To find the rate of balls hit to times at bat, we can use the formula:
\[ \text{Rate} = \frac{\text{Number of hits}}{\text{Number of times at bat}} \]
Given that the player hit the ball 100 times and went up to bat 350 times, we can substitute these values into the formula:
\[ \text{Rate} = \frac{100}{350} \]
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 100 and 350 is 50.
Now, dividing both the numerator and the denominator by 50:
\[ \text{Rate} = \frac{100 \div 50}{350 \div 50} = \frac{2}{7} \]
Thus, the rate of balls hit to times at bat, expressed as a simplified fraction, is:
\[ \frac{2}{7} \]