What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
3 to 9

Answer

To find out what fraction of a clockwise revolution the hour hand of a clock turns through when it goes from 3 to 9, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Positions on the Clock:**
- The hour hand starts at 3 and moves to 9.

2. **Count the Hour Marks:**
- On a clock, there are 12 hour marks (1 through 12).
- From 3 to 9, we count the hour marks: 4, 5, 6, 7, 8, and then it reaches 9.
- This means the hour hand moves through 6 hour marks (4, 5, 6, 7, 8, 9).

3. **Determine the Total Number of Hour Marks:**
- The total number of hour marks on the clock is 12.

4. **Calculate the Fraction of the Revolution:**
- The fraction of the revolution that the hour hand has turned is given by the formula:
\[ \text{Fraction} = \frac{\text{Number of hour marks moved}}{\text{Total number of hour marks}} = \frac{6}{12} \]

5. **Simplify the Fraction:**
- Simplifying \(\frac{6}{12}\) gives us:
\[ \frac{6 \div 6}{12 \div 6} = \frac{1}{2} \]

6. **Conclusion:**
- Therefore, the hour hand of the clock turns through \(\frac{1}{2}\) of a clockwise revolution when it goes from 3 to 9.

### Final Answer:
The hour hand turns through \(\frac{1}{2}\) of a clockwise revolution when moving from 3 to 9.

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