When is it possible to find a rational number between two giving rational numbers

Answer 1

It is always possible to find a rational number between two given rational numbers.

Let's say you have two rational numbers, a/b and c/d, where a, b, c, and d are integers. To find a rational number between them, you can use the midpoint formula.

The midpoint between two numbers is given by the formula:

Midpoint = (First Number + Second Number)/2

So, the midpoint between a/b and c/d would be:

Midpoint = (a/b + c/d)/2 = (ad + bc) / (2bd)

Since a, b, c, and d are integers, ad + bc and 2bd will also be integers. Therefore, (ad + bc) / (2bd) is a rational number.

Thus, there is always a rational number between any two given rational numbers.