuck in the slot). The LCD models marked the beginning of the end.

My dad showed me how to do sums on these handheld computers using Reverse Polish Notation.

This seems to me to be a much more logical method of performing arithmetic, keeping the result in plain view from the beginning and performing sums on it. rather than trying to gradually boil down a line of figures and symbols into a single resolution.

Originally posted by Phanerothyme
Nope.

Lots of calculators have computational errors embedded into them, although they have sharpened up their act somewhat.

The crucial difference between doing maths on a calculator and doing it on paper or even in your head, is that a calculator cannot check its own results, whereas your head can.

A calculator is useless to someone who doesn't know enough maths. Dangerous even,

How is a mathematically disinclined individual going to tell the difference between a wildly inaccurate result (caused by mis-keying a digit or decimal point,) and a result that sounds about right?

what computational errors? I imagine if it can display 10 decimal places and you divide two numbers accurate to 10 decimal places then yes some rounding is doen and it isnt totally accurate. But the average person isnt going to have this situation. Are there other computational errors?

Originally posted by Phanerothyme
of course the benefit of having a calculator is that when you do divide by Zero, you get err and not a long argument about sheep and sandwiches.

Actually the errors I was referring to were nothing to do with division by zero which is incalculable. I've googled vainly for a link here, but earlier calculators used a chip where the "firmware" that performed the calculations actually had major flaws particularly rounding recurring fractions and the like.

Worst of the lot is a calculator that would give you

1 + 2 x 3 = 9

instead of 7

Lots of normal calculators make life almost impossible by not allow

reading that left to right: 1 +2 is 3. If you type that into a caclulator it gives 3. Then press x 3. What is 3 x 3? It is 9, and not 7.

So I dont understand the problem. I dont believe most calculators (and mine doesnt) will give 7 if you type 1 +2 x 3 in; all calculators I have ever had do things in the order you type them which seems pretty sensible to me.

Originally posted by nightrider
reading that left to right: 1 +2 is 3. If you type that into a caclulator it gives 3. Then press x 3. What is 3 x 3? It is 9, and not 7.

So I dont understand the problem. I dont believe most calculators (and mine doesnt) will give 7 if you type 1 +2 x 3 in; all calculators I have ever had do things in the order you type them which seems pretty sensible to me.

You obviously haven't thought about the answers you are getting out of your machine, or your calculator was created before LCD displays were invented. All calculators these days are arithmetic, not sequential unless the box says otherwise.


I once had a customer bring me a 'faulty' calculator in John Lewis. I enquired as to the symptoms, and was informed as to the outcomes of some basic arithmetic problems.

I asked for them to come back in half an hour, and carried out a couple of quick tests.

As I suspected, it was an adding machine which follows a completely different set of rules. I gave them a quick tutorial, and they left quite happy :thumbsup:

Originally posted by Strix
You obviously haven't thought about the answers you are getting out of your machine, or your calculator was created before LCD displays were invented. All calculators these days are arithmetic, not sequential unless the box says otherwise.




I *have* thought about it and it makes perfect sense to me to do the calculation in sequential order. My casio does this (10 years old) and so does the calculator in windows->accessories.

If I bought a "modern" calculator I would soon notice if it wasnt sequential and be able to use common sense to work out exactly how it works. In neither case is the calculator "wrong" - it does exactly what it was programmed to do.

Originally posted by nightrider
... My casio does this (10 years old) and so does the calculator in windows->accessories.

In neither case is the calculator "wrong" - it does exactly what it was programmed to do.

Nobody said it was wrong.

The calculator in windows can be set either way :thumbsup:

Originally posted by Strix
You obviously haven't thought about the answers you are getting out of your machine, or your calculator was created before LCD displays were invented. All calculators these days are arithmetic, not sequential unless the box says otherwise.

Dunno who rattled my cage. That wasn't the best way to answer that. Sorry.

Yes, give me a bit of paper and a pencil I can still do long division - although at work I use calculators or spreadsheets depending on the job. Brain always does a raincheck on the outcomes though.

What worries me is when I see people using a calculator to multiply by ten (and this was somebody in a finance dept)!!!!!

Phan was highlighting the negatives about using the calculators by not following the order of operations according to BOSMAS rule of calculation - search BOSMAS in google for more information.

