What rational number is between #-2/6# and #-1/6# ?
There are infinitely many, but the one midway between
Like any two distinct real numbers, there are infinitely many rational numbers between them.
Since they are both rational, their average is also a rational number.
We can arrive at the average by adding the two numbers then halving the result.
#1/2((-1/6)+(-2/6)) = (-1/12)+(-2/12) = -3/12 = -1/4#
When two fractions are too close to have another one in between, just re-write them with larger denominators to spread them apart enough to fit other fractions in.
It looks like there is no room between
Now you can see that
If you need even more room, just use an even larger denominator.
Find three fractions between
Using tenths as the denominator doesn't open up enough room for 3 fractions to fit between them. Only one fraction (3/10) fits.
But don't give up if that happens.
Just try again with a bigger denominator.
This time, try 25ths as the denominator.
Now you can easily see four fractions lying between