At a restaurant, 1/2 of the dishes on the menu are vegetarian. of the vegetarian dishes, 4/5 are pasta dishes. what fraction of the dishes are
vegetarian pasta dishes? answer in simplest form.

Most of the information's that are required for solving this question is already given in the question. Based on those given details the answer to the question can be easily reached.
Amount of dishes on the menu that are vegetarian = 1/2
Number of dishes that are pasta dishes out of the vegetarian dishes = 4/5
Then
Fraction of the dishes that
are vegetarian pasta dishes = (1/2) * (4/5) 
                                              = (2/5)
 So the fraction of the vegetarian dishes that are pasta dishes is 2/5. I hope the procedure is clear enough for you to understand.