You have shown that 1 + 2 x 3 according to the calculator (in your hand) is being calculated as (1 + 2) x 3 = 9

However, 1 + 2 x 3 according to BOSMAS rule, should be calculated as 1 + (2 x 3) = 7

So, by following BOSMAS the rules which is what we use in carrying out the order of calculation in mathematics, 7 is the correct answer and not 9.

Granted, you said, the calculator is doing what it is programmed to do, but humans failure to use calculators correctly by not following BOSMAS rule as [most] calculators won't do this for you, just as you have done on your calculator, you will end up with the wrong result of 9.

This is extactly what Phan point was.

Originally posted by John
Phan was highlighting the negatives about using the calculators by not following the order of operations according to BOSMAS rule of calculation - search BOSMAS in google for more information.

You have shown that 1 + 2 x 3 according to the calculator (in your hand) is being calculated as (1 + 2) x 3 = 9

However, 1 + 2 x 3 according to BOSMAS rule, should be calculated as 1 + (2 x 3) = 7

So, by following BOSMAS the rules which is what we use in carrying out the order of calculation in mathematics, 7 is the correct answer and not 9.

Granted, you said, the calculator is doing what it is programmed to do, but humans failure to use calculators correctly by not following BOSMAS rule as [most] calculators won't do this for you, just as you have done on your calculator, you will end up with the wrong result of 9.

This is extactly what Phan point was.

Its just a notation though and you must follow whatever rule the calculator uses to get the correct anwser. Its no use blindly using bosmas if the calculator is designed to not follow this rule.

(1 + 2) x 3 is just as correct as 1 + (2 x 3) - though of course they give different anwsers because they are different questions. A calculator is free to choose to put the brackets where it likes so 9 is the correct anwser (as is 7).

Originally posted by nightrider
A calculator is free to choose to put the brackets where it likes so 9 is the correct anwser (as is 7).

Freedom of choice for calculators? :hihi:

Is that funny or am I tired?

Originally posted by nightrider
(1 + 2) x 3 is just as correct as 1 + (2 x 3) - though of course they give different anwsers because they are different questions. A calculator is free to choose to put the brackets where it likes so 9 is the correct anwser (as is 7).

Nope. 1 + 2 x 3 reads 1 + (2 x 3) if there are no brackets to say otherwise, therefore the correct way to enter 1 + 2 x 3 into a sequential calculator is 2 x 3 + 1 :thumbsup:

Well there are three possibilities in programming a calculator when the user is not specific with brackets

1. It does a purely left to right version
2. It has a BOSMAS rule or similar sort of rule
3. It gives an error message

Now, if I was told to perform a similar calculation I would do the human equivalent of "give an error message" and ask you to be more specific.

As has been stated before, a calculator is only really useful so long as the user knows exactly what the calculator is actually calculating, so in my opinion it doesn't really matter what system the calculator uses but it would make sense if there was a standard that was always used (in much the same way as 3*5 always equals 15 no matter what calculator you use - as long, of course, as you are not set to using a base other than 10)

I have to disagree with Phan's assertion that the sequential nature of early calculators was an error. It was just the way they worked, any error resulting from it was user error.

Originally posted by Strix
Nope. 1 + 2 x 3 reads 1 + (2 x 3) if there are no brackets to say otherwise, therefore the correct way to enter 1 + 2 x 3 into a sequential calculator is 2 x 3 + 1 :thumbsup:

I dont see why people here insist 1 +2 x 3 is the same as 1 + (2 x 3) - this is just a convention and everyone could just as easily say 1 + 2 x 3 is the same as (1 + 2) x 3 - and lots of (older apparently ) calculators do do this.

Writing 1 + 2 x 3 doesnt really mean anything until you put the brackets. To make it mean what you want to ask you put the brackets in the appropiate place. Real numbers are commutative so 3 x (1 +2) must be the same as (1 +2 ) x 3 - therefore one is free to put the brackets anywhere. Since you dont type brackets into a caculator it has to choose a convention in order for your qeustion to mean something - buts that all it is: a convention.

Originally posted by nightrider
I dont see why people here insist 1 +2 x 3 is the same as 1 + (2 x 3) - this is just a convention and everyone could just as easily say 1 + 2 x 3 is the same as (1 + 2) x 3 - and lots of (older apparently ) calculators do do this.

