Set up a proportion:
(1/3) cups over 6 servings = x cups over 20 servings. $${\frac{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{{\mathtt{6}}}} = {\frac{{\mathtt{x}}}{{\mathtt{20}}}}$$
Then, cross multiply:
$$\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{20}} = {\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}$$
Multiply it out:
(20/3) = 6x
Divide both sides by 6. Dividing by 6 is the same as multiplying by (1/6)
x = (20/3) * (1/6)
x = 20/18
Simplify.
x = 10/9 or 1.11111111...cups.