let , that is let them be consecutive integers. Then here is a list of infinitely many rational numbers in between these.
where i is any positive integer.
also, the numerator need not necessarily be 1, as long as the numerator is less than the denominator, if you add that number to n it will still be in between these numbers.
I'm thinking it might help if you posted the detailed exercise...?
At a guess, you've been given a list of values, from which you are to choose those which are rationals. But we cannot begin to help you learn to distinguish the rationals from whatever other sorts of number types are included in the list until we can see that list.
Basically you are looking for any number between 1 and 2 (1.375, 1.001, 1, 1.9999 etc)
I assume that the other answers in your book either A) Lay outside that range or B) The decimal neither ends nor repeats. So basically when doing this sort of problem
1. Look for any fraction with a denominator of zero, these are not rational.
2. Look for any fraction which lays outside the wanted range (1 to 2 in this case)
(Such as if I saw 13/2 I would know that easily was outside)
3. Now you need to work out the other fractions to see if they lay inside the 1-2 range and remember numbers that have a non-ending non-repeating decimal are not rational, the rest are.
(Just to show you the values you gave us come out to 1.25, 1.375, 1.625, 1.75)