The three rational numbers between 3 and 4 are:a. 5/2, 6/2, 7/2b. 13/4, 14/4, 15/4c. 12/7, 13/7, 14/7d.11/4, 12/4, 13/4

The correct answer is b. 13/4, 14/4, 15/4.

Here's why:

Step 1: Convert the whole numbers 3 and 4 into fractions that have the same denominator as the options given. In this case, we'll use 4 as the denominator. So, 3 becomes 12/4 and 4 becomes 16/4.

Step 2: Look at each option and see if the fractions fall between 12/4 and 16/4.

a. 5/2, 6/2, 7/2 - When these fractions are converted to have 4 as the denominator, they become 10/4, 12/4, 14/4. 10/4 and 12/4 are less than 12/4, so this option is incorrect.

b. 13/4, 14/4, 15/4 - These fractions are all between 12/4 and 16/4, so this option is correct.

c. 12/7, 13/7, 14/7 - When these fractions are converted to have 4 as the denominator, they become approximately 6.857/4, 7.429/4, 8/4. These are all less than 12/4, so this option is incorrect.

d. 11/4, 12/4, 13/4 - 11/4 and 12/4 are less than 12/4, so this option is incorrect.