Final answer:
To find the unit rate of vanilla to sugar, convert the vanilla measurement to cups, yielding 1/24 cups for 2 teaspoons. Then divide 1/24 cups of vanilla by 3/4 cups of sugar and simplify to get a unit rate of 1/18 cups of vanilla per cup of sugar.
Step-by-step explanation:
To compute the unit rate for vanilla to sugar in the recipe, we first need to convert all measurements to the same unit. Typically, we use cups for such calculations because the sugar quantity is already given in cups. We know that 1 teaspoon is equivalent to 1/48 of a cup (since there are 48 teaspoons in a cup). The recipe calls for 2 teaspoons of vanilla, which we convert to cups:
2 teaspoons × (1 cup / 48 teaspoons) = 2/48 cups of vanilla
We can simplify 2/48 to 1/24 cups of vanilla. Now that we have both ingredients in the same units, we can compute the unit rate:
(1/24 cups of vanilla) / (3/4 cups of sugar) = (1/24) / (3/4)
To simplify the fraction, we multiply by the reciprocal of 3/4 (which is 4/3):
(1/24) × (4/3) = 4 / (24 × 3) = 4 / 72
Simplifying 4/72, we find that it equals to 1/18. Therefore, the unit rate of vanilla to sugar is 1/18 cups of vanilla per cup of sugar.