Final answer:
The fraction among the given options that has an equivalent repeating decimal value is A: 2/3.
Step-by-step explanation:
To determine which fraction has an equivalent decimal value that repeats, we can examine each option. A fraction will have a repeating decimal if its denominator has prime factors other than 2 or 5 since these are the prime factors of the base 10 system. Let's examine the given fractions:
- A: 2/3 - Dividing 2 by 3, we cannot simplify it into a decimal with a finite number of digits. Therefore, the decimal form of 2/3 is 0.666..., which repeats indefinitely.
- B: 3/4 - Dividing 3 by 4, we get 0.75. This is a terminating decimal, so it does not repeat.
- C: 4/5 - Dividing 4 by 5, we get 0.8. This is also a terminating decimal, so it does not repeat.
- D: 7/8 - Dividing 7 by 8, we get 0.875. This is another terminating decimal, so it does not repeat.
Therefore, the fraction with an equivalent decimal value that repeats is A: 2/3.