Writing 1 + 2 x 3 doesnt really mean anything until you put the brackets. To make it mean what you want to ask you put the brackets in the appropiate place. Real numbers are commutative so 3 x (1 +2) must be the same as (1 +2 ) x 3 - therefore one is free to put the brackets anywhere. Since you dont type brackets into a caculator it has to choose a convention in order for your qeustion to mean something - buts that all it is: a convention.

I type brackets into calculators.....
if a calculator doesn't have brackets its not worth using!

Yes the BOSMAS order is a convention, but it is sensible if everyone uses the same convention.

Originally posted by nightrider
I dont see why people here insist 1 +2 x 3 is the same as 1 + (2 x 3) - this is just a convention and everyone could just as easily say 1 + 2 x 3 is the same as (1 + 2) x 3 - and lots of (older apparently ) calculators do do this.

Writing 1 + 2 x 3 doesnt really mean anything until you put the brackets. To make it mean what you want to ask you put the brackets in the appropiate place. Real numbers are commutative so 3 x (1 +2) must be the same as (1 +2 ) x 3 - therefore one is free to put the brackets anywhere. Since you dont type brackets into a caculator it has to choose a convention in order for your qeustion to mean something - buts that all it is: a convention.

convention defines everything to do with maths or any other language. If we no longer agree on a convention then we cannot communicate. So producing a dictionary that I've decided will use a different convention to the rest of the world is slightly stupid.

1 + 2 * 3 means something. The fact that you have to be aware of the common convention for operator precedence doesn't render it meaningless.
You also have to be aware how your calculator works as well, that's all.

Originally posted by Cyclone


1 + 2 * 3 means something. The fact that you have to be aware of the common convention for operator precedence doesn't render it meaningless.


1 +2 *3 means nothing until you insert brackets or apply some ordering principle (which is essentially doing the same thing).

Originally posted by Yodameister
I type brackets into calculators.....
if a calculator doesn't have brackets its not worth using!

Yes the BOSMAS order is a convention, but it is sensible if everyone uses the same convention.

fair enough it is better if everyone uses the same convention. It doesnt make it "wrong" to use a different convention though. In some cases (not to do with numbers) it is very sensible that different people use different conventions to describe things.

Originally posted by nightrider
fair enough it is better if everyone uses the same convention. It doesnt make it "wrong" to use a different convention though. In some cases (not to do with numbers) it is very sensible that different people use different conventions to describe things.

It wouldn't be a 'convention' if it wasn't conventional!

(It wouldn't be a 'convention' if it wasn't the rule)

There is no way you would get through a maths exam with your own theory on how to manipulate numbers, nightrider. The examiner would just mark your answers 'wrong' ;)

The ignorance that is fashionably applied to English doesn't work with maths

Originally posted by Strix
It wouldn't be a 'convention' if it wasn't conventional!

(It wouldn't be a 'convention' if it wasn't the rule)

There is no way you would get through a maths exam with your own theory on how to manipulate numbers, nightrider. The examiner would just mark your answers 'wrong' ;)

The ignorance that is fashionably applied to English doesn't work with maths

If the question said 1 + 2 *3 then obviously I would use whatever rule the exam board uses to transform it into a meaningful question.

As for conventions given many calculators seem not to use your convention it seems unlikely you can claim your method is the sole one that is valid to give 1 +2 *3 meaning.

And it isnt ignorant to say your bosmas method is not the sole valid method. In fact it is far more ignorant to claim it is the sole method!

Originally posted by nightrider
If the question said 1 + 2 *3 then obviously I would use whatever rule the exam board uses to transform it into a meaningful question.

As for conventions given many calculators seem not to use your convention it seems unlikely you can claim your method is the sole one that is valid to give 1 +2 *3 meaning.

And it isnt ignorant to say your bosmas method is not the sole valid method. In fact it is far more ignorant to claim it is the sole method!

calculators have existed for about 40 years, maths has been around for at least several millenia. The precedence of operators is well established, the problem was that the simple electronics weren't capable of applying the rules correctly. Or rather that they evaluated each 2 value expression before carrying the result forwards to form 1 input to the next expression.

Originally posted by Cyclone
calculators have existed for about 40 years, maths has been around for at least several millenia. The precedence of operators is well established, the problem was that the simple electronics weren't capable of applying the rules correctly. Or rather that they evaluated each 2 value expression before carrying the result forwards to form 1 input to the next expression.

this isnt really a maths question so how long maths has been around is not really relevant. The issue is of notation and if large numbers of calculators are/were using a different notation to bosmas then that is/was a valid notation.

