Poll: 6÷2(1+2)

[rgritchie]

Blame the question. It's written badly

 

[FoxEye]

When ever you write a number, ANY number, it is short hand notation for 1(x) == x ie one lot of that number

1+2=3 == 1(1) + 1(2) = 1(3)

one one plus one two equals one three.

Which is NOT the same as saying
1*1 + 1*2 + 1*3

one times one plus one times 2 plus 1 times three

For instance, in spoken language you would say 'I have one fish' or 'I have three fish' NOT 'I have one times a fish' or 'I have three times a fish'

Bonus points for creativity, but this is strictly something you've invented, rather than mathematics.

 

[titaniumx3]

When ever you write a number, ANY number, it is short hand notation for 1(x) ie one lot of that number

1+2=3 == 1(1) + 1(2) = 1(3)

one one plus one two equals one three.

Which is NOT the same as saying
1*1 + 1*2 + 1*3

one times one plus one times 2 plus 1 times three

For instance, in spoken language you would say 'I have one fish' or 'I have three fish' NOT 'I have one times a fish' or 'I have three times a fish'

Sorry you are wrong.

ab = a*b

3*2 = 3(2)

The only reason we use brackets in the second case is so that we don't confuse it with the number 32.

 

[p4radox]

How to create a heated argument on OcUK:

1. Think up a seemingly simple but flawed question with multiple interpretations on a subject that many are passionate about
2. Post the troll question
3. Watch as both sides flail around wildly whilst the moderates try to calm everybody down
4. Add an oversimplified poll to further polarise the debate
5. ????
6. PROFIT

 

[Rroff]

I've always been taught - and always used in programming, that you work from left to right but do the brackets first - anything inside brackets is also done left to right.

If you stick it into any programming language you will get 9.

(I haven't bothered to read every post in this thread so someone might have already covered this).

 

[RomanNose]

Troll maths

(a) (n + 1)² = n² + 2n + 1

(b) (n + 1)² - (2n + 1) = n²

(c) Subtracting n(2n + 1) from both sides and factoring, we have

(d) (n + 1)² - (n + 1)(2n + 1) = n² - n(2n +1)

(e) Adding ¼(2n + 1)² to both sides of (d) yields

(n + 1)² - (n + 1)(2n + 1) + ¼(2n + 1)² = n² - n(2n + 1) + ¼(2n + 1)²

This may be written:

(f) [(n + 1) - ½(2n + 1)]² = [(n - ½(2n + 1)]²

Taking square roots of both sides,

(g) n + 1 - ½(2n + 1) = n - ½(2n + 1)

and, therefore,

(h) n = n + 1

 

[sk82jack]

When ever you write a number, ANY number, it is short hand notation for 1(x) ie one lot of that number

1+2=3 == 1(1) + 1(2) = 1(3)

one one plus one two equals one three.

Which is NOT the same as saying
1*1 + 1*2 + 1*3

one times one plus one times 2 plus 1 times three

For instance, in spoken language you would say 'I have one fish' or 'I have three fish' NOT 'I have one times a fish' or 'I have three times a fish'

I understand where your coming from but it is all the same thing because multiplication is commutative and associative.

1+2=3 == 1(1) + 1(2) = 1(3)

one one plus one two equals one three.

can also be written as

1+2=3 == 1(1) + 2(1) = 3(1)

one one plus two ones equals three ones.




If you was buying packets of fish (just because you used fish lol) which came in packs of 3, and you wanted to buy, say, 100 packets. You wouldn't sit there and say:

1*3 + 1*3 + 1*3 +.....

you would do 100*3

which is essentially (1+1+1+1......)*3

 

[Hatter The Mad]

I've always been taught - and always used in programming, that you work from left to right but do the brackets first - anything inside brackets is also done left to right.

If you stick it into any programming language you will get 9.

(I haven't bothered to read every post in this thread so someone might have already covered this).

This is the correct. It is called the standard order of operations.

 

[N19h7m4r3]

I've always been taught - and always used in programming, that you work from left to right but do the brackets first - anything inside brackets is also done left to right.

If you stick it into any programming language you will get 9.

(I haven't bothered to read every post in this thread so someone might have already covered this).

Someone posted this a few pages back.

 

[wmb]

Ambiguous question is ambiguous...


Just goes to show the need for clear brackets when entering an eqn into a comp, whoever writes such an ambiguous eqn is asking for trouble!

The problem here is that people don't appear to realise it's ambiguous and can be interpreted either as z*(x+y)/y or z/(y*(x+y) in algebraic form and either answer is valid because of the incorrect mathematical notation used.

And worrying still is people who rely on calculators to solve it. You know the answer is only as good as its programming, the intelligent answer is "clarify the question for me" if you typed that equation in!

 

[Rroff]

Someone posted this a few pages back.

You'd always enter AB or A(B+C) as A*B or A*(B+C) into a programming language, there is no ambiguity as to how 6/2(1+2) would be entered into a programming language either.

 

[N19h7m4r3]

You'd always enter AB or A(B+C) as A*B or A*(B+C) into a programming language, there is no ambiguity as to how 6/2(1+2) would be entered into a programming language either.

Exactly, it just shows that the sum is badly written.

I consider it one of the best trolls ever.

