# Simple Maths.



## Drew

15 - 12 ÷ (6 ÷ 2) x 4 + 3 = ?

What is the answer to the above equation.


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## Pudsey_Bear

I give up, absotively rubbish at maffs.


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## GMJ

I'll play - 7?


Graham :smile2:


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## JanHank

I go with Grahams 7 do we need to show how?


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## nicholsong

Well obviously not written by a mathematician because it could mean

(15-12) divided by (6 divided by 2) x 4 + 3

OR

15 - [12 divded by (6 divided by2)] x 4 + 3

OR

Either of the above but with ' x (4+3)' at the end.

Go back to square one.

Annotation is all.

Geoff


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## JanHank

nicholsong said:


> Well obviously not written by a mathematician because it could mean
> 
> (15-12) divided by (6 divided by 2) x 4 + 3
> 
> OR
> 
> 15 - [12 divded by (6 divided by2)] x 4 + 3
> 
> OR
> 
> Either of the above but with ' x (4+3)' at the end.
> 
> Go back to square one.
> 
> Conotation is all.
> 
> Geoff


I don't think Uncle Geoffrey understood the question , we don't need another riddle, just an answer to Uncle Drews simple maths question.
Or am I wrong Drew?


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## peejay

Three


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## Drew

Due to the lack of posts on the forum I thought I would set a relatively easy arithmetic problem containing, addition - subtraction - multiplication and division.

I can assure you that it is correctly written with only on answer. So far no one has given the correct answer.

Drew


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## ob1

Eight? 

No - it's 7, which we are already told is wrong! :surprise:


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## GEMMY

47................... forty seven


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## JanHank

Where has my answer of 4 got to?


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## p-c

Hi
I agree with 7. 
But very tentively
9 1/3
BODMAS but never really understood it.
Regards
p-c


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## dghr272

2

Terry


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## GEMMY

Someone has just googled it :surprise::frown2:


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## Drew

Right Terry,

How did you come to your answer?


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## barryd

2 


ish


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## dghr272

15-12/(6/2)x4+3
15-12/3x4+3
15-4x4+3
15-16+3
-1+3
=2

Edit: BODMAS, my maths teacher would be proud.


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## dghr272

GEMMY said:


> 47................... forty seven


Still wearing the rose tinted glasses, as to your great Mensa score, did you mark your own paper ???:grin2:


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## Drew

*B O D M A S *

1, *B*rackets

2, *OF* (Multiplication)

3, *D*ivision

4, *M*ultiplication,

5, *A*ddition.

6, *S*ubtraction.


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## JanHank

Obviously Drew that was not a simple sum coz I still haven't a clue how Terry came to that answer.:frown2:


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## GEMMY

dghr272 said:


> Still wearing the rose tinted glasses, as to your great Mensa score, did you mark your own paper ???:grin2:


I googled AFTERWARDS unlike ????????????


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## dghr272

JanHank said:


> Obviously Drew that was not a simple sum coz I still haven't a clue how Terry came to that answer.:frown2:


See my step by step workings out above Milly or ask Hans he'll know.

Terry


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## JanHank

dghr272 said:


> See my step by step workings out above Milly or *ask Hans he'll know.
> *
> Terry


Not so sure about that :grin2:


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## JanHank

He doesn't have a clue either.


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## p-c

p-c said:


> BODMAS but never really understood it.
> p-c


I said I never understood it.
So even knowing BODMAS I couldn't do the sum.
Hey ho
p-c


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## eurajohn

According to my calculator the answer is 2.

.


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## GMJ

eurajohn said:


> According to my calculator the answer is 2.
> 
> .


...or according to posts #13 , #15 , #17 and #19 above!

Graham:smile2:


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## Drew

An easier one, just follow B O D M A S.

*4 + 3 (5 - 2) =*


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## charlieivan

Using BODMAS it should be 13


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## Pudsey_Bear

Why have we gone back to skool Drew:?:


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## caulkhead

Kev_n_Liz said:


> Why have we gone back to skool Drew:?:


It's a crafty ploy to get us behind the bike sheds so he can cadge some **** of us:wink2:


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## Pudsey_Bear

I have no idea what that means ???


