a recipe used 2/3 cup of sugar for every 2 teaspoons of vanilla. What is the unit rate in cups per teaspoon ?

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Or do you mean teaspoons per cup?

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To find the unit rate in cups per teaspoon, we need to determine the amount of sugar used for 1 teaspoon of vanilla.

We know that the recipe uses 2/3 cup of sugar for every 2 teaspoons of vanilla. Let's simplify this ratio by dividing both values by 2:

(2/3) รท 2 = 1/3

This means that 1 teaspoon of vanilla requires 1/3 cup of sugar. Hence, the unit rate is 1/3 cup per teaspoon.