Question: what is a quarter past 1?
Answer: Both “quarter past” and “quarter after” are equally correct. So, when it's 7:15, we say it's “quarter past seven”. Or when it's 1:15, we say it's “quarter after one”. At minute 45, we say it's “quarter to” the next hour. For example, at 5:45, we say it's “quarter to six” (or 15 minutes before 6:00).