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When a somebody asks you to solve a problem and "show your work," how much detail should be shown?

For a simple example, if I were to solve $5x+7=17$, should I do: $$5x+7=17$$ $$5x+7-7=17-7$$ $$5x=10$$ $$\frac{5x}{5}=\frac{10}{5}$$ $$x=2$$ or $$5x+7=17$$ $$5x=10$$ $$x=2$$

In my math class, I have actually seen it both ways.

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Depends upon the proficiency of the reader. – check123 Nov 29 '12 at 16:31
The best person to answer this question is the person who will be grading the work. I recommend showing these examples to that person and seeing which one they say is more like what they are looking for. Every teacher has their personal preferences and grading style, and your best bet to make sure you are not showing too little work is to check with every teacher who wants you to show work exactly what they are expecting. I've never been or seen anyone marked off for showing too much work, either, so if in doubt, put in extra steps. – Todd Wilcox Nov 29 '12 at 16:50

I concur with glebovg about college-level algebra.

If you are just learning algebra, for the first time (if you are taking your first course in algebra at the pre-college level, or are taking remedial algebra and are in the early stages of the course), then your instructor might want you to show all the work you show in your top example. But later on in such a course, your instructor would likely be looking for the kind of work you show in your second example.

A good gauge for how much work to show for any problem might be to mirror the amount of work shown by your instructor during lectures.

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In college, the latter would seem much more appropriate because everyone assumes you know how to add and multiply. Even if your instructor demands many steps, the second and the fourth line in the former solution are not necessary.

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Write however much detail is needed to communicate your thinking.

Homework is not assigned for the benefit of the teacher/grader. It is assigned for the benefit of the student. Therefore, write homework as if you were writing an instruction manual for yourself. Put what is necessary to make the solution process clear; not so much information as to distract from the material.

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You should include enough detail to convince the grader that you understand what you’re doing. The actual amount will depend on the grader and on the level of the course. In your example the first answer might be appropriate in a first introduction to algebra in secondary school or in a low-level remedial course in college and the second in a brush-up pre-calculus algebra course, while at any higher level you could probably go directly from $5x+7=17$ to $x=2$.

Once the term is well under way, it may also depend on the impression that you’ve already made: I’ve generally wanted to see a bit more detail from weaker students than I need to see from the stronger students.

If you find the material fairly easy, you may also find that more detail is wanted than you think is necessary. You may well be right as far as explaining the calculation to yourself is concerned, but that’s not what you’re doing (except as a secondary goal): as I said, you’re really trying to convince the grader that you understand what you’re doing, and that may require more detail than you need to convince yourself.

The most direct way to find out what’s expected is to follow Todd Wilcox’s suggestion in the comments: prepare some sample answers, and ask the instructor. Failing that, a good rule of thumb is:

When in doubt, give a little more detail rather than a little less.

It’s certainly possible to overdo the detail $-$ in almost all college-level settings your first example would be overdoing it $-$ but in my experience it’s much safer to err on the side of too much until you discover the instructor’s sweet spot.

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