Final answer:
Upon simplifying the fractions 16/14 and 64/56 by dividing both the numerators and denominators with their greatest common divisors, it is shown that both fractions reduce to 8/7, proving that they are equivalent. The correct answer is A) They are equivalent.
Step-by-step explanation:
The fractions 16/14 and 64/56 might initially seem like they are not equivalent because at first glance the numerators and denominators are different. However, upon closer inspection and simplifying both fractions, we can determine their equivalence. To simplify, we find the greatest common divisor (GCD) for each fraction and divide the numerator and the denominator by it.
For the fraction 16/14, the GCD of 16 and 14 is 2. Therefore, when we divide both the numerator and the denominator by 2, we get 8/7. Similarly, for the fraction 64/56, the GCD of 64 and 56 is also 8. Dividing the numerator and the denominator by 8 yields the same result of 8/7.
When simplified, both fractions reduce to the same fraction, which shows that they are indeed equivalent. Therefore, the correct answer is A) They are equivalent.