1) Given that the recipe calls that amount we can set a proportion to find the unit rate:
cup of sugar teaspoon
2/3 -------------------------------------- 6
x ---------------------------------------- 1
2) Cross multiplying those numbers since it is a proporton, we'll have:
6x = 2/3 Multiply both sides by 3
18x = 2 Divide both sides by 18
x =2/18 Simplify
x= 1/9
3) So the unit rate is 1 teaspoon per each 1/9 cup of sugar