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From a notational standpoint, mixed fractions have a tendency to be confused with multiplication of a number and a fraction, for example $2 \frac{1}{3}=\frac{7}{3}$ vs $2 \frac{1}{3}=\frac{2}{3}$. Of course technically the multiplication should have parenthesis, but the omission of them is fairly common. The convention that adjacent objects indicate multiplication thus creates confusion with the common method for writing mixed fractions.

I have been having a lot of issues with this when tutoring students, who will tend to read the notation in whichever form they were taught first. It's a major problem since reading the notation wrong completely changes the statement. Since the notation is identical, I do not have a way to tell them how to distinguish; in fact my only way to tell which it is is to look at what part of the text the problem came from.

Does anyone have a good way to deal with this ambiguity?

Elliot
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The solution is simple . . .

Never use $2 \frac{1}{3}$ to mean the product of $2$ and $\frac{1}{3}$, precisely because it would usually be interpreted as a mixed number.

If you want to write the product of $2$ and $\frac{1}{3}$, choose one of the notations $$2\bigl({\small{\frac{1}{3}}}\bigr),\;\;\;\;\;\;2\cdot {\small{\frac{1}{3}}},\;\;\;\;\;\;2{\,\times\,}{\small{\frac{1}{3}}}$$ which are all clearly products.

I don't know of any standard textbook, at any level, that uses the notation $2\frac{1}{3}$ to mean the product of $2$ and $\frac{1}{3}$.

quasi
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    The issue comes up more when teachers give written HW assignments or solutions. – Elliot Nov 03 '17 at 13:39
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    Then teach the teachers not to do that (i.e., have the students complain, and have the students show the teacher how it's written in books). I suspect there aren't too many such teachers, anyway. – quasi Nov 03 '17 at 13:41
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    I would rather never use “mixed fraction” notation. It is a notational monstrosity that can be resolved by a simple +. I have no idea why the textbooks that teach this “notation” want to confuse students for no reason. – user76284 Oct 28 '19 at 00:14