i have another question 4/7 of birthday cake was eaten on your birthday. The next day dad ate 1/2 of what was left. You get to finish the cake how much is left

Question

i have another question
4/7 of birthday cake was eaten on your birthday. The next day dad ate 1/2 of what was left. You get to finish the cake how much is left
in my book
let x be cake
x-4x/7 =3x/7
now 3x/7*1/2
answer come 3/14

my confusion is
4/7 of cake means 4/7 is part of cake so we took 4x/7
now when dad ate 1/2 part of remaining cake so it should be like this 3x/7*x/2 why i take x/2 because it is part of cake like previously but when i trying to solve this answer come 3x^2/14.
So for only first sentence why we took 4x/7 and second sentence took 1/2.
therefore how we know when to use x

please sent me detail information

Answer 1

4/7 eaten which leaves 3/7 left

(1/2)*(3/7)=3/14 eaten by dad

3/7 left and dad ate 3/14 of the 3/7

3/7-(3/14)=6/14-3/14=3/14 left