To express "14 programming errors for every 56 programmers" as a rational number, you would write it as a fraction:
\[ \frac{14}{56} \]
Now, we can simplify this fraction by finding the greatest common divisor (GCD) of 14 and 56, which is 14:
\[ \frac{14 \div 14}{56 \div 14} = \frac{1}{4} \]
Thus, the simplified version of the rational number is \( \frac{1}{4} \), but none of the answer choices provided directly express \( \frac{1}{4} \).
However, if we are focusing on the fraction itself, the answer choice that directly represents the scenario before simplification is:
14 over 56
This corresponds to \(\frac{14}{56}\).