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## caulkhead

Kev_n_Liz said:


> I have no idea what that means ???


Bludy predictive text! See my edit......:frown2:


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## Pudsey_Bear

Ah, he has a cunning plan, wasted on me, didn't start til I left school, STUPID BOY, someone said about 12 years ago "don't die of stupidity", I stopped soon after, had asthma since then :roll:


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## barryd

caulkhead said:


> It's a crafty ploy to get us behind the bike sheds so he can cadge some **** of us:wink2:


Ahhh! The back of the bike sheds. Happy memories (but I Didnt smoke)


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## Pudsey_Bear

Spill, wot/who were you doing.


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## Drew

For those interested.

*"Example: *

*In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?*

We know there are 14 chairs, but how do we write this calculation? If we just write  2 + 3 x 4  how would you know whether the answer is  2 + 3 = 5, then multiply by 4 to get 20 or  3 x 4 = 12, then 2 + 12 to get 14?

 There are two steps needed to find the answer; addition and multiplication. Without an agreed order of when we perform each of these operations to calculate a written expression, we could get two different answers.

For all of us to arrive at the "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.

One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this: 2 + (3 x 4) The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.

Another example: Calculate 15- 10 ÷ 5

If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13.

Therefore we need an agreed order, hence *B O M D A S*

I hope that this explains everything. Thank you to all who have joined in.


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## nicholsong

I had never heard of BOMDAS until this thread and I managed to pass 'A' Level Mathematics in 1960.


As far as I can see it is a convention which effectively avoids correct annotation.


I wonder in how many countries it is used. If not universal, then scientists communicating across cultures would still need to use fuller annotation, instead of relying on a convention which is not universal.



I therefore stick with the various interpretations of the question format posed in my post number 5, which interpretations, if worked through, give widely different answers.


Conventions are only useful if everybody adhers to them, but if some people, e.g. me, have never been introduced to them then all interpretations are open.


I rest my case.


Geoff


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## GMJ

I was taught BODMAS not bomdas!


Anyway, I'm off as I'm bored by this now...


Graham :smile2:


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## nicholsong

Drew said:


> For those interested.
> 
> *"Example: *
> 
> *In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?*
> 
> We know there are 14 chairs, but how do we write this calculation? If we just write  2 + 3 x 4  how would you know whether the answer is  2 + 3 = 5, then multiply by 4 to get 20 or  3 x 4 = 12, then 2 + 12 to get 14?
> 
> There are two steps needed to find the answer; addition and multiplication. Without an agreed order of when we perform each of these operations to calculate a written expression, we could get two different answers.
> 
> For all of us to arrive at the "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.
> 
> One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this: 2 + (3 x 4) The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.
> 
> Another example: *Calculate 15- 10 ÷ 5*
> 
> If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13.
> 
> Therefore we need an agreed order, hence *B O M D A S*
> 
> I hope that this explains everything. Thank you to all who have joined in.


If the question had read 15 - (10 divided by 5) then one would not need a convention like BOMDAS.

My point in my post before yours.

Geoff


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## Pudsey_Bear

Any danger of an answer to the OP Drew.


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## HurricaneSmith

I was drilled in BODMAS at SCHOOL and can't forget it.

It pays to think uniformally, especially when using automated space flight:
https://en.m.wikipedia.org/wiki/Mars_Climate_Orbiter

OK, that was a unit error, but the principle stands, I think.


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## Drew

Therefore we need an agreed order, hence *B O M D A S*

Typing error, should be as in my previous post, *B O D M A S* my apologies.


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## Drew

GMJ said:


> I'll play - 7?
> 
> Graham :smile2:





GMJ said:


> I was taught BODMAS not bomdas!
> 
> Anyway, I'm off as I'm bored by this now...
> 
> Graham :smile2:


Unfortunately your answer, *-7* using the system you were taught was wrong.

