If it is 3:15. how many degrees are between the little and big hand?

At quarter past the hour, the minute-hand is exactly at 3:00 but the hour-hand has moved 1/4 of the way between 3:00 and 4:00. Therefore 1/4 times 1/12 = 1/48 of the clock. With the clock having 360 degrees, 360/48 = 7.5 degrees.

7.5 degrees For every 360 degrees the little hand moves, the big hand moves 30 degrees; therefore, when the little hand moves 90 degrees (to the 15 minute mark), the big hand moves 7.5 degrees.

7.5 degrees

7.5 degrees