Can I ask you something? yes !

I learned some expression in English.

1. The boy cut the pizza into thirds.
2. She cut the apple into quarters.

Regarding them, Why do they use 's'(thirds, quarter)? and can I use them as below?

1. I cut the bread into halves. then I had one half of bread and gave my friend the other half.

thirds, quarters etc because there are more than one of them (plural).
We are discussing a specific quarter of the pizza then it's just one of them
If we are discussing all of the quarters, then the subject is plural (more than one quarter)

Ex.

1. She cut it up and gave me a quarter of the pizza (here the subject is the quarter of pizza)

2. She cut the pizza into quarters (here the subect is the pizza, not the quarters)

Ex2.

He cut the loaf of bread in half (singular because the subject is the loaf, not the halves)

He gave me both halves of the bread after cutting it (subject is the halves of bread, not the bread itself)

is this clear ?

Regards,
Andrew.