I didn't say fractions is the wrong way. I said lining up units is the wrong way. Sure, when units are different this method of checking works. But you should understand _why_ it works.
What does it mean a is proportional to b? It means a=kb, where k is a constant.
So, 1 cup lemon juice is proportional to 8 cups of lemonade => 1 cup of LJ = k * 8 cups of L => k = 1/8
x cups of lemon juice is proportional to 16 cups of lemonade => x = k * 16 => k = x/16
Therefore, 1/8 = x/16 - these are your fractions.
As a shortcut you can write it down in plain English, but in _LOGICAL_ manner:
1 cup lemon juice makes 8 cups of lemonade
x cups lemon juice makes 16 cups of lemonade
This results in proportion 1/8 = x/16
You don't write
1 cup lemon juice makes 8 cups of lemonade
16 cups of lemonade makes x cups lemon juice
which would result in an incorrect proportion 1/8 = 16/x
See the difference? If you checked units you would not have caught this error.
