One important use of fractions is being able to divide recipes into parts, that is, smaller sizes?

Absolutely, many recipies call up quantities in items, cups, 1/2 cups table & tea spoons, and of course in imperial measures (16 ounce in a pound is easily diveded into 1/2, 1/4, 1/8 & 1/16 of course more readily than metric), all of which can be easily factored and use fractions to produce a balanced as per recipe smaller portion.
The traditional way to teach fraction is by dividing a pie up into equal portions after all.