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Stupid question: 6:2(2+1). I am pretty sure it should be 9 but why Wolfram Alpha says is 1? (self.math)

nishizonoshinji が 投稿

Hi guys pretty stupid thing, I am not a mathematicians but I am a big redditor so I came here to solve my problem.

I am pretty sure 6:23 should have division first since it comes first and even if make 6/2 (2+1) it makes 33= 9

So when does multiplication go first?

Thank you all guys!

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[–]quack_the_quinoa 3ポイント4ポイント  (10子コメント)

The : symbol doesn't work like a division sign. It represents a ratio between what's to its left and what's to its right. Thus the expressions on each side will be evaluated before the ratio is evaluated.

[–]overconvergent 2ポイント3ポイント  (9子コメント)

And even if it did work like a division sign, the expression 6/2(2+1) is ambiguous. Different people and software packages would interpret it different ways. There is no "correct" way of interpreting 6/2(2+1), and you need to use parentheses when writing such an expression to make it clear what you mean.

[–]almightySaplingLogic -2ポイント-1ポイント  (8子コメント)

There is no "correct" way of interpreting 6/2(2+1)

What? Order of operations exists and, unless it was poorly explained (and it usually is), it's not ambiguous at all.

This is correct:
6/2(2+1)
6/2(3)
3(3)
9

The following is wrong:
6/2(2+1)
6/2(3)
6/6
1

[–]skullturf 3ポイント4ポイント  (3子コメント)

Expressions of the form

a/bc

are genuinely ambiguous. Some well-regarded authorities (e.g. "Concrete Mathematics" by Graham, Knuth, and Patashnik) adopt the convention that

a/bc means a/(bc).

Wolfram Alpha is inconsistent on this matter. It interprets

x/2x

as (x/2)x = x2/2, but it interprets

a/ab

as a/(ab) = 1/b.

http://www.wolframalpha.com/input/?i=x%2F2x
http://www.wolframalpha.com/input/?i=a%2Fab

[–]almightySaplingLogic -2ポイント-1ポイント  (2子コメント)

They adopt a convention. They find that something differing from the norm is more useful in their specific context, and they state that explicitly. There is nothing wrong with that. It doesn't mean that order of operations doesn't exist in the context of arithmetic evaluation.

And I don't consider Wolfram's behavior to be indicative of standards by any means. It tries really hard to make guesses based on convention and it does a surprisingly good job (I think) but I would be vary cautious to trust anything it says on faith alone.

[–]skullturf 1ポイント2ポイント  (0子コメント)

They adopt a convention

It doesn't mean that order of operations doesn't exist

Order of operations is also just a convention. Yes, it "exists" but it wasn't handed down from the heavens.

[–]overconvergent 0ポイント1ポイント  (0子コメント)

There are no "norms," "conventions," or "standards" here and I don't know where you're getting that idea. Order of operations is something that really only exists in k-12 education and in software (calculators, CASs, programming languages, etc.) and there are differing conventions even in those contexts.

[–]overconvergent 7ポイント8ポイント  (2子コメント)

Order of operations is something we made up in an attempt to get k-12 students to understand how to work with expressions like 4+5*6, which is unambiguously equal to 34. It was not meant to be applied to expressions like 6/2(2+1). This is not an expression that a mathematician would ever write, and there is no correct way of interpreting it. In fact, if I had to chose, I would have assumed it meant what you said is the "wrong" interpretation, since "implied multiplication" usually takes precedence over division.

[–]jmwbb 5ポイント6ポイント  (0子コメント)

Honestly, just the fact that any degree of disagreement is present here demonstrates that the author should definitely clarify with parentheses.

[–]almightySaplingLogic -5ポイント-4ポイント  (0子コメント)

All math is "something we made up". And Order of Operations has jack all to do with school children.

We have an order of operations so that we can write out complicated expressions without requiring dense collections of parentheses, and the only way this works is if there is an agreed upon interpretation.

And thus we have arrived at the expression above equaling 9, and I have no clue what you mean when you say "implied" multiplication coming before division. Concatenation is generally understood to be multiplication (if this is what you meant by "implied"), and it comes neither before nor after division.

Obviously there are differences in hand (where vertical alignment and spacing can imply grouping), but there is none of that here.

[–]ben1996123 0ポイント1ポイント  (0子コメント)

so you're saying you should always do division before multiplication? what about the fact that some people learn "pemdas" which says multiplication first?

[–]KillingM -4ポイント-3ポイント  (0子コメント)

Btw, those parentheses are first, not the division. So 2+1 is 3. 2*3->6 . 6/6=1