Final answer:
Each person receives 1/7 of the birthday cake when it is divided equally among 7 people. This fraction is in simplest form and represents an equal share for each person.
Step-by-step explanation:
When a birthday cake is divided equally between 7 people, each person receives an equal fraction of the cake. To find out what fraction of the cake each person gets, you would divide the whole cake into 7 equal parts. Since there is one whole cake, each part is 1/7 of the cake. Therefore, each person gets 1/7 of the entire cake. This fraction is already in its simplest form, as the numerator 1 and the denominator 7 have no common factors other than 1.