Noone is saying 2*3 doesnt equal 6. It always does. But how you interpret 1 + 2 *3 (which is actually lazy - people should put the brackets in to show what they mean) is changeable. If calculators had to use a notation other than bosmas then I would say that was the main convention of the time. If they all use bosmas now then ok bosmas is the main convention nowadays.

Originally posted by nightrider
As for conventions given many calculators seem not to use your convention it seems unlikely you can claim your method is the sole one that is valid to give 1 +2 *3 meaning.

At the risk of repeating myself:

Originally posted by Strix
Nope. 1 + 2 x 3 reads 1 + (2 x 3) if there are no brackets to say otherwise, therefore the correct way to enter 1 + 2 x 3 into a sequential calculator is 2 x 3 + 1 :thumbsup:

You just need to undersand how to use the equipment :thumbsup:

Originally posted by nightrider
Noone is saying 2*3 doesnt equal 6. It always does. But how you interpret 1 + 2 *3 (which is actually lazy - people should put the brackets in to show what they mean) is changeable.

No it isn't. And Slough isn't pronounced 'Sluff'

Originally posted by Strix
At the risk of repeating myself:

Nope. 1 + 2 x 3 reads 1 + (2 x 3) if there are no brackets to say otherwise, therefore the correct way to enter 1 + 2 x 3 into a sequential calculator is 2 x 3 + 1

You just need to undersand how to use the equipment :thumbsup:

well some calculators would differ with you. They interpret 1 + 2 *3 as (1 +2 ) *3.

As I have already said 1 + 2 * 3 means nothing without some rule to interpret it. You had better understand the rule being applied rather than assuming it is and must always be bosmas.

Originally posted by Strix
No it isn't. And Slough isn't pronounced 'Sluff'

bad example. Does everyone pronounce grass or bath in the same way in this country? No they dont do they...

How about tomatoes? Does everyone in the english speaking world pronounce this the same way?

Originally posted by Strix
No it isn't. And Slough isn't pronounced 'Sluff'

clearly it is changeable. If this were not possible a calculator could not be programmed to interpret this in a different way to another calculator. Yet clearly this has happened and people were still able to do maths and get the correct anwser to their question (as long as they understood what they were actually asking the calculator).

Originally posted by nightrider
If this were not possible a calculator could not be programmed to interpret this in a different way to another calculator.

Well - GIGO

Garbage in - Garbage out :rolleyes:

To save all this nonsense - can you find us some documentation somewhere that supports your mathematical theories?

Originally posted by Strix
Well - GIGO

Garbage in - Garbage out :rolleyes:

To save all this nonsense - can you find us some documentation somewhere that supports your mathematical theories?

read the manual of any calculator that doesnt conform to bosmas. This is nothing to do with mathematical theories.

Is there some fudamental axiom or theorem etc that says * must be evaluated before +. I dont mean a rule which is what bosmas is. I mean a proper mathematical proof that you cant write ( 1 +2 ) *3. Its just a convention and nothing more. Just like the metre is a convention that you dont have to use.

Originally posted by nightrider
read the manual of any calculator that doesnt conform to bosmas. This is nothing to do with mathematical theories.


What a calculator does and in what order is irrelevant to the answer to the equation. The operator needs to understand how the calculator 'thinks' and enter the numbers accordingly.

Prodding buttons mindlessly on a machine doesn't give you correct answers.

Originally posted by nightrider
Is there some fudamental axiom or theorem etc that says * must be evaluated before +. I dont mean a rule which is what bosmas is. I mean a proper mathematical proof that you cant write ( 1 +2 ) *3.

You can write that equation, but without brackets bosmas applies.

Originally posted by nightrider
Just like the metre is a convention that you dont have to use.
To use your terminology:

Bad example. Measuring in imperial instead of metric doesn't increase the distance between the points, whereas your 123 argument does change the size of he answer!

Originally posted by Strix
No it isn't. And Slough isn't pronounced 'Sluff'

No, but slough is!:D

I'll get my coat, then!

:hihi: :suspect:

No wonder I coudn't figure out what BOSMAS was. I knew it was supposed to tell us what order to do stuff in,

it's BODMAS :hihi:

Originally posted by Strix
What a calculator does and in what order is irrelevant to the answer to the equation. The operator needs to understand how the calculator 'thinks' and enter the numbers accordingly.

