Final answer:
Multiplying or dividing both the numerator and the denominator of a fraction by the same nonzero constant leaves the value of the fraction unchanged. This principle is used to create equivalent fractions and does not alter the original ratio between the numerator and denominator.
Step-by-step explanation:
Given a fraction, multiplying or dividing both the numerator and the denominator by the same nonzero constant leaves the value of the fraction unchanged. This is because any nonzero number divided by itself is equal to 1. Considering the fact that multiplication or division should apply to every term on either side of the equality, when you apply the same operation to both the numerator and denominator, the original ratio between them does not change. For example, multiplying the numerator and the denominator of the fraction 1/2 by 2 gives us 2/4, which simplifies back to 1/2 since both the numerator and denominator were divided by the same number.
Indeed, as long as we perform the same operation on both the numerator and denominator, the fraction's value does not alter. This relates to the concept of creating equivalent fractions. Whether we simplify the fraction 30/120 to its reduced form 1/4 by dividing both the top and bottom by the common factor of 30, we can see that the value of the fraction remains the same.