My example is 1/2 divide by 8.

The correct answer given : 1/16

However, in my mind this answer is 1 divide by 16, which to me is not what the question is asking.

When I construct the argument, it seems it should equal 1/8
as the question is asking "What is the division of 1/2 into 8 pieces?"

Not

"What is the total division of the whole when 1/2 is divided into 8 pieces?"

Why give the answer to the whole, when it is the fraction that is in question?

If I have a box, and I cut it into half, and then I ask "What is the division of this box into 8?" Why would I give a division of the whole box?

***Edit***

Thank you for the many answers, I believe it boils down to absolute quantity vs relative measurement, and the mass of the object.

So, 1/3 of half a tea spoon is an absurd but correct measurement.

but, say you have a house divided into 2 apartments, both having 8 rooms.

You would say : "An apartment has 8 rooms" not "The house has 16 rooms"

**Edit**

Absolute measurement, as a method of reaching an answer that is limited in complexity, is preferable to an infinite number of sets of fractions.

1/18 = Absolute Measurement

1/8 = Sets of fractions into infinity

UPDATE EDIT
Just an update for visualisation.

Imagine one whole cube, then cut that cube 8 times, now divide that cube into half and you have 16.

I believe this is what the sum is describing and the problem with my visualisation.

This has really helped me appreciate set theory, thank you for your time.