Prodding buttons mindlessly on a machine doesn't give you correct answers.

so if the calculator does not use bosmas then you have to not think in bosmas. I never suggested one should mindlessly prod buttons. Before you use the calculator for serious work you need to understand the convention (i.e. bosmas or something else?) and phrase your question accordingly. Neither convention is wrong. Both wil give correct anwsers to your questions as long as you know how to ask the questions.

Originally posted by Strix

You can write that equation, but without brackets bosmas applies.


To use your terminology:

Bad example. Measuring in imperial instead of metric doesn't increase the distance between the points, whereas your 123 argument does change the size of he answer!

the point is you have to understand the convention being used. If you measure something in inches and assume the number you measured is in metres then the anwser is not telling you what you think it does.

If you use a calculator and assume it uses bosmas, when in fact it does not, then the anwser to your question is not telling you what you think it does.

So in that way the analogy does hold.

You cant say slough is pronounced one way and use that to suggest that for all other issues there is only 1 method to be used.

Originally posted by cgksheff
No, but slough is!:D

I'll get my coat, then!

Which means something entirely different, and proves my point further!

Thanks CGK :thumbsup:

Sling the calculator out of this argument nightrider. It's confusing the issue.

if you see 1 + 2 x 3 written down on paper, the answer your head should give you is 7.

If you can't make the calculator tell you this, then you'll get the answer wrong.

Calculators don't write the rules.

Some reading material ;) :
http://www.easymaths.com/
http://www.easymaths.com/What_on_earth_is_Bodmas.htm

And if you prod all those figures sequentially into an adding machine it will give you the answer 5, which is clearly wrong!!!

Originally posted by Strix
Sling the calculator out of this argument nightrider. It's confusing the issue.

if you see 1 + 2 x 3 written down on paper, the answer your head should give you is 7.

If you can't make the calculator tell you this, then you'll get the answer wrong.

Calculators don't write the rules.

Some reading material ;) :
http://www.easymaths.com/
http://www.easymaths.com/What_on_earth_is_Bodmas.htm

1 + 2 * 3 doesnt mean anything unless you know what the person who wrote it intended it to mean. How can you be sure they are using bosmas? You cant. If they are not then when you apply bosmas you get an unintended anwser.

Who said calculators write the rules? They dont. But the people who program them can.

Originally posted by nightrider
Who said calculators write the rules? They dont. But the people who program them can.
The people who program them have maths/computing qualifications so take for granted mathematical rules and assume we all know them :rolleyes:

According to your way of thinking, x could mean 'subtract 4', because that's what the person who wrote it intended it to mean (just to prove how silly you are being)

We're still waiting for your 'evidence' that maths bends to your will.

I've got better things to do. I'm off. :wave:

Originally posted by Strix
And if you prod all those figures sequentially into an adding machine it will give you the answer 5, which is clearly wrong!!!

The anwser would be 6 though surely? (1 + 2 ) +3 is 6, as is 1 + (2 +3 ).

Anyway if it adds things in some other way to get 5 then it does give the correct anwser to the question being asked. The user has to understand what he is asking the machine though for the anwser to be useful.

The BOSMAS (or BIDMAS as I was taught) has to be followed, otherwise algebra doesn't work properly.

For example, the equasion 1 + 2x = 3x - 4, if BIDMAS is followed, the answer is x=5. If you do it sequencially like night rider is suggesting, you get as follows:

(1+2)x = (3x) - 4
...
3x = 3x - 4
...
3x - 3x = -4
...
0 = -4 :confused:

Doesn't work as you can see...

Originally posted by Strix
The people who program them have maths/computing qualifications so take for granted mathematical rules and assume we all know them :rolleyes:

According to your way of thinking, x could mean 'subtract 4', because that's what the person who wrote it intended it to mean (just to prove how silly you are being)


No it couldnt. You cant change what multiplication is. You can change the order in which you apply operators since it is a choice to be made. See:

http://mathforum.org/library/drmath/view/52582.html

e.g. this is relevant from the above

3. Some of the specific rules were not yet established in Cajori's own
time (the 1920s). He points out that there was disagreement as to
whether multiplication should have precedence over division, or
whether they should be treated equally. The general rule was that
parentheses should be used to clarify one's meaning - which is still
a very good rule. I have not yet found any twentieth-century
declarations that resolved these issues, so I do not know how they
were resolved. You can see this in "Earliest Uses of Symbols of
Operation" at:

Originally posted by Sidla
The BOSMAS (or BIDMAS as I was taught) has to be followed, otherwise algebra doesn't work properly.

