I was talking with a child who, I was told, has learned some basic multiplication that he can do in his head, so I asked him
Сколько будет восемь на семь?
I'm not a native speaker, but I've given lectures in Russian on higher math and I say just
на in place of
умножить на and
разделить на; the context makes it obvious which one is meant. With the child also it was obvious (to me) that I meant multiplication, since division, square roots, etc. are not yet part of the child's lexicon.
Anyway, the parent corrected me by repeating the task but said
восемь умножить на семь. That made me realize that perhaps when children learn multiplication this operation is always given in the form
умножить на instead of
When does the transition usually take place to abbreviate multiplication (and division) to
на when the choice is clear from context?