How to explain why 10/0 is an okay grade book entry?

Question

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?

Answer 1

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.

Answer 2

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.