I unfortunately typed BOMDAS instead of BODMAS in my last post. Sorry to bore you Graham. As I explained, I only started this to fill the gap in the threads.


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## Drew

Kev_n_Liz said:


> Any danger of an answer to the OP Drew.


15 - 12 ÷ (6 ÷ 2) x 4 + 3

15 - 12 ÷ 3 x 4 + 3

15 - 4 x 4 + 3

15 - 16 x 4 + 3

-1 + 3

*2*


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## nicholsong

Drew said:


> Therefore we need an* agreed order*, hence *B O M D A S*
> 
> Typing error, should be as in my previous post, *B O D M A S* my apologies.


 Drew you wrote to Graham that

'Unfortunately your answer, *7* using the system you were taught was wrong.' Not correct; using one system it was the correct answer, but maybe you meant to say he was taught the 'wrong' system. If so, that seems a bit dictatorial. There are many ways of using mathematical systems and none of them are perfect - not even yours.

But getting and distributing that 'agreed order(system)' is not so easy - certainly that one had not reached me - nor have I agreed.

I prefer an 'unequivocal' system, not one 'agreed', of which I had not heard.

How would your 'system' work with a mathematical formula using base 'e' or base 'n' ?

I once flew an aircraft where the fuel guages were in Imperial gallons, the flow meters were in pounds, the tank drip-sticks were in US gallons and for the load sheet we used kilograms. I cannot remember what Specific Gravity assumptions the CAA required us to use at different airfields. I always made the Co-Pilot and I do a cross-check with the papers, the guages and the re-fuellers upload.

Geoff


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## erneboy

Drew said:


> 15 - 12 ÷ (6 ÷ 2) x 4 + 3
> 
> 15 - 12 ÷ 3 x 4 + 3
> 
> 15 - 4 x 4 + 3
> 
> 15 - 16 x 4 + 3 ?? *Surely that's 15-16+3 as Terry said?* My insertion.
> 
> -1 + 3
> 
> *2*


The bold comment 2 lines up is mine.

Here's Terry's which eventually made sense to me
15-12/(6/2)x4+3
15-12/3x4+3
15-4x4+3
15-16+3
-1+3
=2


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## Pudsey_Bear

I did it on my phone the other day Drew, to get the 2 I posted (if it posted) but for some reason it willn't do a screendump, so here it is all Googlified

http://tinyurl.com/y6uad349


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## Pudsey_Bear

Aha, got it to do it, had to do it twice because it disappears when you press the =


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## Pat-H

I vaguely remembered there was a preferred order in mathematical calculations but its far easier to be clear with brackets why would anyone want to leave it less clear? Also as the equation gets more complex and larger without brackets its far easier to make a mistake.


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## Pudsey_Bear

I just worked from left to right.


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## nicholsong

Pat-H said:


> I vaguely remembered there was a preferred order in mathematical calculations but its far easier to be clear with brackets why would anyone want to leave it less clear? Also as the equation gets more complex and larger without brackets its far easier to make a mistake.


Applause Pat.:grin2:


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## GMJ

Drew said:


> Unfortunately your answer, *-7* using the system you were taught was wrong.
> 
> I unfortunately typed BOMDAS instead of BODMAS in my last post. Sorry to bore you Graham. As I explained, I only started this to fill the gap in the threads.


No Drew you are wrong!

I was taught the correct system which is still in use today.

Whether I remembered it when I did your sum is another matter altogether!:grin2:

Graham :smile2:


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## barryd

I Was totally crap at Maths at school and they told me I Could never be allowed to use the single computer we had as I wasnt mathematical and as part of my HND in computer science later at college I had to pass a "Quantitative Methods" one year module which is a posh word for Maths. I flunked it of course and had to do a resit. If I had failed I would have never had an IT career probably. I sat it on my own with the lecturer adjudicating. He was a fab bloke and everyone loved him. We used to go drinking together now and again and every now and again he would pass my desk during the resit, Cough a bit or mumble some help when I Was cocking it up. I scraped through by about 5%. 

