Google Calculator said that 6/2(1+2) is 9, but the answer is 1.

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Google Calculator said that 6/2(1+2) is 9, but the answer is 1. EvilKarmaAngel 4/27/11 6:32 PM
Can you teach a calculator PEMDAS? Because that is pretty bad.
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. bluequoll 4/27/11 11:07 PM
Google Calculator follows standard precedence rules:
• terms in parentheses
• exponents and roots
• multiplication and division
• addition and subtraction
• left to right evaluation for operators of equal precedence

If you want the result of your example to be 1, you'll need to override the equal left-to-right precedence of multiplication and division by including an extra set of parentheses (and preferably also include the implied multiplication):  6/(2*(1+2))
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. pgj99 5/3/11 1:57 PM
I'm pretty sure I am correct in saying 6÷2(1+2)= 1, However 6÷2 x (1+2)= 9    Seems there's a lot of confused people out there on the web.  I'm begging to question what I know myself.

Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. bluequoll 5/3/11 3:49 PM
Our point of difference is that you seem to be suggesting implied multiplication should have a higher precedence than explicit multiplication?

If we agree that the terms in parentheses should be evaluated first, then the query simplifies to 6/2x3. My little throw-away pocket calculator evaluates this as 9. So does my mobile phone. Why should we expect Google to confuse things by following different precedence rules and providing a different answer?
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. tanmay100 5/15/11 2:03 AM
how about we go to the basic rules
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. Thomas P. 5/15/11 6:42 AM
In: 6/2(1+2), you're really missing an operator.
Lets assume the missing operator is multiplication, so the expression really is: 6/2x(1+2)

Parenthesis has the highest order of precedence, turning 6/2x(1+2) into 6/2x3
Division and Multiplication rank with equal order of precedence.
and acc. to your own reference: >>Divide and Multiply rank equally (and go left to right).
so proceeding left-to-right: 6/2x3 becomes 3x3 becomes 9

Case Closed!

Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. maxowlPang 5/26/11 11:50 AM
                  6÷2(1+2)

THREE WAYS to solve this question: 

1st WAY:
just forget about the PEMDAS or BODMAS rules, 
lets come back to the origin of mathematics which is solving human's problem:

assumption: Have 6 apples,  with 2 classes where combination of 2 boys & 1 girl.   
                    So, each of them get how many apple(s)?!                

                   thus,   2 classes , 2 boys & 1 gals =   3 students + 3 Students =  total 6 students 

                   Now, only have 6 apples

                   6 apples  for   6 students.
                       
                   Therefore,  1 student only have 1 apple         = 1       (answer)

2nd Way: 
6÷2(1+2)

lets assume     y =2                    so that , 6
÷y(1+y) = 6 ÷ (y+y^2)

now   replace 2 into y                 it shows  6 ÷ ( 2 + 2^2) = 6 ÷ (2 + 4)
                                                                                  = 6 ÷ 6 
                                                                                  = 1          (answer)

3rd way:
6÷2(1+2) 

lets assume    (1+2) = a     so that,     6÷2a                      
                                           now    = 6/(2a)             2a  is slightly different with 2 x a ; please dun tell me that is (6/2)x a !!
            
                         lets simplify           = 3/a

now replace (1+2) into a                  = 3 (1+3)
                                                    =  3/3 = 1      (answer)                 if you not agree again! fine lets go for the 4th way

4rth Way
6÷2(1+2)                 from this equation , we would say  it has two group , A = 6  ;  B = 2(1+2)

lets   6÷2(1+2)   = z              so that,  A/B = z
                                                        A    = zB
                                                        6    = z[2(1+ 2)]
                                                          6  = 6z
                                                         z   = 6/6   =  1  (answer)                   


come on, don't be stubborn any more.  
i am going to END this Equation now.
                   

Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. AhTatZai 6/2/11 9:43 AM
The problem in it's simplest form, with nothing implied would look like this: 
(1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1)) 
From here, nothing is implied, This again, works out to 9. 
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. mooredc54 6/2/11 10:02 AM
Note:  Some calculators do not follow the standard rules of precedence, but bluequoll is correct for standard precedence [aka PEMDAS]: http://en.wikipedia.org/wiki/Order_of_operations.
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. Jouten 6/25/11 2:51 AM
@maxowlPang

You did it wrong. Every time. You always added extra parenthesis around 2 and (1+2) and made it [2(1+2)]. You can't do that, because it comes after the division sign.

