Mathemagicians - Help my brain fog here!

Scott

Scott

Behold The Ford Mondeo
Moderator
Ok, I saw an equation on FB that's apparently dividing the world. The world is already split... you either know how to do this stuff.... or you don't, so it's hardly a time to call Ripley's when people disagree. However, I'm disagreeing with myself now as I can't for the life of me rationalise the logic.

Here is the exact problem

8 ÷ 2(2 + 2) = ?

Now.... to me, the answer is 16... because.....

8 ÷ 2(4) = ? (Brackets first)
8 ÷ 2 * 4 = ? (Spread out)
4 * 4 = ? (Left to right)
16 - Answer

The foggy part for me, is automatically assuming that 2 of something means multiplication. Here is where my head is taking me...

8 ÷ 2(x)

Why is the above 8 ÷ 2 * x and not 8 ÷ 2x

If it were 2x, and we substitute the 4 for the x, the answer becomes 1.

Is it as grey an area as it seems where there isn't really a rule, it's just an accepted given?

I completely understand that these equations are written with that particular grey area to cause the division..... but my real question is, with the grey area in play. Does that mean that both answers are in fact potentially correct?

I've tried numerous ways to rationalise the problem. I've tried multiplying both sides of the equation by the problematic part.... but that only makes it more difficult. If 2(x) is an actual thing..... and there isn't an assumption to be made..... does that make BODMAS incomplete and in need of an additional letter being stuck in there?

Or is 2(x) simply 2*x and not 2x?

Answers on a postcard please.
 
Scott

Scott

Behold The Ford Mondeo
Moderator
TonyCarter said:
Strict BODMAS would be
  • 8 ÷ 2(4) (brackets first) - and complete all the bracket-related sums first
  • 8 ÷ (2x4) don't remove the brackets, then you have to do the 2(4) first which equals 8
  • 8 ÷ 8 = 1
Click to expand...

Why do you have the 2 going inside the brackets though? The 2 was external to the brackets and you moved it inside to complete.

It's widely accepted that the answer is 16. Even following strict BODMAS.... which is what I did :D
 
D

Deleted member 17413

Guest
Half the issue is theres two different working sets of how to multiply it out, and US I think does brackets last, where we dont...

8 / 2(2+2)
8 / 2(2+2)
8 / 2(4)
8 / 8

The issue comes in when it comes to multipling the contents of the brackets, US i beleive teach 8 / 2 then x(2+2)
BODMAS (what we do here) multiples out the brackets first as above with what Tony says.

The reason its 1 is because theres no space or multiplication sign between the 2 and brackets,
8 / 2 x (2+2) = 16
8/2(2+2) = 1
 
D

Deleted member 17413

Guest
You're working with (effectively) two sets of numbers
(8) / (2(2+2))

And for an actual definitive answer, you would have to write it out fully...
xNE3cin.png
 
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steaky360

steaky360

Moderator
Moderator
sibun1 said:
The reason its 1 is because theres no space or multiplication sign between the 2 and brackets,
8 / 2 x (2+2) = 16
8/2(2+2) = 1
Click to expand...
I don't think this is correct, traditionally in the US and UK as far as I'm aware: 2(blah) is 2 x blah - you don't need additional notation to indicate a product/multiplication... its the same as 2x (where x is a discrete variable). ie 2x implies 2*x, 2(x) implies 2*(x) etc.

I guess that is unless you're using some alternative non-standard notation which didn't seem to be the case in the original statement... but I suppose this is where the disagreements lie :) - hence the prevalence of such questions on social media ;)
 
D

Deleted member 17413

Guest
For it to be written linearly, and equal 16, you would need another set of brackets
(8 / 2)(2+2)=16
 
D

Deleted member 17413

Guest
AgentCooper said:
I read it as 16... but this conversation is making my brain ache so that's where I'll sign off o_O
Click to expand...
The point is, theyre BOTH kinda answers are correct, and the only way to actually know which is which, it to write out the equation in its full terms, not as a linear chain.... but, its 1 if you follow BODMAS which tells you to do the brackets, multiple it by 2 and then divide 8 by your answer
 
Scott

Scott

Behold The Ford Mondeo
Moderator
The correct answer is definitely 16.... this isn't what I'm looking to debate. If you calculate 1 as being the answer, it'll throw my thread off topic.

My query is to ask why it's correct.

I understand that it's standard to assume...

8 ÷ 2(2 + 2) is the same as 8 ÷ 2 * (2 + 2)

but why is this....? It could so easily be interpreted as......

8
________
2(2 + 2)

Linearly is 8 ÷ (2(2 + 2)), or without the PITB accepted assumption - 8 ÷ (2 * (2 + 2))

8
__ * (2 + 2)
2

Linearly is 8 ÷ 2(2 + 2), or again without the grey assumption - 8 ÷ 2 * (2 + 2)


as @sibun1 is showing, it leaves the door open to interpretation when not wise to the accepted "norm" of doing something.

