What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from a 3 to 9, 4 to 7, 7 to 10, 12 to 9, 1 to 10, and 6 to 3?

The hour hand of a clock makes one full revolution (360 degrees) in 12 hours. Therefore, each hour represents a fraction of this whole revolution. Specifically, each hour is equal to 1/12 of a full revolution.

Let’s break down each transition:

• From 3 to 9: This is 6 hours.
  The fraction of a revolution is:
  6 hours ÷ 12 hours = 1/2.
• From 4 to 7: This is 3 hours.
  The fraction of a revolution is:
  3 hours ÷ 12 hours = 1/4.
• From 7 to 10: This is also 3 hours.
  The fraction of a revolution is:
  3 hours ÷ 12 hours = 1/4.
• From 12 to 9: This is 9 hours.
  The fraction of a revolution is:
  9 hours ÷ 12 hours = 3/4.
• From 1 to 10: This is 9 hours.
  The fraction of a revolution is:
  9 hours ÷ 12 hours = 3/4.
• From 6 to 3: This is 9 hours as well.
  The fraction of a revolution is:
  9 hours ÷ 12 hours = 3/4.

In summary:
3 to 9 = 1/2
4 to 7 = 1/4
7 to 10 = 1/4
12 to 9 = 3/4
1 to 10 = 3/4
6 to 3 = 3/4