 

[plasmahal]

I'd say 1, and I've done a lot of maths in my time.

However, the question is ambiguously written, and it doesn't help that it's all on one line so there's no way of discerning what actually belongs where. The argument is basically whether the question is:

(6/2)*(1+2)

which gives 9

or

6
_____
2(1+2)

which gives 1.

Without seeing it written properly one way or another, it's impossible to tell really. The stupid thing is that one way or another the question assumes that people are comfortable with the idea that adjacent items in a sum are multiplied together, regardless of whether a multiplication sign is present or not, which I think plenty of people will have trouble with.

However, having solved more equations than I care to recall, if I personally were writing that one line, then I would get to 1.

Totally agree with everything you have said there.

My Engineers brain does:

6
_____
2(1+2) and hence I get 1 as the answer.

I asked my daughter who is doing her GCSE's this year and she said 9.

It's all down to how we interpret a poorly constructed sum.

To all those who say it's 9 and don't understand that it can be either 1 or 9 because the of the way it's written, you are all WRONG.

 

[413x]

6/2*(1+2) comes out as 9, i thought it was 9 but i gotta say its interesting

i was taught BIDMAS [a-level B in maths here]

excel also gets 9 with the 6/2*(1+2)

for me the confusion comes with not putting * which i think is lazy as you would put a / if it were divide

 

[BunnyKillBot]

If you was buying packets of fish (just because you used fish lol) which came in packs of 3, and you wanted to buy, say, 100 packets. You wouldn't sit there and say:

1*3 + 1*3 + 1*3 +.....

you would do 100*3

which is essentially (1+1+1+1......)*3

Yes but its still semantically a question of whether you are buying 100 singular packets of fish or 1 quantity of a unit comprised of 100 packets of fish.

The 100 singular packets of fish CAN be broken down into smaller units(100*1(1)), but the 1 100 packets of fish CAN NOT be broken down into smaller units.(1*1(100))

Imagine if packs of fish were offered up as 1, 3 or 10, and you want 7 fish. You cannot get 2 and a third lots of the 3 pack, you HAVE to get 2 3 packs and 1 1 pack. The packet sizes are implicitly defined single unit sizes that consist of a specific quantity.

100 * 1(fish) : Only the 100 can be altered, to give 99 fish, 101 fish, 102 fish etc

1 * 100(fish) : Only the 1 can be altered to give 200 fish, 0 fish, 300 fish etc etc

 

[sk82jack]

Yes but its still semantically a question of whether you are buying 100 singular packets of fish or 1 quantity of a unit comprised of 100 packets of fish.

The 100 singular fish CAN be broken down into smaller units(lower order), but the 1 100 fish CAN NOT be broken down into smaller units.(higher order)

Imagine if packs of fish were offered up as 1, 3 or 10, and you want 7 fish. You cannot get 2 and a third lots of the 3 pack, you HAVE to get 2 3 packs and 1 1 pack. The packet sizes are implicitly defined single unit sizes that consist of a specific amount of content.

I'm just confused now with all this fish and what not, it's probably best to just agree to disagree lol

 

[D.P.]

I've always been taught - and always used in programming, that you work from left to right but do the brackets first - anything inside brackets is also done left to right.

If you stick it into any programming language you will get 9.

(I haven't bothered to read every post in this thread so someone might have already covered this).

Except the order standard programming languages operate at is not the same as mathermatics read by humans, and in general if you entered the equation as is into almost any language it wont compile.
You would have to specify additional operators to disambiguate the mathematical grammar.

 

[dowie]

To all those who say it's 9 and don't understand that it can be either 1 or 9 because the of the way it's written, you are all WRONG.

It is 9!!!

I can see why people arrive at the answer 1 as they read the equation as 6/(2(1+2))

but this isn't how the question was stated nor how '/' is generally used to represent division

with the correct use of the '/' symbol to represent division 6/2(1+2) is the same as (6/2)(1+2)

6/2(1+2) is confusing but isn't actually ambiguous - the divisor is just '2' - that is how the '/' symbol is used - there is one answer and that is 9

It is understandable why some people get '1' but it is also wrong and not an equally valid answer. The question does illustrate the problems with using '/' to represent division and the question would never actually arise in mathematics where the divisor is quite clear. Tis however an issue for anyone who wants to build a calculator etc....

 

[Lord_Kokain]

my 2 cents on the issue...its 9.

Why? Well,first of all about the debate, its an ambiguous question aimed at more maths-interested students to ponder upon which wouldn't be something that we all encounter, hence, we end up with 27 page discussion. Why wouldn't we encounter it? Because in 6÷2(1+2), the division sign would normally be represented by fraction line of 6/2. That way most of us recognize it as 6/2=3 --> 3(1+2).

In other words, for people that do not like the explanation "you do whatever comes up first from left to right", another way of thinking of it is that 6 and 2 have an unfinished business i.e. we cannot take the 2 only but need to complete this mini-calculation before proceeding. Its a rather psychological trick as solving/expanding brackets is what we tend to be taught to look for and do.

 

[gambitt]

6/2(1+2) is confusing but isn't actually ambiguous - the divisor is just '2' - that is how the '/' symbol is used - there is one answer and that is 9

What is your solution for this one please:

9÷3÷3