The problem asks what fraction of a turn does the minute hand of a clock rotate by between 03:20 and 03:55. The answer must be in simplest form.

1. Problem Description

The problem asks what fraction of a turn does the minute hand of a clock rotate by between 03:20 and 03:

5

5. The answer must be in simplest form.

2. Solution Steps

First, find the number of minutes between 03:20 and 03:

5

5. $55 - 20 = 35$ minutes.

The minute hand completes a full turn in 60 minutes.

Therefore, in 35 minutes, the minute hand rotates $\frac{35}{60}$ of a full turn.

Now, simplify the fraction $\frac{35}{60}$.

The greatest common divisor (GCD) of 35 and 60 is

5. Divide both the numerator and denominator by

5. $\frac{35 \div 5}{60 \div 5} = \frac{7}{12}$.

3. Final Answer

The fraction of a turn is $\frac{7}{12}$.