I have to say though that in nearly 30 years of working in IT even as a programmer for several of the early years only a basic understanding of Algebra and basic maths for creating arrays and stuff like that was ever required. Total fantasy that you needed complex mathematical ability to work in IT.


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## GMJ

I got a grade A for my O Level and was then eternally grateful to leave the subject behind...


As it was done in pre-calculator days I am very proud of my mental arithmetic which is still very sharp. 



I never fail to be amazed at how poor young people's mental arithmetic is due in part because they are lazy; and they have phones to do sums on; and because of the use of calculators for at least part of their GCSE Maths meant that they didn't have to think too hard!


Graham :smile2:


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## emmbeedee

GMJ said:


> I got a grade A for my O Level and was then eternally grateful to leave the subject behind...
> 
> As it was done in pre-calculator days I am very proud of my mental arithmetic which is still very sharp.
> 
> I never fail to be amazed at how poor young people's mental arithmetic is due in part because they are lazy; and they have phones to do sums on; and because of the use of calculators for at least part of their GCSE Maths meant that they didn't have to think too hard!
> 
> Graham :smile2:


A new branch of Screwfix opened here recently & they had a discount event to publicise it. I went along to get a few electrical items which were advised as 15% off, with both regular & 15% off prices marked up. I pointed out that the discount prices of some items were incorrect as even though my mental arithmetic is not that great 15% is dead easy. Great consternation, none of the staff could check this out. They had to fetch the manageress & then she had to send for a calculator. I was quite shocked TBH.


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## charlieivan

A few years ago I went into a pet shop for some dog food. I asked for 10 lbs of food priced at 18p/ lb. Young girl assistant who served me worked out the price as £1.65. I queried her price and the shop owner checked it for her and eventually came up with £1.80. He then remarked that multiplying by ten should be easy as all you need to do is add a zero. The poor young girl just couldn't work it out !!!


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## emmbeedee

nicholsong said:


> I once flew an aircraft where the fuel guages were in Imperial gallons, the flow meters were in pounds, the tank drip-sticks were in US gallons and for the load sheet we used kilograms. I cannot remember what Specific Gravity assumptions the CAA required us to use at different airfields. I always made the Co-Pilot and I do a cross-check with the papers, the guages and the re-fuellers upload.
> 
> Geoff


Geoff, are you aware of the "Gimli Glider"? This was an Air Canada flight, an almost new 767, which attempted to fly across Canada with only about half the fuel required. This was due to an incorrect conversion being used, in the early days of metric being introduced by Air Canada. By great good fortune, one of the pilots was also a glider pilot & he used gliding techniques to bring the plane down at a de-commissioned RCAF base, in use as a car race track at the time. Amazing story, details here:

https://en.wikipedia.org/wiki/Gimli_Glider


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## bennyyorkie

Right....I work in advanced math so from my point of view...the problem arises from the 4+3.
Because it is not in brackets (4+3)...then the rest is =1 and this then must be multiplied by 4 and add 3 to the answer.
Therefore the answer is indeed 7. 
In maths there is a standard order to calculations, so I cant see how there could be another answer 
If there is...God help us all..hehe!!


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## Pudsey_Bear

I don't know about all that but Google says it = 2. 

If there were/are special conditions or considerations to take into account they should be in the OP, unless it was meant to be a trick question.


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## nicholsong

barryd said:


> I have to say though that in nearly 30 years of working in IT even as a programmer for several of the early years only a* basic *understandingof Algebra and basic maths for creating arrays and stuff like that was ever required. Total fantasy that you needed complex mathematical ability to work in IT.


We will let that pun wash over our heads.


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## DBK

I'm new here but I'll give it a go. 

15 – 12 ÷ (6 ÷ 2) x 4 + 3 = ?

The convention is to do the multiplication and division first working from the left but tackling stuff in brackets first.

15 – 12 ÷ (3) x 4 + 3 = ?

15 – 4 x 4 + 3 = ?

15 - 16 + 3 = ?

Then you do the addition and subtraction, again working from the left.

-1 + 3 = 2

So the answer is 2.


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## Pudsey_Bear

Hi DBK, I just worked left to right, got 2 too.


