Final answer:
To choose the fraction that satisfies the inequality 1/2 < ___ < 4/5, we evaluate each given option to find the fraction that is greater than 1/2 and less than 4/5. The fraction that satisfies the given inequality is 2/3.
Step-by-step explanation:
To choose the fraction that satisfies the inequality 1/2 < ___ < 4/5, we need to find a fraction that is greater than 1/2 and less than 4/5. Let's evaluate the given options: a) 1/3: 1/3 is less than 1/2 and does not satisfy the inequality. b) 2/4: 2/4 is equivalent to 1/2, which is the lower bound of the inequality. c) 2/3: 2/3 is greater than 1/2 and less than 4/5, so it satisfies the inequality. d) 5/6: 5/6 is greater than 4/5 and does not satisfy the inequality.
Therefore, the fraction that satisfies the given inequality is 2/3.