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# Math: 6÷2(1+2) = ?

Anonymous Coward
User ID: 1255402
Poland
05/03/2011 09:12 AM
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Re: Math: 6÷2(1+2) = ?
Alright, there's a lot of self-proclaimed experts around these parts. Let's see how your logic holds up against some basic mathematics.

6÷2(1+2) = ?

I'll give two hints. This is NOT a trick question, and there is only 1 correct answer.

All tools used for computation are fair game.

(Yes, I saw this somewhere else and decided to post it here.)

Best of luck to all you geniuses .
Quoting: Syrius

This thread is created to divert the attention away from Obama and his lies.
Anonymous Coward
User ID: 1259266
United States
05/03/2011 09:15 AM
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Re: Math: 6÷2(1+2) = ?
Christ why are we doing this again? It's the same problem as before with different numbers.
Quoting: Anonymous Coward 1284566

Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:19 AM
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Re: Math: 6÷2(1+2) = ?
The answer is 9
Multiplication and Division left to right at the same time!

The standard order of operations, or precedence, is expressed here:

terms inside parenthesis
exponents and roots
multiplication and division

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.
Quoting: Anonymous Coward 1304583

Fascinating. Wikipedia <3

So where does it say I should put the denominator 2(1+2) up there with the numerator 6?
Quoting: Syrius

Syrius, using the mult inverse is simply a more complicated method for solving a very simple problem. The answer either way is 1!
Quoting: ANNONYMOUS 1275893

I thought so to at first but forgot that multiplication and division are at the same level, in which case you MUST work left to right.

A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12, but is rather 5 × 4, because, going from left to right, you get to the division first. If you're not sure of this, test it in your calculator, which has been programmed with the Order of Operations hierarchy.

I fell into the trap

9 is the only correct answer
Quoting: Anonymous Coward 1362610

I thought it was 1 at first too then I remembered you do multiplication and division, addition and subtraction at the same time left to right.
Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:22 AM
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Re: Math: 6÷2(1+2) = ?
The answer is 9
Multiplication and Division left to right at the same time!

The standard order of operations, or precedence, is expressed here:

terms inside parenthesis
exponents and roots
multiplication and division

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 &#8722; 4 = 3 + (&#8722;4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 - 2 + 3 as the sum of 1, negative 2, and 3, and add in any order: (1 - 2) + 3 = -1 + 3 = 2 and in reverse order (3 - 2) + 1 = 1 + 1 = 2. The important thing is to keep the negative sign with the 2.

The root symbol, &#8730;, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand.

Stacked exponents are applied from the top down.

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws.
Quoting: Anonymous Coward 1304583

Fascinating. Wikipedia <3

So where does it say I should put the denominator 2(1+2) up there with the numerator 6?
Quoting: Syrius

6÷2(1+2)

6*1/2*3 = 9
Anonymous Coward
User ID: 1267814
United States
05/03/2011 09:27 AM
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Re: Math: 6÷2(1+2) = ?
PEMDAS
please excuse my dear aunt sally

order of operations to do first
parenthesis
exponents
multiplication
division
subtraction

1+2=3
6/2 = 3
3(3)= 9

hopefully I followed the rules above
Anonymous Coward
User ID: 1296336
United States
05/03/2011 09:29 AM
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Re: Math: 6÷2(1+2) = ?
It's 1, thx for playing.
Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:29 AM
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Re: Math: 6÷2(1+2) = ?
6÷2(1+2)

=

6*1/2(1+2)

either way you do this new equal equation its 9
when its only multiplication it doesn't matter if you go left to right on that step
Syrius (OP)

User ID: 1289074
United States
05/03/2011 09:30 AM
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Re: Math: 6÷2(1+2) = ?
We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.*

Now, did I write this equation 6/2x1+2? No.

It's: 6÷2(1+2)

However, it would be a fallacy to imply that 2(1+2) is multiplied first because of juxtaposition because we are not dealing with variables.

We're dealing with fractions. There is no other way to correctly annotate this linearly without causing more confusion or using extra parenthesis (brackets) *[]*

Good day.
All around me are familiar faces... Worn out places...Worn out faces...
Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:33 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:34 AM
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Re: Math: 6÷2(1+2) = ?
We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.*

Now, did I write this equation 6/2x1+2? No.

It's: 6÷2(1+2)

However, it would be a fallacy to imply that 2(1+2) is multiplied first because of juxtaposition because we are not dealing with variables.