To your 1st WAY:


Your assumption is wrong. You pictured the problem, so that your 6 (apples) are first divided by 2 (classes of scholars) and then divided again by (1+2) (boys and girls). So instead of 6÷2(1+2) you got 6÷2÷(1+2). And that's obviously 1.

Multiplication in math text problems has to be set different. Like this:
There are 6 Mice, where always 2 mice become one pair. One pair gets 1 male mouse and 2 female mous offspring. How many offspring do all mice together have?


Answer: 6 mice, 2 make a pair, so 6÷2=3. Offspring 1 male, 2 female (1+2)=3. 3*3=9


Your 2nd WAY:


You assume 2=y, so that 6÷y(1+y). Now why did you take the y into the parenthesis? There is not parenthesis"[]" around y(1+y), otherwise it would be written as 6÷[y(1+y)]. But since it's 6÷y(1+y) it's ((6÷y)1+(6÷y)y), because 6÷y is one single number. That's how the rational numbers are even defined.


So solving the term will get (6÷y+6)=6÷2+6=3+6=9

Your 3rd Way:

(1+2)=a, so 6÷2a. Now look what you did. You added extra parenthesis around (2a). You cannot do that, because there is a division sign before the 2. You hurt the associative property. It really goes 6÷2y=3y. Now replace y by (1+2= =3(1+2)=9

Your 4th Way:

Ok seriously look 6÷2(1+2)=z. You turned that into 6=z[2(1+2)]. As I said you simply added extra parenthesis to make your answer right. Here it is pretty obvious.

Now let's do it the right way:
6÷2(1+2)=z |*2
6(1+2)=2z   |÷6
(1+2)=2z÷6
(1+2)=1/3z
3=1/3z        |*3
9=z



Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. pgj99 8/12/11 3:51 AM
Lets clarify this a bit......

The answer is 1.

If you expand a / b(c+d) is it 

i)   a / (bc + bd)   or
ii)  (a/b) * (c + d)

Anyone who knows what they are talking about would know that its (i)   a / (bc + bd)  which of cause = 1

Hope this helps.

My quals are GCSE and A-Level maths + Qualitative Methods at MSc level. ( Not wikipedia which actually doesn't have an example matching this anyway)

Also my £100 graphical calc says the same thing as me (if we are to put all our faith in technology).  I think making comments about the results a throw away returns is a bit of a silly remark, no offence.  In fact I'm surprised a calculation like this could be input into a cheap calculator.  I would have though you would have needed to type it as 6 / 2 x (1+2) which does give you 9!   6 / 2(1+2) is however 1


Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. mooredc54 8/13/11 4:52 AM
As stated earlier, not all calculators follow rules of PEMDAS.

To be clear 6/2(1+2) is not even a valid computation, it is shorthand notation for 6/2*(1+2).

http://www.wolframalpha.com/input/?i=6%2F2%281%2B2%29 = 9 [using shorthand notation].
http://www.wolframalpha.com/input/?i=6%2F2*%281%2B2%29 = 9 [using proper notation of 6/2*(1+2)].

Microsoft Excel throws a formula error using the shorthand notation, and asks if you really meant 6/2*(1+2).
Microsoft Excel shows 9 as the answer when proper notation is used.

The built-in Windows calculator shows the answer as 9 when properly notated.
For reasons I do not understand [perhaps Garbage-In-Garbage-Out applies] it shows the answer as 2 when it is not properly notated.

The Built-in iPhone calculator behaves exactly like the built-in Windows calculator.  They both interpret the improper notation as 6 / (1 + 2), my speculation would be they both ignore the first 2 because it is not followed by a valid operator.


 



Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. Thomas P. 8/13/11 6:10 AM
On a final side-note:
Some expensive calculators may distinguish a colon and a slash as being a division operator and a fraction-line to be extended (causing everything entered right/after the slash as being in the denominator).
Hence causing different results for below two expression
   6:2*(1+2)
   6/2*(1+2)

Fun fact: WolframAlpha interprets a slash as a division operator, and a colon as a ratio (i.e. not to be mathematical evaluated, but rather to be interpreted).
http://www.wolframalpha.com/input/?i=6%2F2*%281%2B2%29
http://www.wolframalpha.com/input/?i=6%3A2*%281%2B2%29

Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. maxowlPang 10/20/11 12:49 AM
@ Jouten 

i think there is some misunderstanding of question that we discuss.

