Okay, say the equation was ab(c+e) =

In middle school we saw the operators "a*b" or "a x b". Then we were taught later that "ab" is implied multiplication.

The issue I am seeing is where people distribute the "b" with the "c" and "e" and just leave the "a" all by itself. The "a" and the b together is one term. Since division is just multiplying by the reciprocal, nothing should change about how it is interpreted:

a(1/b)(c+e) = a/b(c+e)

Basically, we were taught to see ab(c+e) as (ab)(c+e), and a / b(c+e) as a / (b(c+e)).

@Lenny, even if the forward slash was the division symbol? The actual photo used the division symbol. I should have clarified. If that is still the case, I wonder where the oversight happens (as the answer is 9). Even more, if that is not the case, then how does one become a software engineer and come even close to saying the answer is 2? Not in this thread, but on LinkedIN.

Someone pointed out that Excel math says it is 9.

I had to look at it again. I see how people are seeing it:

6/(2(1+3))

It would be seen as 6 divided by the quantity 2(1+3), which would yield 1. But in the event that is what was asked, I would have typed just that, or I would have hoped that that is how it would have been asked.

I voted for 7.

"Implied multiplication" has a different precedence than multiplication?? Is that really a thing?

It sounds as silly as multiply and divide having different precedence.

Does any post-basic-schooling math actual use such wacky precedence rules?

I just saw that link Chris. Didn't know it was such a big deal as that haha. But his explanation is right on point, especially how he says that multiplication and division have the same precedence because of division being multiplication by the reciprocal.

I figured it had a lot to do with perception why it seems engineers say 1. But even before I programmed, I would still say 1.

Interesting conquest nonetheless.

Does any post-basic-schooling math actual use such wacky precedence rules?

My impression is that most post-basic-schooling math would use a better notation that wouldn't have these sorts of ambiguities. :)

Does any post-basic-schooling math actual use such wacky precedence rules?

My impression is that most post-basic-schooling math would use a better notation that wouldn't have these sorts of ambiguities.

Even in University we would write stuff like: y = x(x+1)
Which means: y = x * (x+1)

There's no ambiguity there - this is the only thing that it can mean.

In primary school we didn't ever use these "implied multiplies" -- we'd always write the second (explicit) version.

I had no idea that this kind of "implied multiplication" was controversial though, and especially had no idea that some people are taught that an implicit multiply has different precedence to an explicit multiplication...

To get an answer other than 9 from the OP's equation, you need to be using a precedence scheme where multiplication (or "implied multiplication") has a higher precedence than division... which goes against everything I've ever been taught. I don't see how such an interpretation is justifiable.

You're right, that isn't ambiguous. 6/4(3*2) is ambiguous. What I was saying was that the proper notation would have it be written out something like how Bacterius did it. So it would be explicit simply from the formatting whether that meant (6/4)(3*2) or 6/(4(3*2)).

To get an answer other than 9 from the OP's equation, you need to be using a precedence scheme where multiplication (or "implied multiplication") has a higher precedence than division... which goes against everything I've ever been taught. I don't see how such an interpretation is justifiable.

I was one of the ones who answered '1' at first. I don't recall ever being taught explicitly that "implied multiplication" has a higher precedence, but in every case that I've seen that uses the notation, the expression is written in such a way that the precedence turns out that way, anyway, so I think I've just been conditioned to assume that it does have higher precedence even if technically it doesn't and I don't consciously think of it as having a higher precedence. In my intuition, the '2' just rendered as a part of the bracketed expression and was therefore to be evaluated along with it.

Upon further research, I have rethought my response.

I watched several videos and read a few posts over the internet. Both answers are correct because the problem poses merely a communication problem.

Inline notation is sort of dangerous in this respect (which is what programmers have to use).

Supposedly, it was common for people to note what set of rules they were using when writing about such equations. This oversight has caused bugs in computer programs and perhaps in engineering projects?

One thing is certain, this needs to be dealt with in the education system. However, one video stated that the forward slash is not a division bar, and is just like the division symbol, or the colon.

So the answer is both solutions depending on the set of rules used to interpret the question.

It's crazy that this is how I learn this though. Once again school has failed me.

You're right, that isn't ambiguous. 6/4(3*2) is ambiguous. What I was saying was that the proper notation would have it be written out something like how Bacterius did it.

I still don't see how it's ambiguous -- Bact wrote out two equations:

\[6/2(1 + 2) = 9\]

\[6/(2(1 + 2)) = 1\]
The OP posted the first equation. Bact's working, which I've cut out, shows you the nicer looking way to write those equations... but doesn't show an ambiguity.

[edit]

After reading wikipedia, it appears that some universities did actually used to teach that "implied multiplication" has higher precedence than explicit multiplications/divisions... which would mean that both of the above result in 1 (or the top line is false)...

But there seems to have been a shift where this is now a non-standard way of reading/writing formulae... so to get 1 as the answer from the OP's equation, you've got to be using archaic interpretations of it, instead of the now common way of interpreting it.