confusion for word problem experts

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

x = whole cake (7 slices are divided into the cake or 7/7)

4/7 (4 out of the 7 slices) were eaten

x - 4/7 or 7/7 - 4/7 = 3/7 (3 out of 7 slices) is left

 

"Dad eats 1/2 (half) of what was left (3/7)" or

"Dad eats 1/2 (half) of each slice of cake that was left (3 out of 7 slices)"

 

Now, you are cutting each slice of cake that was left (3 out of 7 slices) in half (1/2).  Now you have a total of 6/14 (6 out of 14 new slices) of the cake that was left.  If dad eats half, he will eat 3/14 (3 out of 14 new slices) and you will have 3/14 (3 out of 14 new slices) left.

 

3/7 * 1/2 = 3/14