For example, the equasion 1 + 2x = 3x - 4, if BIDMAS is followed, the answer is x=5. If you do it sequencially like night rider is suggesting, you get as follows:

(1+2)x = (3x) - 4
...
3x = 3x - 4
...
3x - 3x = -4
...
0 = -4 :confused:

Doesn't work as you can see...

thats because you are refferring to equations and they need a slightly more complex explanation:

Clearly if an equation is correct you cannot arbitrailty insert brackets if you want it to still work. 1 + 2 *3 is not an equation because you have not set it equal to anything at all.

If someone wrote

1 + 2 *3 = 9

then clearly you can only insert the brackets one way in order to keep the equation correct.

Same goes for the equation 1 +2 *3 = 7. It can only mean 1 +(2 *3) =7.

As long as you define what the convention (bosmas or other) is then you can write equations and they will work as long as you know the correct way to interpret them.

If someone (e.g. certain calculator builders) defines that + should be evaluated before * then the equation 1 +2 *3 = 7 is valid and algebra still works.

This is the whole point - bosmas/bidmas or whatever is just a notation, albeit perhaps a widelly used one. It is not any sort of fundamental mathematical truth.

Originally posted by nightrider
what computational errors? I imagine if it can display 10 decimal places and you divide two numbers accurate to 10 decimal places then yes some rounding is doen and it isnt totally accurate. But the average person isnt going to have this situation. Are there other computational errors?


Famously it seems -
from wikipedia
A curious episode of the mid 1970s involved the Melcor 635, a scientific calculator with a bug in its trigonometric functions. Because the CORDIC algorithms used in most calculators cannot compute the inverse functions of zero, these need to be hardcoded—and some engineer at Melcor got it wrong. For any input other than exactly zero, even for instance 1.0E-99, the calculator worked correctly; the user simply had to remember not to compute the arc-cosine of zero

A calculator is only as good as the person who programmed it.

Considering it is impossible to prevent anyone entering incalculable arithmetic, programmers need to write all the required exception handlers for a pocket calculator. I'm still googling but there have been many instances of bad programming of calculators, underline the point that your brain is much more reliable than a calculator. If my life depended on a sum, I would do it on paper, not on a calculator.

Reason 1. Mis-keying the sum
Reason 2. Bad calculator programming
Reason 3. Faulty Readout (bar from LCD missing - 8 becomes 0 etc)
As regards calculators and arithmetic order - this is an inescapable feature of simple arithmetic calculators if they continuously update the total, rather than just waiting until you hit the "=" button.

Solution, have a calculator without an = button. Simple!

Originally posted by nightrider
thats because you are refferring to equations and they need a slightly more complex explanation:

Clearly if an equation is correct you cannot arbitrailty insert brackets if you want it to still work. 1 + 2 *3 is not an equation because you have not set it equal to anything at all.

If someone wrote

1 + 2 *3 = 9

then clearly you can only insert the brackets one way in order to keep the equation correct.

Same goes for the equation 1 +2 *3 = 7. It can only mean 1 +(2 *3) =7.

As long as you define what the convention (bosmas or other) is then you can write equations and they will work as long as you know the correct way to interpret them.

If someone (e.g. certain calculator builders) defines that + should be evaluated before * then the equation 1 +2 *3 = 7 is valid and algebra still works.

This is the whole point - bosmas/bidmas or whatever is just a notation, albeit perhaps a widelly used one. It is not any sort of fundamental mathematical truth.
My point was that you don't need the brackets, with or without algebra. Multiplication first is the only logical way of doing sums. If you do need to do addition first then you use brackets.

Originally posted by Sidla
My point was that you don't need the brackets, with or without algebra. Multiplication first is the only logical way of doing sums. If you do need to do addition first then you use brackets.

On the one hand you say you dont need brackets and on the other you must do multiplication first - this is equivalent to inserting a pair of brackets. So I disagree with you here. 1 + 2 *3 is meaningless without a method to interpret what it means - insert brackets in a certain way or choose which order to evaluate the operators (which in the end is the same thing essentially).

Originally posted by Sidla
My point was that you don't need the brackets, with or without algebra. Multiplication first is the only logical way of doing sums.

why is it the only logical way?

