I really don't understand how people got this wrong... This is like elementary math.

That's why it shocked me conq, and as the numbers keep rolling in (12,000+ comments) not only 1 and 9 pop up, but I saw a 5. Haha

I think I have a better question for us programmers.
What if it were rewritten this way?

b = 3
6÷2b


What’s the result now?


L. Spiro

I'd say 1 to that right away, because there are no parenthesis, and the relationship between the 2 and the b is more defined.

2b = 2×b.

Why the change in the answer?


L. Spiro

Because b is a variable and is unknown until we make it known to be 3 instead of (1+2), which in a real world problem might denote two different constants.

6/2(c+d)

If c =1 and d=2

Does this mean that

6/2(e+f), where e = 2 and f = 1

is equal to the first expression? But we do have another word...

Equivalent?

I think I have a better question for us programmers.
What if it were rewritten this way?
b = 3
6÷2b
What’s the result now?

There's still a tiny multiply hidden in there:

6÷2?b
   ^

So it's still the same. You still have to write 6÷(2b) if you want to compute 1 as the result.

Hmm. I see where the issue is now. That was a very good take on the answer. But regardless, what is plain isn't so plain. Say I posted that first, then the answers would have been much different.

So, what do you say the answer is Hodgman.

The question I am left with is, "when does the order of operations apply?

I think it has more to do with the relationship of the numbers because at the end of the day, we are communicating an idea. This is why I say the answer is one or the other depending on notes that specify now...

Let me propose an alternative example that shows why I think implicit multiplication became a thing.

Suppose you wanted to compute 6 meters / 2 seconds. This is obviously 3 m/s, right?

I was taught to think of the expression 6m as 6 * 1 meter and 2s as 2 * 1 second.

If it weren't the case that the unit multiplication has a higher precedence than other kinds of multiplication/division, then this would evaluate to 6 * m / 2 * s which according to the more standard precedence rules would come out to (6*m)/2)*s, or 3ms, NOT 3m/s. Right quantity, wrong units, and there went my marks on the exam.

I assume that this sort of thinking got applied to other cases, resulting in a way of thinking that treats implicit multiplication as being higher precedence. The result of this is that, when nested inside a larger expression, 2b would be treated as "(2*b)", not just "2*b". This thinking would percolate down through teachers and students until eventually it just got stuck in people's minds.

I think it might also be the way that we read it. If I were reading the expression out loud, I would have said 6/2b was "six over two bee," not "six divided by two times bee." This is definitely a habit I've picked up from my schooling, though I don't recall if that was from the teachers or the students (and nobody corrected us). So the 2 and b terms appear, simply from listening to the English pronounciation of the sentence, to be more tightly bound than the 6 and the 2, meaning the implicit multiply has a higher precedence.

I just throw it in Google and let them super computers figure it out.

https://www.google.com/#q=6/2(1%2B2)