Understanding PEMDAS in Math: Is There an Exception?

[Petenerd]

On my assesment it had a question that said x+3/3, when x=3. I thought you do 3/3 first so did the teacher, but when he looke at the answer key it showed you were suppose to do 3+3 then divide by 3. And also on my test booklet, it doesn't have 4 which is the answer if you do it with PEMDAS. Instead they have 2, the answer you get when you add first... :?: Isn't that weird? The same thing happened on my state test. On one of the sample answers the state test gives a question just like that and when my teacher and the student found out the answer on the answer key, the answer only works if you add the two number then divide. And also the state test doesn't offer you the answer you'll get when you do it with PEMDAS. Who's right and who's wrong and what is the correct way to do this? :|

 

[CRGreathouse]

Division always happens before addition unless parentheses change the order. If they want addition first it should be written
(x+3)/3
or
$$\frac{x+3}{3}.$$

I'm not entirely sure I like the abbreviation PEMDAS, though. The order is
P
E
MD
AS
which could easily be forgotten in that form.

 

[Petenerd]

The funny thing is on the sample answer it doesn't follow PEMDAS. Do you think the other questions like that will follow PEMDAS? Because when I followed PEMDAS to do the problem, there wasn't a choice for my answer which was 4.

 

[CRGreathouse]

Do you think the other questions like that will follow PEMDAS?

Yes. I think it's more likely that the question was changed but not the answer, then that someone used the wrong order of operations in setting up the question. (This actually happens more than you realize!)

 

[Petenerd]

I think I got the hang of this now!

 

[Hurkyl]

On my assesment it had a question that said x+3/3

Just checking... that is exactly what the problem said, right? The expression was

$$x + 3 / 3$$

and it was not

$$(x + 3) / 3$$

and it was not

$$\frac{x+3}{3}$$

?

 

[Petenerd]

I think the question meant $$\frac{x+3}{3}$$, instead of $$x+\frac{3}{3}$$.

 

[Petenerd]

If the question meant this $$\frac{x+3}{3}$$, I would add first then divide?

 

[CRGreathouse]

If the question meant this $$\frac{x+3}{3}$$, I would add first then divide?

Yes.

 

[Irrational]

i think that unless the assessment is to test PEMDAS (first time i heard of that actually), then giving something like x+3/3 is just lazy. however, if i was given that, i would have assumed it meant (x+3)/3. no reason why someone would actually put 3/3 in an equation unless the intention was to trick.

 

[Petenerd]

Thanks for the help! :)