What does 6÷2(1+2) equal?

Wil

Apr 29, 2011 16:24

Here is one that has been going around Facebook and I don't get why so many people have chosen the wrong answer...

6÷2(1+2)=?

Choose

a) - 1
b) - 9

@Nyuszika7H Yeah, but I hardly use it

Nyuszika7H

@Wil 9

Sathya

neither?

Wil

@Nyuszika7H Yeah, that is what I came to, but almost half a million people chose 1... my brother included who is very smart at maths - he said it could be either as there isn't enough brackets... I am sure it is 9 and can only be 9 as BODMAS states you do the division on the left first!

@Sathya Don't you start :P what did you get to?

Sathya

4

woops

sorry, 1

Wil

So... How did you get to 4, then 1!?

Sathya

Apr 29, 2011 16:28

my eyes deceived me, saw 6 ÷2 as 6+2

Wil

8*3 = 24? :S

lol, I am going to open a question on the maths site!

Sathya

well they may not accept it as it's not "research level"

Nyuszika7H

@Wil what's your IRC client of choice?

Wil

@Nyuszika7H Mirc

Nyuszika7H

@Wil irssi ftw. Have you tried it?

Wil

Apr 29, 2011 16:29

@Sathya No where else to ask :S I am researching the answer to this!!!

Sathya

it was a disclaimer anyways, I'm curious to know

and I still have no clue as to how I came up with 4 :|

oh yeah, this is how I interpreted it first

Wil

@Sathya lol, well, I am certain the answer is 9 if you follow Bodmas rules

Sathya

6÷2(1+2) = 6÷2(3) = 2÷2(1) = 1

that's how I came up with 1

Nyuszika7H

6÷2(1+2) = 6÷2*1+2 = (6÷2)*(1+2)

Wil

I don't get how you went from 6/2 to 2/2 ? :S

Sathya

Apr 29, 2011 16:34

@Nyuszika7H it can also be interpreted as 6÷(2*(1+2)) = 6÷(2*(3)) = 6÷(6) = 1

@Wil ^

Nyuszika7H

@Sathya No. You should count from left to right in this case.

Wil

but... I had a little chat with my brother and I just don't see it, I thought BODMAS was one of the basic rules of maths

@Nyuszika7H Agreed, BODMAS states you always do brackets first and in any conflict, you do left to right, so the division happens first

Sathya

@Nyuszika7H I am, doing left to right, no ?

Wil

well, that is what I thought...

DMA57361

afternoon all

Sathya

Apr 29, 2011 16:36

goes to facebook to stalk @Wil

'ello @DMA57361

Wil

I suppose, this is why this question has had so many answers!!! It would be interesting to read what proper mathematicians say... I was sure it was 9, but my brother is smart - he did his maths A levels a year early and got an A*... so when he said that (and now you are as well) I sort of question myself

@Sathya feel free, nickname /wilhil

...just so long as you don't post any of my pictures on here!!! mind you, none are that bad!

DMA57361

PS: the answer is 9 -> wolframalpha.com/input/?i=6%C3%B72%281%2B2%29

Sathya

►

oh, Google agress to @DMA57361

well, no arguing with WA

DMA57361

@Wil I have 1.5 A levels - it's nine. 6÷2(1+2) -> 6÷2(3) -> 6÷2×3 -> 3×3 -> 9

you perform the division before the multiplication

studiohack

yeah, its all about the order of operations

Sathya

Apr 29, 2011 16:41

well, it's about how you interpret them anyways

studiohack

as long as you perform the operations in a certain order, its easy

DMA57361

ah, you've covered BODMAS already, so job done there :P

Sathya

Math gone viral

DMA57361

this is why Reverse Polish notation wins, 6 2 ÷ 1 2 + × is completely unambiguous (assuming I've got it right ;)

Wil

0

Q: What does 6÷2(1+2) equal?

