What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
6 to 3

Answer

To find the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 6 to 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Clock Positions**:
- A clock has 12 hours marked on it. The hour hand moves from one hour to the next as time passes.

2. **Identify the Starting and Ending Points**:
- The hour hand starts at 6 and moves to 3.

3. **Count the Hours Between 6 and 3**:
- From 6 to 7 is 1 hour.
- From 7 to 8 is another hour (2 hours total).
- From 8 to 9 is another hour (3 hours total).
- From 9 to 10 is another hour (4 hours total).
- From 10 to 11 is another hour (5 hours total).
- From 11 to 12 is another hour (6 hours total).
- From 12 to 1 is another hour (7 hours total).
- From 1 to 2 is another hour (8 hours total).
- From 2 to 3 is another hour (9 hours total).

4. **Calculate the Total Hours in a Full Revolution**:
- A full revolution of the clock is 12 hours (from 12 back to 12).

5. **Set Up the Fraction**:
- The fraction of the revolution is given by the formula:
\[ \text{Fraction} = \frac{\text{Required Hours}}{\text{Total Hours}} \]
- Here, the required hours (from 6 to 3) is 9 hours, and the total hours in a full revolution is 12 hours.

6. **Calculate the Fraction**:
- Substitute the values into the formula:
\[ \text{Fraction} = \frac{9}{12} \]
- Simplify the fraction:
\[ \frac{9}{12} = \frac{3}{4} \]

### Final Answer:
The hour hand of a clock turns through \(\frac{3}{4}\) of a clockwise revolution when it goes from 6 to 3.

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