So, um, what exactly IS the correct answer?

[mjr]

To the following:

6 ÷ 2(1 + 2) = ???

Now, if you grew up when I did, and learned order of operations, the answer is, obviously, 1.

Parenthesis, (brackets, if present), Multiply, Divide, Add, Subtract.

Even if you use PEMDAS, multiply comes first.

The video, however, claims that once you get to

6 ÷ 2(3), which is essentially 6 ÷ 2 * 3, that you're supposed to do 6 ÷ 2 first, to get 3, then multiply by 3, to get 9.

So, which is the actual correct answer? This seems like it would jack up a lot of actual proven equations and formulae. I'm not sure this guy is on the right track...

Video here:

https://www.youtube.com/watch?v=URcUvFIUIhQ

[Lachrymose]

I grew up when you did and learned the order of operations. The answer is 9 for the reason he stated.

Multiplication and division are on the same level, you work left to right when you encounter either. Same with addition and subtraction.

Would you still have the same issue with 6-2+4? I mean, obviously the answer isn't zero.

[mjr]

I grew up when you did and learned the order of operations. The answer is 9 for the reason he stated.

Multiplication and division are on the same level, you work left to right when you encounter either. Same with addition and subtraction.

Would you still have the same issue with 6-2+4? I mean, obviously the answer isn't zero.

I was generally taught you were always supposed to multiply first.

The comments under the video pretty hotly debate the answer. The parenthesis matter, though, since people say that 2(x) is one term.

At least that 's the way me, and many, many others across the world were taught...

Couldn't you also write the expression as this:

6
------------
2(1 + 2)

And wouldn't the answer, in that case, be 1? And how is it different than how the problem is written? Both the ÷ and

X
---
Y

Are division, correct?

Or perhaps another way of thinking of it.

6 apples, two classes of three children each.

6A = 2(3)
6A = 6
A = 1

So 1 apple per child, correct?

Right??

[Lachrymose]

Hmm..interesting point.

I think when you are dealing with all constants, the parentheses only matter until the final operation is made *within* them.

As far as using variables go...that's something I didn't think of. I'm thinking that's a whole other deal that doesn't follow the usual order of operations, but I'll have to do some research on that. But yes, in that case I would be inclined to do the multiplication first.

Edit: To address your edit, I realize he mentioned the historical reason of putting all those values in the denominator of a fraction, however, the only way I could see it that way is if everything after the division sign is in parentheses. In other words: 6 ÷ (2(1 + 2)).

You're a programmer, right? Me too, although I think you have much more experience in that than I do. How would some of your software handle it?

[mjr]

You're a programmer, right? Me too, although I think you have much more experience in that than I do. How would some of your software handle it?

Well, remember: In programming it would look something like this:

x = 6 / 2*(3)

But I am curious...

So I put together something really quick...

int x = 6 / 2*(1 + 2);

C# gives 9 as an answer. Which I do find strange.

So I guess it just depends on how the problem is interpreted...which is weird to me, because like I said, I was always taught (along with many others around the globe, so it's not just where I grew up), that you did multiplication first before division.

[Lachrymose]

It does indeed seem to be about interpretation and convention.

I just found this article, which certainly doesn't really clear things up exactly but is interesting nonetheless.

http://www.slate.com/articles/health...ar_answer.html

[TheHuckster]

I was taught PEMDAS, but in actuality it was more like PE(MD)(AS).

Multiplication and division are on the same level, above addition and subtraction, which are also on the same level.

And, yes, in software, this is also the case. When you do something like x = 9 / 3 * 3 x will be equal to 9, not 1. At least in all the languages I've known.

[Daskinor]

I think I see in the misunderstanding people are having;

6 ÷ 2(1 + 2) is not correct interpretation. It is convenient shorthand based on the most common application of the math in question. When we see 6 ÷ 2(1 + 2) the correct notation is, 6 ÷ 2 * (1 +2).

Then you get your 6 ÷ 2 * 3, then it’s left to right like normal.

3 * 3 and then

9

Also "multiplication first before division" is not taught because it is incorrect. Math does not bend to interpretation. Most people confuse "multiplication first before division" for the correct saying that is taught in schools "multiplication first before addition"
Division is a representation of multiplication where one of the operators is less than 1. So the standard notation of ‘6 ÷ 2’ is equal to ‘6 * ½’. That means Division is no different from multiplication from the perspective of numbers. So there is no preferential treatment for one over the other.
In the context of this question 6 ÷ 2(1 + 2) is equivalent to 6 * 1/2(1 + 2)

6 * 1/2 * 3

Now the reason we follow the left to right rule is because of the division symbol. When you remove it from the equation you can work whatever pair you want first. In theory pairs factors with like operators can be done in any order. But standard notation division is an abomination in our math education, I am glad it is going away.

6 * 1/2 * 3 = 3 * 3 = 9

or

6 * 1/2 * 3 = 6 * 3/2 = 18 /2 = 9

or

6 * 1/2 * 3 = 6 * .5 * 3 = 6 * 1.5 = 9

This goes hand in hand why we are trying so hard in this country to change how we teach math in schools. We don’t teach how numbers work, or how they are fluid and can be manipulated within the rules that govern them.
We teach the quickest and most efficient way to solve the problem. And that is the WORST way to teach math. Number lines may take longer to draw out then standard notation. But number lines teach the properties of addition. And that is WAY more important than doing quick mechanical method for math that does not require understanding of math beyond being able to do addition and subtraction up to 10.

6 ÷ 2(1 + 2) is such a wonderful problem, because it allows us to see exactly where a mistake is being made in the order of operations.

[SkullKing]

I never heard of any method that put multiplication over division in priority.

As Daskinor said, division is just particular case of multiplication, the same way subtraction is particular case of addition. Make sno sens for one to have priority over the other.

[D_Yeti_Esquire]

Daskinor has probably the cleanest pure math expression I've seen of this (which I'll crib.)

I always hated questions like this because this was always the kind of silliness someone would throw into a bonus question without ever really going over the why prior or after but its also (as far as I can tell) a way to make something that's visually slightly ambiguous mean one thing by rigidly applying rules.

The expression as they've written it (removing division is) 9 * 1/2 * (1+2). The confusion is that because of the standard convention of parenthesis, a human would expect and then attempt to distribute the 2. It's a terrible expression of the problem in human terms.

To get the answer you expect mjr, you would have to rewrite 9 / (2(1+2)). It's that second set of parenthesis most people reading it will apply by default because someone wrote it in a common arithimatic form because its a terrible way to write it. In Algebra/Calculus though, no one would ever logically write it that way (for just this reason). I think its a goofy question for everyone except for programmers because they need to know exactly how a computer is going to evaluate. If you're doing equations though, you wouldn't expect to see something written that way.

[Greenday]

I was taught PEMDAS, but in actuality it was more like PE(MD)(AS).

This. Multiplication doesn't take place before division. It takes place at the same time, from left to right.

[jackfaire]

I was taught PEMDAS but like was previously stated MD and AS are on the same levels respectively

The way I think of it is that it's like walking down stairs. First you have to walk down the Paraentheses, then continue down the exponential step, then there is a little landing called MD and you walk over whichever is first before reaching the hallway or AS and again you take them as they come in order.

Multiplication and Division are the same level you do which ever comes first They just abbreviate it the way they do because PEMDAS is easier to say than PEDMSA