What rational number is between #-2/6# and #-1/6# ?
2 Answers
There are infinitely many, but the one midway between
Explanation:
Note that
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.
So:
#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.
Explanation:
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.
Example:
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