Confused about what the standard order is?

1. Tyrion101

153
In my previous two math classes I'd get the answer wrong if I put the number first then the variable as my answer. Now in this class this way of doing it is wrong. I'm seriously confused now. For instance the last two classes said that it was standard practice to write an answer like: 3x+4. This class doesn't say it's standard or even that I should write. It as: 4+3x. I'm confused, which is more usually done? I like 3x+4 because to me things are more obvious when written that way, 4+3x doesn't show me anything. I'm going to come out of this class completely confused, and don't know which I should assume would be a right answer?

2. jbunniii

3,378
Since ##4+3x = 3x + 4##, there is nothing mathematically wrong with your answer. If your instructor is imposing rules about how the answer must be written, then the only sure way to know what those rules are is to ask him/her.

Based on the data point you have given, I would guess that the instructor wants to see a polynomial written with the terms in ascending order, so for example
$$4 + 5x + 7x^2 + 4x^3$$
would be acceptable but
$$4x^3 + 7x^2 + 5x + 4$$
would not. The second form is more "standard" in the sense that people traditionally write it that way. In the absence of any other considerations, it's probably better to write it in the second form so people will find your work easier to read. However, if your instructor demands the first form, then you have to do that if you don't want to lose points for such an arbitrary reason.

One reason to prefer writing the terms in descending order is that you can immediately see the degree of the polynomial by looking at just the first term. Another is that it is consistent with how we write decimal numbers: the number ##3241## is equal to ##3x^3 + 2x^2 + 4x + 1## where of course ##x=10##.

But again, pragmatism requires that your instructor's demands should trump all other considerations, at least while you are doing work for that course!

Last edited: Apr 15, 2014
3. Tyrion101

153
Well I don't think it's my instructor the is an online class and it could just be that the particular program is set ti read the answer in one way. I'm glad you said something, because I've looked at my answers a few times and have noticed nothing that could be mathematically wrong. Now I could be forgetting parenthesis when doing ordered pairs, but most often it's not. I was just a bit confused, thank you.

4. micromass

19,657
Staff Emeritus
See, this is why people hate math. Because of some instructors/computer programs saying that ##3+4x## is wrong but ##4x + 3## is somehow correct. No wonder students are confused when instructors/computer programs make completely arbitrary and unreasonable demands like that. It goes against the very spirit and freedom of mathematics.

5. jbunniii

3,378
Sounds like it's a badly written software application that is auto-checking your answer. Bummer, in that case all you can do is try to adapt your answers to whatever arbitrary order it wants to see. :yuck:

6. micromass

19,657
Staff Emeritus
I know it's an online class and all. But I think that teachers using software to check student's homework is a very bad thing. Mathematics is about the thought process and about the intermediate steps, while the software only cares about the final answer.
But ok, I don't know a good alternative for online classes.

7. Tyrion101

153
The reason I did it because the class I wanted didn't meet my schedule, the homework you have an infinite number of chances to get it right, and if you complete it, it counts as 100%, but the problem might be on tests, guess I'll just have to be more careful. I'd hate to get a test question wrong for putting it in the "wrong" order.

8. jbunniii

3,378
When I was in college we had multiple choice exams in some of the large freshman classes, to make the grading easier. I thought that was bad, but this is much worse. I guess they don't use multiple choice because they don't want the student just guessing answers, but now a different sort of guessing is required.

9. disregardthat

1,841
Does it at least tell you the answer is incorrect? If I had answered "3x+4" while the answer was "4+3x" and lost points on a test I'd be furious.

10. pwsnafu

938
You can use prob to illustrate just how unreliable multiple choice tests are: suppose a test has 4 answers, and a student wished a score of 73% overall, then he'll need to correctly know the answers to only 64% of the question and guess the rest.

One way to get around this is deduct 0.25 marks per wrong answer, but that has the other issue of what if the student didn't guess but got the wrong answer. Should you be penalizing?

11. Tyrion101

153
So I just experimented. Apparently the gripe with me is I forget the parenthesis on the ordered pair. Not the order it's in. Whoops.

12. DrewD

498
What ordered pair? The example you gave has neither an ordered pair nor a need for parentheses.

13. Tyrion101

153
For a solution set that has infinite possibilities (the same line) should be written as (3x+4, x), is this how it's generally done?

14. micromass

19,657
Staff Emeritus
I see what you mean. Order is important in that case. For example, if you want to describe all points on the line ##y=3x+4## then that would be

$$\{(x,3x+4)~\vert~x\in \mathbb{R}\}$$

if you write it in set-builder notation. Writing it as

$$\{(3x+4,x)~\vert~x\in \mathbb{R}\}$$

would be wrong

15. Tyrion101

153
Thank you, this has been a sore point this whole class.

Staff: Mentor

Points in the plane are written as ordered pairs with the x coordinate first and then the y coordinate. Points in space are written as ordered triples, in the order x, y, and z. Every point on the line y = 3x + 4 (micromass's example) could be written as (x, 3x + 4). If you wrote the order backwards it would be wrong.

I would imagine that this order of the coordinates of points would be something that was covered in an algebra or even prealgebra class.

17. Tyrion101

153
If it is something like: -3x+4, would this be written as: (x, 4-3x)?

Staff: Mentor

Yes, provided we're talking about points on the line whose equation is y = -3x + 4.

When you started this thread, our understanding was that you were asking about, for example, -3x + 4 as opposed to 4 - 3x, both of which mean exactly the same thing. As it turns out, though, what you were apparently asking about was the order in an ordered pair; e.g., about (x, -3x + 4) vs. (-3x + 4, x). The order in which the expressions in an ordered pair is very important.

19. Tyrion101

153
I am sorry, I have difficulty getting my point across. Sorry again about the confusion.