6÷2(1+2)=?

[dougy83]

B O D M A S
B Brackets ( )
O Of
D Division /
M Multiplication x
A Addition +
S Subtraction -
so the answer is 1

'O' is for Orders (powers/indices/exponents); following only BODMAS strictly actually gets the answer of 9.

 

[Gobbledok]

...to me it's about as interesting as a discussion on proving which faith is correct

Well nobody's forcing you to participate

I think you've added some extra brackets up there... You have done a substitution based on the assumption that the implicit has the higher precedence.

The implicit does have the higher precedence.

On this page, the American Mathematical Society says "We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division."

 

[dougy83]

Well nobody's forcing you to participate

You are of course correct in that statement. What I was meaning by my related comment was that without an accepted rule/convention for precedence it cannot be objectively argued either way.

The implicit does have the higher precedence.

If that's the accepted practice, then you know the correct answer to the original question & there's no debate to be had.

 

[DerStrom8]

I have answered this on the other forum, as well
The answer is definitely 9.
Using PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction), parentheses come first. 1+2=3. M and D are of equal importance, as are A and S. They are completed left-to-right. In this case, you MUST do 6/2, then multiply THAT answer (3) by (1+2) which we found earlier (3). The answer is 9.

 

[DerStrom8]

B O D M A S

B Brackets ( )

O Of

D Division /

M Multiplication x

A Addition +

S Subtraction -

so the answer is 1

Multiplication and division are of equal importance, as are addition and subtraction. For this reason, they are to be completed left-to-right (whichever comes first). In this case, the division comes first, so that is what must be done before the multiplication.
Depending on the order of the problem, this rule could also be written BOMDSA, for example.

 

[KeepItSimpleStupid]

I had some time (overnight) to think about it and my feelings is that the implicit parenthesis notion of a non-typeset quantity is AMBIGUOUS. I've written algebraic to RPN expression evaluators for class and later, for work, I wrote a BASIC RPN input expression input with units conversion so I could type L/A dimensions of circles and square cross-sections. e.g. "1.2 cm 100 um 1 mm * /" as input. I could also use PI as a constant. It worked very well.

I never had to deal with the implicit multiplication.

6÷2(1+2) when you do the distributive property: 6 / (2 + 4), you do end up with 1. Even with parenthesis first, you end up with 1.

I'm more inclines to change my mind. I posed this as a possible bug on wolframalpha. Let's see what they have to say.

Excel asks you to accept a suggestion where it adds explitit operators.

 

[misterT]

6÷2(1+2) when you do the distributive property: 6 / (2 + 4), you do end up with 1. Even with parenthesis first, you end up with 1.

I think you should be able to insert the omitted multiplication operator in that kind of situation. Then:

6÷2(1+2) = 6÷2*(1+2) = 9.

If

6÷2(1+2) = 1,

that would imply:

6÷2(1+2) = 1 = 6÷2÷(1+2)

Which is clearly wrong.

 

[DerStrom8]

Here are a few links to sites that say that M/D and A/S are equally important, and must be done left-to-right:
Order of Operations - PEMDAS
The Order of Operations: PEMDAS
Order of operations - Wikipedia, the free encyclopedia
Evaluating Algebraic Expressions Order of Operations/P.E.M.D.A.S.
How to Solve a Math Problem Using PEMDAS | eHow.com
Order of Operations

And that is just a few

 

[MrAl]

Hello again,


I dont know why you guys want to argue about something so simple. There are two ways of doing it, and that's really all there is to it.

For example, two well known calculators made by TI do it differently. For 6/2(1+2) typed exactly like that in BOTH calculators we get a different result:
The TI85 gives a result of 1, while the TI89 gives a result of 9.

Now which one are we going to say is right or wrong? I've used both calculators in the past for tons of calculations and i would not ever throw either of them in the garbage.

The only problem that comes in is when we try to use the same equation in both calculators...we have to know how they will handle it. BTW the TI89 reformats the equation into 6/2*(1+2) before giving the result. That at least tells us how it decided to handle it.