This question FIRST come out in internet is

 

6÷2(1+2) which is NOT 6/2(1+2)

 

i think there is one thing a lot of people wont understand is difference between ÷ & /. so do you? Let’s study the symbol,

 

http://en.wikipedia.org/wiki/Table_of_mathematical_symbols_by_introduction_date

 

http://jeff560.tripod.com/operation.html

 

The obelus (÷) was first used as a division symbol by Johann Rahn (or Rhonius) (1622-1676) in 1659 in Teutsche Algebra

 The Slash (/) was first used as a division symbol by Thomas Twining (1718 )

 

==========================================================

There is minor difference meaning between these two symbols, however both are represent division.

 

For the simple math    

1 add 2, will write as 1 + 2.

a subtract b , will write as a – b

10 times 20 , will write as 10 x 20

x divide y, will write as x ÷ y  

 

we used to understand these questions consist TWO groups. A and B (from left to right)

 

However, Mathematics was during the Scientific Revolution at 17th century.

http://en.wikipedia.org/wiki/History_of_mathematics

For simplify and solving more question, Slash(/) initiated for division. The purpose of slash(/) not only represent division but also simplify into ONE group.

 

Which mean?

x ÷ y     ;  x as GROUP A     &   y  as GROUP B

x/y       ; will be saying as     ONE group only      

 (Because simplify or solve the rest complicated equation)

 

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

 

so that, for clarify the origin question 6÷2(1+2) does not mean by 6/2(1=2)

 

6÷2(1+2)       6/2(1+2)

 

P/S: you were saying I added extra parenthesis 6÷[2(1+2) ], sometimes extra parenthesis clarify the question.

But you also add your parenthesis as (6/2)*(1+2) for getting your answer to 9 . don’t you ?

P/S: there is difference between  x & ( )  as multiplication   also. 

Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. maxowlPang 10/20/11 2:45 AM

The argument we have before us is obelus vs. solidus.

Notice, when obelus is typed-out, a red line appears underneath notifying the writer of an error. This is in fact false. I can only deduce that in today's word, we may classify the term as archaic.

The original meaning that many have came to infer when presented with the symbol is outlined here:


If you closely read the following link WITHOUT bias you will come to understand that when presented with the current formula 6÷2(1+2), this is meant to be read as:

__6__ =
2(1+2)

The reason behind it is simple.

Taking the ratio x/y of two numbers x and y , also written x÷y. (Backbone)

Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called a solidus (sometimes, the "diagonal"), and the symbol "÷" is called the obelus. (Extra Info)

If left unevaluated, x/y is called a fraction, with x known as the numerator and y known as the denominator. (Key)

One must, with the above rules, conclude that because this equation is OBVIOUSLY UNEVALUATED it is actually a fraction. Considering this principle, the x is 6, the y is 2(1+2), there can only be one valid and logical answer to this problem.

1
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. maxowlPang 10/20/11 2:45 AM
you may refer
 
 
good luck
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. Sohail 3/1/12 5:49 PM
Well well i just did lil research and found that the calculation in hand *6÷2(1+2)=?* is not as simple as it seems, there is alot of debate going on this seemingly simple calculation. The reason is, most of us either are not fully aware or miss out basic rules of Algebra/arithmetic some times. I went through several web pages and found the basic rules:If you want the result of your example to be 1, you'll need to override the equal left-to-right precedence of multiplication and division by including an extra set of parentheses (and preferably also include the implied multiplication): 6÷[2*(1+2)]=1

BUT... in the calculation in hand, the flow follows as:

Parenthesis DO come first so (2+1) equals 3. So you are left with 6÷2(3). Now note here. =>Mathematics does not tell you to multiply OUTSIDE the parenthesis first, just whats INSIDE first only.

Then the rules of multiplication/division come in, Division and Multiplication rank with equal order of precedence but from LEFT to RIGHT whichever comes first, NOT outside the parenthesis UNLESS there are additional parenthesis/brackets. Since there are no additional parenthesis, next step is: 6÷2 (3)=> 3 x 3 = 9 (left to right ÷ comes first)
Case Closed!! 
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. casmith 3/1/12 5:56 PM
it is actually correct.  The answer is 9.  You forgot to add the subtraction sign.  The parenthesis right next to the 2 means multiply.
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. rpkon 4/6/12 12:56 AM
I think your correct
Re: Google Calculator said that 6/2(1+2) is 9, but the answer is 1. Juify 7/27/12 8:47 PM
For those of you think 6/2(1+2) looks like..

__6_______    
  2      (1+2)    =  1

but actually look like..

_6_  (1+2)          _6(1+2)_
  2                =        2            =  9 

look close, ... think again!