To express "14 programming errors for every 56 programmers" as a rational number, you can write it as the fraction:
\[ \frac{14}{56} \]
Now, if you simplify this fraction, both the numerator and the denominator can be divided by 14:
\[ \frac{14 \div 14}{56 \div 14} = \frac{1}{4} \]
However, since the question is asking for the expression as it is stated ("14 programming errors for every 56 programmers"), the correct response is:
14/56 (or "14 over 56").
This correctly represents the scenario before any simplification.