"We are cutting the bread with a knife."
Translation:Kroimy chleb nożem.
So, I'm guessing that we don't need any words for "with" here because noz changes case to indicate that it is what we are doing it with?
to make things complicated - we still have with=z + instrumental. You skip "with" when it means "using" but not when it means "and"
Does that mean that the "z" is optional when it means "with" ? Is it correct to say then, "Kroimy chleb z nożem" ?
It's never optional, it just changes the meaning and using it (or lack of it) wrong results in absurd sentences.
"z" is simple "with", mostly "with someone", but also "ryż z jabłkami" (rice with apples) and similar.
Instrumental without "z" means that something was used as an instrument. "kroić nożem" = to cut with (using) a knife. "kroić z nożem" = to cut, while the knife is also cutting (as if it was animated).
Similarly: "Jem zupę łyżką" = I am eating soup with a spoon (using a spoon), vs "Jem zupę z łyżką" = I am eating soup and the spoon is sitting next to me, also eating soup.