Link to article cited in title, Wikipedia rational number.
According to this answer, some students 14-18 are still struggling to understand fractions. Maybe some students know how to perform the calculations on rational numbers given in fraction notation but don't understand why it works. If they're taught the method described in that section, they might actually understand why it works so well. At first, the teacher could teach the student how to do creative thinking and then ask the student to explain why addition and multiplication can be defined that way and then guide them through to come up with an answer showing that addition and multiplication of ordered pairs in the same class always gives you a result in the same class so two ordered pairs can be defined to represent the same rational number when they're in the same class. Later, they could say that by definition, subtraction is addition of the additive inverse and division is multiplication by the multiplicative inverse. Later so that the student will become smarter, the student could be left with the task to teach themself how to compute a division problem on rational numbers given in fraction notation to get a result expressed in fraction notation. That way, they not only will know how to perform the calculations but will have also been guided to show that they have a real understanding of what the calculations actually mean. Even later to make them even smarter, they could be guided to come up with a proof that $\mathbb{Q}$ is a field.