What are oxidation numbers?
These are typically used to simplify redox equations....
Now I can write the reduction half equation reasonably easily. You know the drill; the difference in oxidation number is accounted for by electrons, which we treat as virtual particles:
Chromium is reduced from
Both charge is balanced, and mass is balanced (is it?), as indeed it must be if it reflects chemical reality. I could have included the counterions, i.e.
Dichromate is sometimes used to oxidize alcohols to carboxylic acids, where the carbon is oxidized from
The overall redox equation typically removes the electrons, and so we take
Which I think is balanced with respect to mass and charge.
Anyway, is this what you want? I am willing to have another try if you refine your question.