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I usually record class grades in my grade book in a format like 9/10, where "9" means how many points a student earned and "10" means how many points they could possibly earn. The computer grade book system then converts this into a percent, e.g. "90%".

Recently, I assigned some extra credit, so I entered student grades as 10/0, following the same conventions above, but meaning "10 extra credit points earned". A large number of students (junior undergraduates) became upset. While I can see where they are coming from (they probably heard about divide by zero), and realize some of them have much stronger math backgrounds than myself, a writing teacher, but the grade book software has no difficulty with an entry for "10/0".

Have I made a mistake? If not, how can I explain why this grade book entry is not a problem?

Village
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    Your students should learn the meaning of "convention" and stop being picky, probably. – Pedro Oct 06 '14 at 01:30
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    You could state it as being 10 points earned from 0 required –  Oct 06 '14 at 01:31
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    you simply overloaded the symbol '/'. It's perfectly fine as long as context clarifies the situation, which in this case it certainly does. Those students who don't see the clarity of this issue should perhaps not be awarded any extra points, and thus get $0/0$, and then they can complain that that is undefined. In which case, you can reply that if they continue their final mark will also be undefined. – Ittay Weiss Oct 06 '14 at 01:32
  • @IttayWeiss But wouldn't that be a good thing then? – Edward Jiang Oct 06 '14 at 02:45
  • what would be a good thing @EdwardJiang ? – Ittay Weiss Oct 06 '14 at 02:46
  • If they're final mark is undefined (infinite). Never mind, it was just a joke. – Edward Jiang Oct 06 '14 at 03:08

2 Answers2

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It would seem reasonable that, at the end, you're planning to sum the total points earned out of total points possible to earn, and hence, your addition looks more like: $$\frac{a}{b}+\frac{c}d=\frac{a+c}{b+d}$$ than, like, actual fraction addition - so you're not literally dividing by zero, you're just repurposing the notation of a fraction to mean a pair of numbers which, conveniently, doubles as individual scores for each graded item.

Milo Brandt
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The reason why the computer doesn't reach an error by recording the marks is because the grades are cumulative. If you score, say, 6/10 on one assignment and 4/5 on another, then your total grade is 10/15. Generally, if you score $a/a_0$, $b/b_0$, ... on the assigments, then your total grade will be

$$\frac{a+b+c+\cdots}{a_0+b_0+c_0+\cdots}$$

In your case, assuming the extra credit is not the first assignment (why would it be!), then the math is perfectly legal.

Edward Jiang
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