To express 14 programming errors for every 56 programmers as a rational number, you can write it as a fraction:
\[ \frac{14}{56} \]
Next, you can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 14 and 56 is 14.
Now, divide both the numerator and the denominator by 14:
\[ \frac{14 \div 14}{56 \div 14} = \frac{1}{4} \]
Thus, the fraction representing the programming errors per programmer simplifies to:
\[ \frac{1}{4} \]
This means that there is 1 programming error for every 4 programmers.