The minute hand takes 1 hour or 60 minutes to complete a whole round, that is, when it moves from 12 and reaches back to 12. Quarter means \\(\\frac{1}{4}\\)th or one-fourth of something. One fourth of 60 minutes is 15 minutes. So “quarter to” means 15 minutes before and “quarter past” means 15 minutes after. Similarly half represents 30 minutes so “half past” means 30 minutes after.