Final answer:
Adding or subtracting the same nonzero constant from the numerator and denominator changes the value of the fraction. For example, 1/2 becomes 2/3 after adding 1 to both, indicating a change in value, unlike multiplication or division by the same number which leaves the value unchanged.
Step-by-step explanation:
When considering the question of what effect adding or subtracting the same nonzero constant from both the numerator and the denominator of a fraction has on the value of the fraction, we must understand the basic properties of fractions. Adding or subtracting the same number changes the value of the fraction, as compared to multiplying or dividing both the numerator and denominator by the same number, which would leave the fraction's value unchanged.
For example, let's take the fraction 1/2 and add 1 to both the numerator and the denominator to get 2/3. Clearly, 1/2 is not equal to 2/3, showing that the value of the fraction has changed. On the other hand, if we were to multiply both the numerator and denominator of 1/2 by 2, we would get 2/4, which simplifies back to 1/2, illustrating that the value remains the same when the same operation (in this case, multiplication) is applied to both.
To directly answer the student's question, option A is correct: Adding or subtracting the same nonzero constant from both the numerator and denominator of a fraction changes the value of the fraction.