Can we add, subtract, multiply, or divide each side of an equation by a unit if there are already units on both sides?
Do they just work like numbers?
Example 1
$$ 12 packs \cdot 10 dollars/pack = 120 dollars. $$
Can it be, say (don't know what the new unit means but is it valid mathemetically?):
$$13meters\cdot (12 packs \cdot 10 dollars/pack) = 13meters\cdot120 dollars.$$
or (be divided by a unit and become pure numbers)
$$ 12 packs \cdot 10 dollars/pack = 120 dollars. $$
$$ 120 dollars = 120 dollars. $$
$$ 1/dollars\cdot120 dollars = 1/dollars\cdot120 dollars. $$
$$ 120 = 120 $$