A recipe calls for 1/3 of a cup of butter, if Ben is making 1/4 of the recipe, how much butter should he use?

Question

I know the answer, but why do you multiply instead of dividing to get the answer?

Answer 1

¼×⅓=1/12 cup of butter

"Of" usually means "multiply by".

If the recipe had said 4 cups of some ingredient then a quarter would have been one cup, because ¼ of 4 is 1. So ¼ of ⅓ = ¹/₁₂. Or you could say ⅓ divided by 4.