Originally posted by nightrider
why is it the only logical way?

you are right that it is not an unyielding law of mathematics that determines the precedence of operators, but a convention. But because of the ambiguity of sums written like
1 + 2 * 3 = ? a widely accepted convention is required, such as BODMAS (Brackets, Order, Division, Multiplication, Addition Subtraction). This is taught, worldwide, as the method for evaulating any equation. Hence the confusion with pocket calculators that simply constantly evaluate the result in the order that the symbols appear.

Better still would be to use RPN if you are actually missing one half of the equation, in our case a simple arithmetic problem.

2 3* 1+ ->7
2 1+ 3* ->9
2 3+ 1* ->5
1 3+ 2* ->8 etc.

no ambiguities there!

Originally posted by nightrider
what computational errors? I imagine if it can display 10 decimal places and you divide two numbers accurate to 10 decimal places then yes some rounding is doen and it isnt totally accurate. But the average person isnt going to have this situation. Are there other computational errors?

I think this was your first post.

In which case you question has been answered with the cosine (0) problem detailed a few posts back.

Originally posted by nightrider
reading that left to right: 1 +2 is 3. If you type that into a caclulator it gives 3. Then press x 3. What is 3 x 3? It is 9, and not 7.

So I dont understand the problem. I dont believe most calculators (and mine doesnt) will give 7 if you type 1 +2 x 3 in; all calculators I have ever had do things in the order you type them which seems pretty sensible to me.

Ah - and then you go on to demonstrate that you don't understand the convention of operator precedence and when it's explained to you you tell us that we are all wrong and that as it's merely convention actually the calculators are perfectly valid.

Well, as I think I said, any language depends on it's conventions.
The operator precendence conventions are well established, and the calculators are the only things in the world that break them. Computer languages follow them, mathematicians follow them and GCSE level students should follow them.
You may continue to assert that it's only a convention, and we agree, it's not a rule of mathematics itself, just one that we apply. But it is accepted by everyone who matters (and I don't count myself amongst that group, not being a professor of mathematics).

Sorry, meant to post this before the previous 2 of my posts.

the text you quote to us there clearly implies that the rules weren't agreed on in the 20's and are now. Otherwise it wouldn't say "were not yet".

So the rules have been agreed, the calculator manufacturers did it differently.

What is your point anyway, I can't actually remember?

Originally posted by nightrider
No it couldnt. You cant change what multiplication is. You can change the order in which you apply operators since it is a choice to be made. See:

http://mathforum.org/library/drmath/view/52582.html

e.g. this is relevant from the above

3. Some of the specific rules were not yet established in Cajori's own
time (the 1920s). He points out that there was disagreement as to
whether multiplication should have precedence over division, or
whether they should be treated equally. The general rule was that
parentheses should be used to clarify one's meaning - which is still
a very good rule. I have not yet found any twentieth-century
declarations that resolved these issues, so I do not know how they
were resolved. You can see this in "Earliest Uses of Symbols of
Operation" at:

Originally posted by Phanerothyme
you are right that it is not an unyielding law of mathematics that determines the precedence of operators, but a convention. But because of the ambiguity of sums written like
1 + 2 * 3 = ? a widely accepted convention is required, such as BODMAS (Brackets, Order, Division, Multiplication, Addition Subtraction). This is taught, worldwide, as the method for evaulating any equation. Hence the confusion with pocket calculators that simply constantly evaluate the result in the order that the symbols appear.


so finally we can all agree the prcedence is a convention. I agree it is sensible that everyone uses a common convention. What I wont agree is that someone can say it is "wrong" or "incorrect" to use another system that is just as valid (in the sense that it gives sensible anwsers if you know the rules of operator precedence in use in that system).

Originally posted by Cyclone
Ah - and then you go on to demonstrate that you don't understand the convention of operator precedence and when it's explained to you you tell us that we are all wrong and that as it's merely convention actually the calculators are perfectly valid.


I understand perfectly well what operator precedence is. The calculators are valid. If you know how to use them they give sensible answers.

Originally posted by Cyclone
Sorry, meant to post this before the previous 2 of my posts.

the text you quote to us there clearly implies that the rules weren't agreed on in the 20's and are now. Otherwise it wouldn't say "were not yet".

So the rules have been agreed, the calculator manufacturers did it differently.

