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

Answer

To find the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 12 to 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Clock Positions**:
- The clock has 12 positions, with each hour representing a position on the clock face.
- The positions are: 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

2. **Identify the Starting and Ending Points**:
- The hour hand starts at 12 and moves to 9.

3. **Count the Number of Hour Positions**:
- From 12 to 9, the hour hand passes through the following positions: 12 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9.
- This is a total of 9 hour positions.

4. **Calculate the Total Positions in One Revolution**:
- A complete revolution of the clock is 12 hour positions.

5. **Determine the Fraction of the Revolution**:
- The fraction of the revolution that the hour hand has turned through is given by the number of positions it has moved divided by the total number of positions in one revolution.
- Thus, the fraction is:
\[ \text{Fraction} = \frac{\text{Number of positions moved}}{\text{Total positions in one revolution}} = \frac{9}{12} \]

6. **Simplify the Fraction**:
- The fraction \(\frac{9}{12}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
- Therefore, \(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\).

### Final Answer:
The hour hand of a clock turns through \(\frac{3}{4}\) of a clockwise revolution when it goes from 12 to 9.

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