We're dealing with fractions. There is no other way to correctly annotate this linearly without causing more confusion or using extra parenthesis (brackets) *[]*

Good day.
Quoting: Syrius

6*1/2(1+2)

6÷2 =3
6*1/2 =3

If you think its 1 you are wrong
Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:35 AM
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Re: Math: 6÷2(1+2) = ?
6 divided by 2 multiply by 3

equals 3 multiply by 3

= 9
Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:35 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423
Anonymous Coward
User ID: 841362
United States
05/03/2011 09:39 AM
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Re: Math: 6÷2(1+2) = ?
PEMDAS
please excuse my dear aunt sally

order of operations to do first
parenthesis
exponents
multiplication
division
subtraction

1+2=3
6/2 = 3
3(3)= 9

hopefully I followed the rules above
Quoting: Anonymous Coward 1267814

nope you did not.
Syrius (OP)

User ID: 1289074
United States
05/03/2011 09:40 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a thread's title?

Oh, 6÷2(1+2).

Last Edited by Stoygon on 05/03/2011 09:41 AM
All around me are familiar faces... Worn out places...Worn out faces...
Anonymous Coward
User ID: 1304583
United States
05/03/2011 09:41 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a post's title?

Oh, 6÷2(1+2).
Quoting: Syrius

there's nothing wrong with the equation except you got the answer wrong when its written that way
Anonymous Coward
User ID: 1310492
Netherlands
05/03/2011 09:42 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a thread's title?

Oh, 6÷2(1+2).
Quoting: Syrius

6
______
2(1+2)

Does not equal

6÷2(1+2).
Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:45 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a thread's title?

Oh, 6÷2(1+2).
Quoting: Syrius

you didnt express it as a fraction

order of operations as you wrote it is 9

to get 1 it should be 6÷[2(1+2)]
Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:47 AM
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Re: Math: 6÷2(1+2) = ?
op is still a fucktard

you cant write a linear equation and calculate it like a fraction
Anonymous Coward
User ID: 1283712
Australia
05/03/2011 09:49 AM
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Re: Math: 6÷2(1+2) = ?
I think the confusion of the 1 vs 9 crowd is that the 1 crowd will try and convince you that the 2 has been factored out of whatever is in the parenthesis.

This is a false assumption - why stop at the 2, how far do you go. Why not include the 6÷2 as the factor? It could equally be possible.

So to state whatever outside the parenthesis is a factor is ambiguous as we don't know the history, and thus you must ignore it. You thus need to simply follow the rules of order of operations, and write it as such:

6÷2*(1+2)

INSIDE parenthesis first

6÷2*(3)

THERE is no more operations to be complete on the parenthesis now, so it can be dropped (remembering stating what is outside is a factor is ambiguous and must be ignored)

6÷2*3

division and multiplication are equal magnitude of preference so must work left to right

3*3

which leaves 9.
Syrius (OP)

User ID: 1289074
United States
05/03/2011 09:49 AM
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Re: Math: 6÷2(1+2) = ?
op is a fucktard

your explanation just backed up 9 is the correct answer

yet you think its 1

its 9
Quoting: Anonymous Coward 282423

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a thread's title?

Oh, 6÷2(1+2).
Quoting: Syrius

6
______
2(1+2)

Does not equal

6÷2(1+2).
Quoting: Anonymous Coward 1310492

Yes, it does.

Solidus, much?

All around me are familiar faces... Worn out places...Worn out faces...
acolyte

User ID: 1368014
South Africa
05/03/2011 09:49 AM
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Re: Math: 6÷2(1+2) = ?
Oh Boy, I'm representing our South African Education system here during apartheid years.

first thing i remember: "÷" is not the same as "/" dont ask me why, I cant bluddy remember, but whenever you see "÷" you must put the unknown in parentheses which changes the direction form left to right TO right to left.