 

[misterT]

The only problem that comes in is when we try to use the same equation in both calculators...we have to know how they will handle it. BTW the TI89 reformats the equation into 6/2*(1+2) before giving the result. That at least tells us how it decided to handle it.

The problem is how would you handle it? If a friend of mine asked me to calculate 6/2(1+2), I would assume that he meant 6/(2(1+2)).. or I could ask him "what do you mean by this?". Especially if he wrote it down like this: 6÷2(1+2)

I would never write 6/2(1+2) when I mean (6/2)*(1+2). But, I could easily write 6/2(1+2) when I mean 6/(2(1+2)).. and that is the big problem here.

 

[MrAl]

Hi there mister T,

Well, if there were two kinds of birds, one brown and one red, and the adult brown ones weighed 1 pound each and the adult red ones weighted 9 pounds each and i asked you the question, "How much does a bird weigh?", what would you say? You'd have to ask me what color it was first. Alternately, you could list both and let me decide:
brown birds: 1
red birds: 9

If you knew the guy had both the TI85 and the TI89 for example you'd have to tell him that "It depends on which calculator you use".
That's just the nature of how some questions are..they need a little more information to go with them before we can really render a correct answer.

It's also interesting i think that the TI89 removes the ambiguity by inserting the "*" sign in there. The TI85 programmer didnt realize that there could be an interpretation difference there.

 

[KeepItSimpleStupid]

I did not say that you could simply add the implicit operator. When you do and ask, "Is this what you want?" your now defining an easily defined form. A typeset the equation could be written easily understood.

Parenthesis first gives rise to the 1 answer.

Never was an issue for me. RPN notation and/oe explicit operators.

 

[misterT]

The TI85 programmer didnt realize that there could be an interpretation difference there.

I think all TI calculators have a good documentation about how they handle "implied multiplication".
https://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110

 

[DerStrom8]

Parenthesis first gives rise to the 1 answer.

The parentheses only say to do WHAT IS INSIDE first, not what is immediately outside. 6/2(1+2) means 6/2(3), and left-to-right, according to PEMDAS, gives 3(3), hence an answer of 9.

 

[misterT]

6/a(1+2), 6/x(1+2), 6/A(1+2), 6/A (1+2) - Wolfram|Alpha
If it is not a bug, I would like to know the logic behind those results.

Wolfram development team just replied to me:


It is a known issue that the input "6/a(1+2), 6/x(1+2), 6/A(1+2), 6/A (1+2)" calculates a,x, and A differently. This is because "a" is interpreted as a function since it is directly followed by parentheses, "x" is always considered a variable, the first "A" is directly followed by parentheses (making it a function), and the last "A" has a space between it and the parentheses, so it is interpreted as a variable and not a function.

 

[Nigel Goodwin]

I can't believe this has gone to four pages

It's a question which is deliberately written incorrectly - if it's written correctly there's no problem at all.

 

[KeepItSimpleStupid]

At least WA tells you how its evaluating.

 

[Black Smoke Customs]

Obviously I'm no brainiac like you guys, and I do mean that with all due respect.
Think about this, you have all used a GPS in which it took you to a certain location that you had input, and after you got there you sat back and said "huh, if it had told us to turn right or left back wherever, we would have already been here having a beer", your calculators are only going to do what they have been programmed to do. As for the equation in question, on my level of math, you would do what's in parentheses first. Either way you look at it you have to know on what level your trying to achieve an answer. That's my 2.5 cents, or is it $.02.5.

 

[Dr_Doggy]

oh wait, it is 9! oops!

 

[atferrari]

Four and more pages in spite of MrAl post

I can't believe this has gone to four pages

It's a question which is deliberately written incorrectly - if it's written correctly there's no problem at all.

Yes Nigel. It is evident for all of us that depending on how you WANT to interpret that, results come out different (not to speak of calculators that were programmed differently, as MrAl says).

I wonder what the OP expected. Just one reply? He knows that the expression has two results depending of how you solve the implied multiplication.

I know this kind of question since elementary school where we used to ask "How much is the half of two plus two?" Discussion went forever.

BTW, I was advised once to use enough parenthesis to never come to this situation. It worked well for me.