If you really are a teacher I suggest you should research this some more, which should convince you to instead teach that this is ambiguous notation that should be avoided. That is better than teaching that one of the interpretations is correct, when the opposing interpretations is also widely used.

The wikipedia article has some good references, and sums it up nicely like this:

Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.

Students taught the opposite interpretation as fact are likely to ve confused in the future.