Basically put, this has come up on Facebook as a poll that nearly 1.5 million people have answered. 673,506 people state the answer as 1 846,676 people state the answer as 9 (including myself) I am certain that following the basic rules of BODMAS, this goes as follows: 6/2(1+2) 6/2(3) 3(3) ...

puzzle

DMA57361

Apr 29, 2011 16:45

time to sign up for a maths account if I don't have one ;P need to do some voting

Wil

LOL, look at the comments, looks like I just asked the maths equivalent of "Why does my computer crash"

2

Sathya

LOL, true :D

DMA57361

indeed, and the answer is "either is valid, whoever wrote the sum is ambiguous and deserves a slap"

Wil

So, who knew... possibly, BODMAS is the natural thing people do, but it isn't an actual 100% rule :S

Sorry @Sathya! :P so, both are correct I guess...

DMA57361

@Wil possibly it's just whatever the UK education system runs with

Wil

Apr 29, 2011 16:52

@DMA57361 I guess... but, BODMAS does seem to make the most sense as it stops problems like this from ever occurring... that is, if @Sathya just "interpreted" it that way rather than using a rational rule/pattern etc.

I just mean, if there is a more complex sum, it could come up with different rules depending on who you ask, BODMAS gives the same answer every time

DMA57361

true, but anyone who knows what they're doing should know to make things explicit with brackets, fractions, etc anyway

Sathya

@Wil dunno why I just found it hard to visualize it the way you, @Nyuszika7H & @DMA57361 mentioned

till I saw WA that is

Also, It is important to note that I suck at Math

Wil

@DMA57361 I would argue that if everybody did follow the same rules (BODMAS) you wouldn't have to.... but, obviously, knowing that not everyone does use BODMAS, it clearly would be the only way to get the same answer

@Sathya Did you ever do BODMAS at school?

Sathya

@Wil I think the question was more of "Why doesn't Windows use all 4 GB"

@Wil yep

DMA57361

@Wil regardless -- explicit is better than implicit. But that might just be the programmer in me talking :)

Wil

Apr 29, 2011 16:56

@Sathya lol :P

Sathya

I seem to have taken the explicit route and thrown away BODMAS

Wil

@DMA57361 I am just playing devils advocate or whatever, as I still feel that BODMAS is best... but I agree fully that the more information the better.

DMA57361

in-fix notation is flawed because of this possibly of ambiguity, see my comment above about reverse polish -- shame no one can really understand it ;P

Wil

ok... that one really is difficult! but I will give it a go...

Sathya

@DMA57361 yeah I couldn't make head or tail out of that

I need to brush up on those

DMA57361

Apr 29, 2011 17:00

6 2 ÷ 1 2 + × == (6÷2)×(1+2)

the other interpretation of the original would be 6 2 1 2 + × ÷ ... I think

Sathya

that would be right

Wil

6 2 ÷ 1 2 + × .... 6x(2/1)(2+x)... 6x(2)(2+x).... 12(2+x)

that is just looking quick... I loved maths, but haven't really done anything complex in years!

DMA57361

2 mins ago, by DMA57361

6 2 ÷ 1 2 + × == (6÷2)×(1+2)

I was using reverse polish notation (so "1 2 +" really means "1 + 2")

oh dear

Sathya

:)

DMA57361

my daughter has just - from somewhere in our bedroom - found an old net curtain and wrapped it round her head >.<

Wil

Apr 29, 2011 17:07

@DMA57361 ok, il shut up, I really don't understand that at all then!

DMA57361

Reverse Polish notation

Reverse Polish notation (RPN) is a mathematical notation wherein every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as Postfix notation and is parenthesis-free as long as operator arities are fixed. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented (prefix) Polish notation in the 1920s. The Reverse Polish scheme was proposed in 1954 by Burks, Warren, and Wright and was independently reinvented by F. L. Bauer and E. W. Dijkstra in the early 1960s to reduce co...

it's just another way of writing formulae, but doesn't suffer ambiguity because the order of values/operators corresponds to the order of calculation

it's useful for computers... but not so much to people

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