Arecipe calls for 2/3 cup of sugar for every 1/2 teaspoon of vanilla. what is the unit rate of cups per teaspoon?

The unit rate of cups per teaspoon is: "1 ⅓ to 1" ; or, simply, "1 ⅓ " .

Explanation:

 The ratio:  (2/3): (1/2); or:  (2/3) / (1/2) ;

(2/3) / (1/2) = (2/3) ÷ (1/2) = (2/3) * (2/1) = (2*2)/(3*1) = (4/3) ;

4/3 = 1 ⅓ .  So, the ratio is  1 ⅓ to 1;  and the unit rate is:  1 ⅓ .