I don't like accepted norms, especially with mathematics. Otherwise the above would surely be a theory? Given it's such a simple equation, this should be very simply a hardened fact.

I don't like not knowing..... maybe the world is flat o_O
 
D

Deleted member 17413

Guest
By not having any space between the 2(2+2), its telling you to create 2 lots of the brackets
for it to be a chain, you have to break the 2(2+2) into 2 x (2+2) which it hasnt done.

Its not written as 8/2 x (2+2)
its been written as 8/ 2(2+2) which is different, as I showed above.. its lazy and incomplete maths, and there are two working methods when it comes to breaking down the equation
 
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Scott

Scott

Behold The Ford Mondeo
Moderator
sibun1 said:
By not having any space between the 2(2+2), its telling you to create 2 lots of the brackets
for it to be a chain, you have to break the 2(2+2) into 2 x (2+2) which it hasnt done.

Its not written as 8/2x(2+2)
its been written as 8/ 2(2+2) which is different, as I showed above.. its lazy and incomplete maths, and there are two working methods when it comes to breaking down the equation
Click to expand...

This is incorrect, this is what I'm trying to explain to you. I can't give you a rule on it.... because I can't find one, as that's what I'm trying to find.

The brackets are to contain something. Only what is within the bracket can be considered part of the brackets. This is a rule and cannot be refuted.

Inside the bracket is 2 + 2, which is obviously 4. Once what is inside the bracket has been solved..... the bracket disappears.

With the way it is written... this leaves 24.... or 2*4.

The human brain cannot work with 24.... so we presume 2(4). The brackets at this point are meaningless as what is inside them has already been solved.

The key to the whole confusion is why 2(4) becomes 2 * 4

It's an accepted norm...... but I cannot find a rule on it. It's just a given when it comes to maths. Well... from what I can tell it is..... and I want it to be a written statement of fact as my brain can see both sides of the argument while my study tells me it's assumed to follow a singular path.
 
Scott

Scott

Behold The Ford Mondeo
Moderator
Maybe..... Occam's razor....

8 ÷ 2(2 + 2) = ?

Is not an acceptable standard of mathematical equation. The acceptable standard is 8 ÷ 2 * (2 + 2) where there can be no misunderstanding.

Writing the equation in the shorthand format given allows for presumption. It's widely accepted that 2(2 + 2) is 2 * (2 + 2) but there is no formal clarification as 2(2 + 2) isn't formally recognised as a presentation of a formula.

It's now written here.... so that makes it official.
 
steaky360

steaky360

Moderator
Moderator
sibun1 said:
By not having any space between the 2(2+2), its telling you to create 2 lots of the brackets
for it to be a chain, you have to break the 2(2+2) into 2 x (2+2) which it hasnt done.

Its not written as 8/2 x (2+2)
its been written as 8/ 2(2+2) which is different, as I showed above.. its lazy and incomplete maths, and there are two working methods when it comes to breaking down the equation
Click to expand...
I don't get it? Why is 2(blah) not the same as 2x(blah) <--- I'm pretty sure it is.... Don't think its lazy or incomplete necessarily, I'd suggest having unnecessary notation could be inefficient ;)

2(a+b) is would still be 2a+2b no matter how you shake it from what I can see? I reckon I may be missing something obvious but can't see it...

Scott said:
It's an accepted norm...... but I cannot find a rule on it. It's just a given when it comes to maths. Well... from what I can tell it is..... and I want it to be a written statement of fact as my brain can see both sides of the argument while my study tells me it's assumed to follow a singular path.
Click to expand...
It is an accepted norm (certainly for my entire time through school, university and throughout my working career) - it reduces clutter in mathematical texts - dots (" . ") or crosses (" x ") are often used to denote multiplications between items but can also be omitted and the implication is that 2(blah) is 2x(blah) [or 2 . blah] and they are all the same operation.

Not a ruling by any stretch but : https://math.stackexchange.com/ques...he-multiplication-sign-before-the-parenthesis has an interesting few points made about this
 
D

Deleted member 17413

Guest
Its all down to the orders of methematical operation, Wiki might be useful here https://en.wikipedia.org/wiki/Order_of_operations
But I would still argue that for it to be 16, it either needs another pair of brackets or a space and multiplication sign...
(8/2)(2+2)=16 or 8/2x(2+2)=16
But 8/2(2+2) is 8 divided by 2(2+2) which is 1

You'd need to talk to proper mathematicians to get more info I think, I only went as far as A Level.
 
Rakk

Rakk

The Awesome
Moderator
I think most of the problems with these things on facebook and whatever you see it on, it is written to confuse and in essence cause arguments, so often they are missing the relevant symbols that would make it mathematically correct notation, and therefore its very easy to read it wrong
 
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