To write 14 programming errors for every 56 programmers as a rational number, follow these steps:
1. Start with the fraction that represents the scenario:
[tex]\[ \frac{14}{56} \][/tex]
2. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator (14) and the denominator (56).
3. The GCD of 14 and 56 is 14.
4. Divide both the numerator and the denominator by their GCD (14):
[tex]\[ \frac{14 \div 14}{56 \div 14} = \frac{1}{4} \][/tex]
Therefore, the rational number that represents 14 programming errors for every 56 programmers is:
[tex]\[ \frac{1}{4} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{\frac{1}{4}} \][/tex]