What is your point anyway, I can't actually remember?

my point was that BOSMAS is not a unique way to do algebra/arithmatic. Some people were insisiting any other way was "wrong" or "incorrect" when in fact it is merely different. It is also inconvenient due to the fact BOSMAS is (apparently) widely used, so noone (except large numbers of calculators) would know what you meantif you used a different system (unless you told them this).

Originally posted by nightrider
I understand perfectly well what operator precedence is. The calculators are valid. If you know how to use them they give sensible answers.

I think this all goes to show that pocket calculators are great for quickly doing long multiplication and division, but its always worth checking your result if a lot depends on it.

Originally posted by Strix
:hihi: :suspect:

No wonder I coudn't figure out what BOSMAS was. I knew it was supposed to tell us what order to do stuff in,

it's BODMAS :hihi:

I've never known it called BOSMAS either. It's changed to BIDMAS now where I=indices. Apparently O=order of is too confusing for the kids.

Taught long division to a top set year seven class a few weeks, many of them got confused and insisted on using a carry over method which is fine when you get factor of the original number as your answer. When you want to calculate to n decimal places it goes wrong.

Many primary schools also teach a repeated subtraction method as opposed to long division now.

Originally posted by jessycar
Many primary schools also teach a repeated subtraction method as opposed to long division now.

How does that work?

You keep taking amounts off

This site explains better than I can on here without being able to set it out properly :0)

http://www.homeschoolmath.net/md2/long_division.php

A teacher friend of mine said when we were talking about these modern methods of teaching arithmetic that the way we we taught in the 40s and 50s were old fashioned and outdated.
I politly pointed out that those old fasioned methods had allowed people to invent steam engines internal combustion engines, radio, television, and put men on the moon . we will have to wait to see what be comes out of these modern methods. Oh forgot and computers)

I have to admit that when I tried to do some of my grandson's way of arithmetic I did'nt have a clue as how they did it, most complicated.
What ever happened to Units Tens Hundred Thousands?

Originally posted by prioryx
I politly pointed out that those old fasioned methods had allowed people to invent steam engines internal combustion engines, radio, television, and put men on the moon . we will have to wait to see what be comes out of these modern methods. Oh forgot and computers)[/B]

The people who go on to invent steam engines, radios etc. are the bright kids who would pick it up whatever method you taught them. I wasn't taught "long division" or "repeated subtraction" but I can do a division sum pretty accurately in my head, and I expect anyone else who is reasonably intelligent could do pretty much the same to a greater or lesser extent.

A good method to teach kids is one that actually makes it clear why they are doing it that way and why it works. If you just mindlessly follow an algorithm like long division then how are you going to know if the answer you get makes any sense?

The actual method you use to do the calculation is not as important as understanding the principles behind it. I don't think anyone is denying that long division "works" though.

Originally posted by jessycar
You keep taking amounts off

This site explains better than I can on here without being able to set it out properly :0)

http://www.homeschoolmath.net/md2/long_division.php
That's quite a good method, for the first time in my life I think I understand long division! Cheers for that.

Having said this though, why would you go to all that effort, when it would be quicker to stick it in a calculator?

Originally posted by Sidla
Having said this though, why would you go to all that effort, when it would be quicker to stick it in a calculator?
:rolleyes: Don't start that again! you still need to know the answer you get is right. If you hit the wrong button without noticing, or the batteries are getting flat, you could get bobbins out of the calculator

It's quite a while now since I left school, but I can still do long division. However, I've never mastered how to use a calculator!

Originally posted by Strix
:rolleyes: Don't start that again! you still need to know the answer you get is right. If you hit the wrong button without noticing, or the batteries are getting flat, you could get bobbins out of the calculator
Yeah, but any fool who can add up should already know approximately the answer they're expecting to get anyway. It's easier to make a mistake on paper than it is to hit the wrong button on a calculator IMO, especially if you're checking the number you input. If you don't trust a calculator and double check all your sums on paper, it would make life excedingly difficult.

Originally posted by Sidla
... should already know approximately the answer they're expecting to get ...
That's the bit that some people overlook though, usually through laziness or too much dependance on 'technology' ;)

I am now going to invent a thing called a PENCIL.
with this you will be able write on another of my inventions called PAPER.
You should then write down on the said paper with the aforesaid pencil the figures required to perform the long division query that started this thread and using the brain( which is in the head) work out the answer.

120 divided by 5
5 divided by 120