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## nicholsong

emmbeedee said:


> Geoff, are you aware of the "Gimli Glider"? This was an Air Canada flight, an almost new 767, which attempted to fly across Canada with only about half the fuel required. This was due to an incorrect conversion being used, in the early days of metric being introduced by Air Canada. By great good fortune, one of the pilots was also a glider pilot & he used gliding techniques to bring the plane down at a de-commissioned RCAF base, in use as a car race track at the time. Amazing story, details here:
> 
> https://en.wikipedia.org/wiki/Gimli_Glider


Yes, knew all the details of that incident.

I nearly added it to my post but thought I would be going too off-topic.

Without the Co-Pilot's RCAF experience of the defunct airfield they might have been in real trouble, because it would not have been on any charts.

That incident reinforced my insisting on cross-checking the fuel up-load.

As an Aviation Lawyer I was also involved in a case where a Viscount landed short of Exeter Airport due to a fuel uplift problem. It was interesting because I had flown Viscounts, but also had known Geoff Whittaker the Captain. It involved getting the Accident Investigation Report altered in favour of our Client. Long story.

Geoff


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## pete4x4

I'd have gone -4


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## GMJ

bennyyorkie said:


> Right....I work in advanced math so from my point of view...the problem arises from the 4+3.
> Because it is not in brackets (4+3)...then the rest is =1 and this then must be multiplied by 4 and add 3 to the answer.
> Therefore the answer is indeed 7.
> In maths there is a standard order to calculations, so I cant see how there could be another answer
> If there is...God help us all..hehe!!


See I knew I was right :grin2::wink2:

Graham :smile2:


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## Pudsey_Bear

SEVEN PAGES is unbelievable Normally there would have been a definitive answer from the questioner by now.

I'm out.


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## raynipper

8.

Ray.


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## p-c

Hi
I'll confuse it more. It is also known as BIDMAS.
Regards
p-c


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## Drew

*


Drew said:



Right Terry,

How did you come to your answer?

Click to expand...

*



DBK said:


> I'm new here but I'll give it a go.
> 
> 15 - 12 ÷ (6 ÷ 2) x 4 + 3 = ?
> 
> The convention is to do the multiplication and division first working from the left but tackling stuff in brackets first.
> 
> 15 - 12 ÷ (3) x 4 + 3 = ?
> 
> 15 - 4 x 4 + 3 = ?
> 
> 15 - 16 + 3 = ?
> 
> Then you do the addition and subtraction, again working from the left.
> 
> -1 + 3 = 2
> 
> *So the answer is 2. *




If I need to spelt out for you Kev. *The answer is 2*


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## raynipper

Well my answer is still 8.

Ray.


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## Drew

raynipper said:


> Well my answer is still 8.
> 
> Ray.


That is entirely up to you Ray. perhaps you will explain how you arrived at 8?

The correct answer is* 2*


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## raynipper

15 – 12 ÷ (6 ÷ 2) x 4 + 3 = ?

Do the calk within brackets first = 3.

15 - 12 = 3.
Divide contents of brackets 3 = 1.

1 x 4 = 4 (my mistake cos I thought it was +)

4 + 3 yes should be 7. My mistake.

Ray.


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## dghr272

After Brackets Division and multiplication should be done before addition and subtraction, dats da rule.

Terry


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## nicholsong

Drew said:


> That is entirely up to you Ray. perhaps you will explain how you arrived at 8?
> 
> The correct answer is* 2*


'Drew's Rule' rules OK.

Have you got that?

Anything else is '*FAKE NEWS'*


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## cerenzop

I wonder in how many countries it is used. If not universal, then scientists communicating across cultures would still need to use fuller annotation, instead of relying on a convention which is not universal.  techzpod download mobdro


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## GMJ

Thanks for that


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## Webby1

Welcome @cerenzop ....you do realise that your first post has brought up a 4 year old thread.
But do tell us more about yourself......do you have a motorhome....................is that an Indian flag I see on your avatar ???


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## GMJ

Good luck with that Pete


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