"When dividing an [unknown] or [x] with "÷" put unknown in parenthesis and calculate first, then remove parenthesis"
"When dividing an [unknown] or [x] with "/" all follow the same rank, left to right.

thus

6 ÷ 2(1+2) is not the same as 6/2(1+2)

Using waht the OP gave us we have to use our parentheses on unknown and it looks like this:

is 6 divided by [2(1+2)]

6 divided by [2(3)]

6 divided by [6] now remove parenthesis

6/6
= 1

6/2(1+2) on the other hand is 9
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Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:51 AM
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Re: Math: 6÷2(1+2) = ?
stupid op
Anonymous Coward
User ID: 1357662
United States
05/03/2011 09:52 AM
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Re: Math: 6÷2(1+2) = ?
6/2 = 3
1+2 = 3
3(3) = 3*3
9

Showed my work
Quoting: patmac 1130776

wow order of operations
Anonymous Coward
User ID: 1368005
Estonia
05/03/2011 09:53 AM
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Re: Math: 6÷2(1+2) = ?
Anonymous Coward
User ID: 1368189
Austria
05/03/2011 09:53 AM
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Re: Math: 6÷2(1+2) = ?
6/2(1+2)... or 6÷2*(1+2)= 9

6÷(2*(1+2))= 1

6
______ = 1
2*(1+2)

Syrius (OP)

User ID: 1289074
United States
05/03/2011 09:54 AM
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Re: Math: 6÷2(1+2) = ?
...

Quoting: Anonymous Coward 1304583

I love when people suffer from dementia.

6
___ = ?

2(1+2)

How can I put that as a thread's title?

Oh, 6÷2(1+2).
Quoting: Syrius

6
______
2(1+2)

Does not equal

6÷2(1+2).
Quoting: Anonymous Coward 1310492

Yes, it does.

Solidus, much?

Quoting: Syrius

All around me are familiar faces... Worn out places...Worn out faces...
Anonymous Coward
User ID: 282423
Australia
05/03/2011 09:54 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
gold for austria
Anonymous Coward
User ID: 1327341
South Africa
05/03/2011 09:55 AM
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Re: Math: 6÷2(1+2) = ?
Oh Boy, I'm representing our South African Education system here during apartheid years.

first thing i remember: "÷" is not the same as "/" dont ask me why, I cant bluddy remember, but whenever you see "÷" you must put the unknown in parentheses which changes the direction form left to right TO right to left.

"When dividing an [unknown] or [x] with "÷" put unknown in parenthesis and calculate first, then remove parenthesis"
"When dividing an [unknown] or [x] with "/" all follow the same rank, left to right.

thus

6 ÷ 2(1+2) is not the same as 6/2(1+2)

Using waht the OP gave us we have to use our parentheses on unknown and it looks like this:

is 6 divided by [2(1+2)]

6 divided by [2(3)]

6 divided by [6] now remove parenthesis

6/6
= 1

6/2(1+2) on the other hand is 9
Quoting: acolyte

I proved this on the previous page.
Anonymous Coward
User ID: 1357662
United States
05/03/2011 09:55 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
Oh Boy, I'm representing our South African Education system here during apartheid years.

first thing i remember: "÷" is not the same as "/" dont ask me why, I cant bluddy remember, but whenever you see "÷" you must put the unknown in parentheses which changes the direction form left to right TO right to left.

"When dividing an [unknown] or [x] with "÷" put unknown in parenthesis and calculate first, then remove parenthesis"
"When dividing an [unknown] or [x] with "/" all follow the same rank, left to right.

thus

6 ÷ 2(1+2) is not the same as 6/2(1+2)

Using waht the OP gave us we have to use our parentheses on unknown and it looks like this:

is 6 divided by [2(1+2)]

6 divided by [2(3)]

6 divided by [6] now remove parenthesis

6/6
= 1

6/2(1+2) on the other hand is 9
Quoting: acolyte

Wow and this is just confusing. Order of Operations. Is the order in which the signs function. Parenthesis first, Exponents, Mutiplication, Division, Addition, Subtraction. That why its 1.
Syrius (OP)

User ID: 1289074
United States
05/03/2011 09:56 AM
Report Abusive Post
Re: Math: 6÷2(1+2) = ?
Oh Boy, I'm representing our South African Education system here during apartheid years.

first thing i remember: "÷" is not the same as "/" dont ask me why, I cant bluddy remember, but whenever you see "÷" you must put the unknown in parentheses which changes the direction form left to right TO right to left.

"When dividing an [unknown] or [x] with "÷" put unknown in parenthesis and calculate first, then remove parenthesis"
"When dividing an [unknown] or [x] with "/" all follow the same rank, left to right.

thus

6 ÷ 2(1+2) is not the same as 6/2(1+2)

Using waht the OP gave us we have to use our parentheses on unknown and it looks like this:

is 6 divided by [2(1+2)]

6 divided by [2(3)]

6 divided by [6] now remove parenthesis

6/6
= 1

6/2(1+2) on the other hand is 9
Quoting: acolyte

I proved this on the previous page.